visual representation of growth

Excel Tutorial: How To Show Growth In Excel Chart

Introduction.

Are you looking to visually represent the growth of your data in an Excel chart? Understanding how to effectively showcase growth in a chart is a valuable skill for professionals working with data. Visual representation of growth allows for better understanding of trends and patterns, which can aid in decision-making and analysis. In this tutorial, we will cover the steps to show growth in an Excel chart, empowering you to effectively communicate your data insights.

Key Takeaways

• Visual representation of growth in an Excel chart is valuable for understanding trends and making data-driven decisions
• Accuracy and organization of data are crucial when selecting and organizing data for a chart
• Customizing the chart, adding trendlines, and formatting for clarity enhances the visibility of the growth trend
• Including annotations and additional data can provide context and a comprehensive view of the growth
• Clear and accurate visualization of growth data is important for effective communication and analysis

Selecting and organizing your data

Before you can show growth in an Excel chart, it's important to first select and organize your data properly. Follow these steps to ensure that your chart accurately reflects the growth you want to showcase.

• Identify the specific data points that you want to display on the chart.
• Ensure that the data accurately represents the growth you are trying to illustrate.
• Arrange the data in a way that makes it easy to create a visual representation of the growth, such as in columns or rows.
• Consider using separate columns or rows for different time periods or categories, depending on the nature of your data.
• Verify that the data is current and reflects the most recent information available.
• Double-check for any errors or discrepancies in the data that could affect the accuracy of the chart.

By following these steps to select and organize your data, you can set a strong foundation for creating an Excel chart that effectively shows growth.

Creating a line chart

When it comes to showing growth in Excel, creating a line chart is an effective way to visually represent the data. Follow these steps to create a line chart that accurately depicts growth:

A. Open Excel and select the data range

B. click on the insert tab and choose the line chart option, c. customize the chart by adding axis labels and a title.

Before creating a line chart to show growth in Excel, open the Excel application and select the data range that you want to use for the chart. This data should include the values that represent the growth over time.

Once the data range is selected, click on the Insert tab at the top of the Excel window. From the Insert tab, choose the line chart option from the various chart types available. This will insert a blank line chart onto the Excel sheet.

After inserting the line chart, customize it by adding axis labels and a title. The axis labels will provide context for the data, and the title will clearly indicate what the chart is representing. Customizing the chart will make it easier for viewers to understand the growth being depicted.

Adding a Trendline to the Chart

Once you have your data plotted in an Excel chart, you can add a trendline to show the overall growth or decline in your data. Here's how you can do it:

Right-click on the data series in the chart

Select "add trendline" from the menu, choose the type of trendline that best fits the data.

To add a trendline to your Excel chart, start by right-clicking on the data series that you want to add the trendline to. This will bring up a menu of options that includes "Add Trendline."

After right-clicking on the data series, select "Add Trendline" from the menu. This will open a dialog box with options for the type of trendline and other customization options.

When the dialog box opens, you can choose the type of trendline that best fits your data. Excel offers several options, including linear, exponential, logarithmic, and more. Select the type of trendline that best represents the growth or decline in your data.

Formatting the chart for clarity

When displaying growth in an Excel chart, it's important to format the chart in a way that makes the growth trend clear and easy to interpret. Here are a few ways to do that:

Adjust the scale of the axes to best display the growth

• Ensure that the axes are appropriately scaled to show the full range of growth in the data.
• Consider adjusting the minimum and maximum values of the axes to best highlight the growth trend.

Add data markers or labels to highlight specific points

• Use data markers or labels to draw attention to specific points on the chart that represent significant changes or milestones in the growth trend.
• These markers or labels can help viewers easily identify key points in the data.

Choose a color scheme that enhances the visibility of the growth trend

• Select colors that make the growth trend stand out visually, such as using a contrasting color for the trend line or data points.
• Consider using a color gradient to represent the growth trajectory, with lighter colors indicating lower values and darker colors indicating higher values.

Adding annotations or additional data

When showing growth in an Excel chart, it's important to provide context and explanations for the data. This can be achieved by including annotations and additional data points.

• Use text boxes: Adding text boxes to your chart can help provide context for the growth by including explanations or highlighting important milestones.
• Utilize data labels: Data labels can be used to directly annotate specific data points on the chart, making it easier for the audience to understand the growth trends.
• Include trendlines: Adding trendlines to your chart can help visualize the overall growth trajectory and provide insights into future trends.
• Compare with benchmarks: Incorporating benchmark data or industry averages can give a comprehensive view of the growth in relation to external factors.
• Limit the number of annotations: While annotations are helpful, it's important not to overdo it and clutter the chart with excessive text or labels.
• Use colors and shapes effectively: Utilize different colors and shapes to differentiate between the main data and the additional elements, making it easier for the audience to interpret the chart.

In conclusion , creating a growth chart in Excel is a valuable skill that can help you visually represent your data in a clear and accurate manner. To summarize, the key steps include selecting your data, inserting a chart, and choosing the appropriate chart type to display growth over time. It is important to emphasize the significance of accurately representing your data to ensure clear and effective communication of growth trends. I encourage you to practice creating your own growth charts in Excel to enhance your data visualization skills and make your presentations more impactful.

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How to Visualize Data using Year-Over-Year Growth Chart?

Some visualization designs are better suited for visualizing year-over-year (YoY) data than others. In other words, they display insights in a clear and easy-to-follow way.

Some of the tested and proven year-over-year growth visualization designs include:

• Double Axis Line and Graph Chart
• Comparison Bar Chart
• Double Axis Line Chart
• Matrix Chart
• Pareto Bar Chart
• Radar Chart
• Sentiment Trend Chart
• Slope Chart
• Tornado Chart
• Progress Chart

The charts highlighted above are amazingly easy to read and interpret, even for non-technical audiences.

Excel has very basic year-over-year growth charts (highlighted above). Yes, the spreadsheet tool comes with pretty Year-over-year Growth Charts that need more time and effort in editing.

You don’t have to do away with Excel. You can supercharge it by installing third-party add-ins to access ready-to-use and visually appealing year-over-year growth charts.

In this blog, you’ll learn the following:

Table of Content:

What is year-over-year growth chart, how to calculate year-over-year growth.

• Best Charts for Presenting Year-Over-Year Growth

How to Create a Year-Over-Year Growth Chart in Excel?

Why do we need a year-over-year growth chart.

Before diving into the how-to guide, we’ll address the following question: What is Year-Over-Year Growth Chart?

Definition : The year-over-year (YOY) Growth Chart showcases the key performance indicators for comparing growth in a financial year to a previous one.

Unlike standalone monthly metrics, YOY gives you a picture of your performance without seasonal effects, monthly volatility, and other factors. You see a clearer picture of your actual successes and challenges over time. Unsurprisingly, this is a key metric for retail analytics.

One of the key advantages of the year-over-year growth chart is in eliminating seasonality from your growth metrics.

Most retailers see a sharp uptick in sales during the holiday season. A single-month basis can give a false indication of massive growth. However, these inflated numbers aren’t truly representative of growth over time if they return to normal levels after the holidays pass.

Comparing similar periods over time gives you a more precise measure of your company’s growth.

That’s not to say that YoY metrics are the be-all, end-all of analysis. Focusing on 12 months may also present you with a broader picture. Combining a longer-term perspective with month-over-month and quarter-over-quarter can help you gain 360-degrees insights into your data.

The year-over-year growth chart is more than just revenue.

You can measure myriad aspects of your growth: conversions, average sale value, and other related metrics.

In the coming section, we’ll cover how to calculate year-over-year growth.

You can calculate year-over-year growth by following a particular formula, which we’ll highlight below.

Follow the steps below to calculate year-over-year growth.

Determine the timeframe you’d like to compare

Before you begin your equation, determine a suitable time. If you’ve just completed a successful season, compare your previous quarter with last year’s.

Also, compare this year’s monthly statistics with last year’s to uncover growth or decline.

Retrieve your company’s numbers from the current and previous years:

Once you’ve established the timeframe, gather data for analysis.

Check your company’s balance sheet if you aren’t sure where these results may be located. This should list your previous performance and financial information for your company.

Subtract last year’s numbers from this year

If you have both numbers, find your growth rate by subtracting last year’s performance numbers from this year’s.

Divide the total by last year’s number

Take the total number from the previous equation and divide it by last year’s number.

Using the earlier example, take the equation’s total, 70, and divide it by 430. The resulting figure is (70 ÷ 430) = 0.1627.

Multiply by 100 to get the final percentage:

The final step of calculating the year-over-year growth chart rate is to convert this total to a percentage.

Multiplying the resulting total number by 100.

Here’s your equation: 0.1627 x 100 = 16.27. (16.3%)

Analyze and evaluate your total:

You can now use this total when showing your success to investors or lenders. This can help them understand how well your business is performing. You can use this number to detail how you plan to perform a higher YOY growth rate next year.

If your total was a negative number and appears as a loss rather than a growth, you can use this to determine the improvements needed to drive a positive result during your next year-over-year growth chart.

In the coming section, we’ll highlight the best charts for presenting year-over-year growth.

The Tested and Proven Best Charts for Presenting Year-Over-Year Growth

A Comparison Bar Chart  (one of the Year-over-year Growth Charts) uses a bar to represent sections of the same category, and these bars are placed adjacent to each other.

It’s a great way of comparing the data visually. Bar graphs are reliable ways of comparing key data points.

Double Axis Line Graph and Bar Chart

A Dual Axis Bar and Line Graph is one of the best year-over-year growth charts for comparing two data sets for a presentation.

The visualization design uses two axes to easily illustrate the relationships between two variables with different magnitudes and scales of measurement.

The relationship between two variables is referred to as correlation. A Dual Axis Bar and Line Chart illustrate plenty of information using limited space, so you can discover trends you may have otherwise missed.

Dual Axis Line Chart

A Dual Axis Line Chart is one of the best graphs for presenting growth year-over-year. The chart has a secondary y-axis to help you display insights into two varying data points.

More so, it uses two axes to easily illustrate the relationships between two variables with different magnitudes and scales of measurement.

The visualization design displays data as an arrangement of information in a series of data points called ‘markers’ connected by straight line segments. You can use the chart to visualize a trend in the data over time intervals. In a typical line chart, you have an x and y-axis. The dual axes line chart features one x-axis and two y-axis.

A Matrix Chart can help you identify the presence and strengths of relationships between two or more lists of items. Besides, it provides a compact way of representing many-to-many relationships of varying strengths.

Use this chart to analyze and understand the relationships between data sets.

A Pareto Bar Chart is a graph that indicates the frequency of defects and their cumulative impact.

The chart is useful, especially in hunting for defects to achieve maximum overall improvement. The key goal of a Pareto Diagram (one of the different types of charts for representing data ) is to separate the significant aspects of a problem from the trivial ones.

Pareto Chart is based on the classic 80/20 rule. The rule says that 20% of the causal factors result in 80% of the overall outcomes. For instance, 80% of the world’s total wealth is held by 20% of the population.

This easy-to-read chart prevents you from attacking the causes randomly by uncovering the top 20% of the problems, negatively affecting 80% of your overall performance.

A Radar Chart is a two-dimensional chart showing at least three variables on an axis that starts from the same point.

The chart is straightforward to understand and customize. Furthermore, you can show several metrics across a single dimension. The visualization design is best-suited for showing outliers and commonalities in your data.

You can use radar charts in excel and google sheets to display performance metrics such as clicks, sessions, new users, and page views, among others.

A Sentiment Trend Chart is one of the Year-over-year Growth Charts examples you can use to display the target market’s opinion of your offerings.

The chart is a must-have, especially if your goal is to show the growth and decline of key variables. The line curve in the chart shows the overall pattern and trend of a key variable over a specified period.

A Slope Chart is one of the Year-over-year Growth Charts that show transitions, changes over time, absolute values, and even rankings.

You can use this chart to show the before and after story of variables in your data.

Slope Graphs in Excel & Google Sheets can be useful when you have two time periods or points of comparison and want to show relative increases or decreases quickly across various categories between two data points.

A Progress Bar Chart is a visualization design that displays the progress made in a task or project. You can use the chart to monitor and prioritize your objectives, providing critical data for strategic decision-making.

Besides, it uses filled bars to display how much of the planned activity or goal has been completed.

The chart is significant, especially in tasks that require continuous monitoring and evaluation. More so, it uses green and red bars to show the growth and decline of a variable under study.

In the coming section, we’ll address how to create a year-over-year growth chart in Excel.

Excel is one of the go-to data visualization tools for businesses and professionals.

However, this freemium spreadsheet tool comes with a very basic Year-over-year Growth Chart in Excel, such as Progress Graphs.

Well, you don’t have to do away with the spreadsheet app.

You can turn Excel into a reliable data visualization tool loaded with ready-made charts, such as Progress and Slope Graphs, by installing third-party apps, such as ChartExpo.

Why ChartExpo?

ChartExpo is a Year-over-year Growth Chart maker that comes as an add-in you can easily install in your Excel.

With different insightful and ready-to-use visualizations, ChartExpo turns your complex, raw data into  compelling visual renderings that tell the story of your data.

This Growth Chart in Excel generator produces simple and clear visualization designs with just a few clicks.

Yes, ChartExpo generates Growth graphs that are amazingly easy to interpret, even for non-technical audiences.

This section will use a Progress Chart to visualize the data below.

To install ChartExpo into your Excel, click this link .

• Open the worksheet and click the Insert button to access the My Apps option.

• Select ChartExpo and click the  Insert button to get started with ChartExpo.

• Once ChartExpo is loaded, you will see a list of charts.

• In this case, look for “ Progress Chart ” in the list as shown below.

• Select the sheet holding your data and click the Create Chart From Selection button, as shown below.

• To edit the chart, click on pencil icon next to chart header.

• Once the Chart Header Properties window shows, click the Line 1 box and fill in the heading. Also, toggle the Show button to the right side.
• Click the Apply button .

• To add a legend, click on pencil icon next to legend.
• Once the Chart Header Properties window shows, toggle the Show button to the right side.
• Complete the process by clicking the Apply button.

In the coming section, we’ll address the following question: why do we need a year-over-year growth chart?

More accurate for seasonal businesses

Some businesses may track their results by comparing them to the previous months or quarters’ results.

While this may be resourceful for some, seasonal businesses, such as ski resorts, may not benefit from this method.

Results look smoother

Since your business’s success can vary per month, its performance throughout each month may make the company look unstable, even if it performed well during its on-season.

With the year-over-year growth chart, comparing specific months or quarters can smooth out periods of abysmal performance.

Simple to track and calculate

Most businesses use spreadsheets apps, such as Microsoft Excel and Google Sheets. So generating year-over-year growth charts in these apps is possible.

Better understand what improvements you can make

Year-over-year Growth Charts can help you view the results of different aspects of your company’s performance for in-depth understanding.

What is the formula for calculating the year-over-year growth?

To calculate YoY, take your current year’s revenue and subtract the previous year’s income.

This gives you a total change in revenue. Then, divide that amount by last year’s total revenue. To get the year-over-year growth value, take that number and multiply it by 100.

Some of the tested and proven year-over-year growth visualization designs include

So, what’s the solution?

We recommend installing third-party apps, such as ChartExpo into your Excel to access a ready-made Year-over-year Growth Chart. Essentially, it’s an add-in you can easily download and install in your Excel app.

ChartExpo comes loaded with all the 10 types of Year-over-year Growth Charts, and many more ready-to-go visualization designs.

Sign up for a 7-day trial to access all the 10 types of YoY Charts. Yes, you’ll enjoy unlimited access to easy-to-interpret and visually appealing charts.

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16 Best Types of Charts and Graphs for Data Visualization [+ Guide]

Published: June 08, 2023

There are more type of charts and graphs than ever before because there's more data. In fact, the volume of data in 2025 will be almost double the data we create, capture, copy, and consume today.

This makes data visualization essential for businesses. Different types of graphs and charts can help you:

• Motivate your team to take action.
• Impress stakeholders with goal progress.
• Show your audience what you value as a business.

Data visualization builds trust and can organize diverse teams around new initiatives. Let's talk about the types of graphs and charts that you can use to grow your business.

Free Excel Graph Templates

Tired of struggling with spreadsheets? These free Microsoft Excel Graph Generator Templates can help.

• Simple, customizable graph designs.
• Data visualization tips & instructions.
• Templates for two, three, four, and five-variable graph templates.

You're all set!

Click this link to access this resource at any time.

Different Types of Graphs for Data Visualization

1. bar graph.

A bar graph should be used to avoid clutter when one data label is long or if you have more than 10 items to compare.

Best Use Cases for These Types of Graphs

Bar graphs can help you compare data between different groups or to track changes over time. Bar graphs are most useful when there are big changes or to show how one group compares against other groups.

The example above compares the number of customers by business role. It makes it easy to see that there is more than twice the number of customers per role for individual contributors than any other group.

A bar graph also makes it easy to see which group of data is highest or most common.

For example, at the start of the pandemic, online businesses saw a big jump in traffic. So, if you want to look at monthly traffic for an online business, a bar graph would make it easy to see that jump.

Other use cases for bar graphs include:

• Product comparisons.
• Product usage.
• Category comparisons.
• Marketing traffic by month or year.
• Marketing conversions.

Design Best Practices for Bar Graphs

• Use consistent colors throughout the chart, selecting accent colors to highlight meaningful data points or changes over time.
• Use horizontal labels to improve readability.
• Start the y-axis at 0 to appropriately reflect the values in your graph.

2. Line Graph

A line graph reveals trends or progress over time, and you can use it to show many different categories of data. You should use it when you chart a continuous data set.

Line graphs help users track changes over short and long periods. Because of this, these types of graphs are good for seeing small changes.

Line graphs can help you compare changes for more than one group over the same period. They're also helpful for measuring how different groups relate to each other.

A business might use this graph to compare sales rates for different products or services over time.

These charts are also helpful for measuring service channel performance. For example, a line graph that tracks how many chats or emails your team responds to per month.

Design Best Practices for Line Graphs

• Use solid lines only.
• Don't plot more than four lines to avoid visual distractions.
• Use the right height so the lines take up roughly 2/3 of the y-axis' height.

3. Bullet Graph

A bullet graph reveals progress towards a goal, compares this to another measure, and provides context in the form of a rating or performance.

In the example above, the bullet graph shows the number of new customers against a set customer goal. Bullet graphs are great for comparing performance against goals like this.

These types of graphs can also help teams assess possible roadblocks because you can analyze data in a tight visual display.

For example, you could create a series of bullet graphs measuring performance against benchmarks or use a single bullet graph to visualize these KPIs against their goals:

• Customer satisfaction.
• Average order size.
• New customers.

Seeing this data at a glance and alongside each other can help teams make quick decisions.

Bullet graphs are one of the best ways to display year-over-year data analysis. You can also use bullet graphs to visualize:

• Customer satisfaction scores.
• Customer shopping habits.
• Social media usage by platform.

Design Best Practices for Bullet Graphs

• Use contrasting colors to highlight how the data is progressing.
• Use one color in different shades to gauge progress.

Different Types of Charts for Data Visualization

To better understand these chart types and how you can use them, here's an overview of each:

1. Column Chart

Use a column chart to show a comparison among different items or to show a comparison of items over time. You could use this format to see the revenue per landing page or customers by close date.

Best Use Cases for This Type of Chart

You can use both column charts and bar graphs to display changes in data, but column charts are best for negative data. The main difference, of course, is that column charts show information vertically while bar graphs show data horizontally.

For example, warehouses often track the number of accidents on the shop floor. When the number of incidents falls below the monthly average, a column chart can make that change easier to see in a presentation.

In the example above, this column chart measures the number of customers by close date. Column charts make it easy to see data changes over a period of time. This means that they have many use cases, including:

• Customer survey data, like showing how many customers prefer a specific product or how much a customer uses a product each day.
• Sales volume, like showing which services are the top sellers each month or the number of sales per week.
• Profit and loss, showing where business investments are growing or falling.

Design Best Practices for Column Charts

2. dual-axis chart.

A dual-axis chart allows you to plot data using two y-axes and a shared x-axis. It has three data sets. One is a continuous data set, and the other is better suited to grouping by category. Use this chart to visualize a correlation or the lack thereof between these three data sets.

A dual-axis chart makes it easy to see relationships between different data sets. They can also help with comparing trends.

For example, the chart above shows how many new customers this company brings in each month. It also shows how much revenue those customers are bringing the company.

This makes it simple to see the connection between the number of customers and increased revenue.

You can use dual-axis charts to compare:

• Price and volume of your products.
• Revenue and units sold.
• Sales and profit margin.
• Individual sales performance.

Design Best Practices for Dual-Axis Charts

• Use the y-axis on the left side for the primary variable because brains naturally look left first.
• Use different graphing styles to illustrate the two data sets, as illustrated above.
• Choose contrasting colors for the two data sets.

3. Area Chart

An area chart is basically a line chart, but the space between the x-axis and the line is filled with a color or pattern. It is useful for showing part-to-whole relations, like showing individual sales reps’ contributions to total sales for a year. It helps you analyze both overall and individual trend information.

Best Use Cases for These Types of Charts

Area charts help show changes over time. They work best for big differences between data sets and help visualize big trends.

For example, the chart above shows users by creation date and life cycle stage.

A line chart could show more subscribers than marketing qualified leads. But this area chart emphasizes how much bigger the number of subscribers is than any other group.

These charts make the size of a group and how groups relate to each other more visually important than data changes over time.

Area graphs can help your business to:

• Visualize which product categories or products within a category are most popular.
• Show key performance indicator (KPI) goals vs. outcomes.
• Spot and analyze industry trends.

Design Best Practices for Area Charts

• Use transparent colors so information isn't obscured in the background.
• Don't display more than four categories to avoid clutter.
• Organize highly variable data at the top of the chart to make it easy to read.

4. Stacked Bar Chart

Use this chart to compare many different items and show the composition of each item you’re comparing.

These graphs are helpful when a group starts in one column and moves to another over time.

For example, the difference between a marketing qualified lead (MQL) and a sales qualified lead (SQL) is sometimes hard to see. The chart above helps stakeholders see these two lead types from a single point of view — when a lead changes from MQL to SQL.

Stacked bar charts are excellent for marketing. They make it simple to add a lot of data on a single chart or to make a point with limited space.

These graphs can show multiple takeaways, so they're also super for quarterly meetings when you have a lot to say but not a lot of time to say it.

Stacked bar charts are also a smart option for planning or strategy meetings. This is because these charts can show a lot of information at once, but they also make it easy to focus on one stack at a time or move data as needed.

You can also use these charts to:

• Show the frequency of survey responses.
• Identify outliers in historical data.
• Compare a part of a strategy to its performance as a whole.

Design Best Practices for Stacked Bar Graphs

• Best used to illustrate part-to-whole relationships.
• Use contrasting colors for greater clarity.
• Make the chart scale large enough to view group sizes in relation to one another.

5. Mekko Chart

Also known as a Marimekko chart, this type of graph can compare values, measure each one's composition, and show data distribution across each one.

It's similar to a stacked bar, except the Mekko's x-axis can capture another dimension of your values — instead of time progression, like column charts often do. In the graphic below, the x-axis compares the cities to one another.

Image Source

You can use a Mekko chart to show growth, market share, or competitor analysis.

For example, the Mekko chart above shows the market share of asset managers grouped by location and the value of their assets. This chart clarifies which firms manage the most assets in different areas.

It's also easy to see which asset managers are the largest and how they relate to each other.

Mekko charts can seem more complex than other types of charts and graphs, so it's best to use these in situations where you want to emphasize scale or differences between groups of data.

Other use cases for Mekko charts include:

• Detailed profit and loss statements.
• Revenue by brand and region.
• Product profitability.
• Share of voice by industry or niche.

Design Best Practices for Mekko Charts

• Vary your bar heights if the portion size is an important point of comparison.
• Don't include too many composite values within each bar. Consider reevaluating your presentation if you have a lot of data.
• Order your bars from left to right in such a way that exposes a relevant trend or message.

6. Pie Chart

A pie chart shows a static number and how categories represent part of a whole — the composition of something. A pie chart represents numbers in percentages, and the total sum of all segments needs to equal 100%.

The image above shows another example of customers by role in the company.

The bar graph example shows you that there are more individual contributors than any other role. But this pie chart makes it clear that they make up over 50% of customer roles.

Pie charts make it easy to see a section in relation to the whole, so they are good for showing:

• Customer personas in relation to all customers.
• Revenue from your most popular products or product types in relation to all product sales.
• Percent of total profit from different store locations.

Design Best Practices for Pie Charts

• Don't illustrate too many categories to ensure differentiation between slices.
• Ensure that the slice values add up to 100%.
• Order slices according to their size.

7. Scatter Plot Chart

A scatter plot or scattergram chart will show the relationship between two different variables or reveal distribution trends.

Use this chart when there are many different data points, and you want to highlight similarities in the data set. This is useful when looking for outliers or understanding your data's distribution.

Scatter plots are helpful in situations where you have too much data to see a pattern quickly. They are best when you use them to show relationships between two large data sets.

In the example above, this chart shows how customer happiness relates to the time it takes for them to get a response.

This type of graph makes it easy to compare two data sets. Use cases might include:

• Employment and manufacturing output.
• Retail sales and inflation.
• Visitor numbers and outdoor temperature.
• Sales growth and tax laws.

Try to choose two data sets that already have a positive or negative relationship. That said, this type of graph can also make it easier to see data that falls outside of normal patterns.

Design Best Practices for Scatter Plots

• Include more variables, like different sizes, to incorporate more data.
• Start the y-axis at 0 to represent data accurately.
• If you use trend lines, only use a maximum of two to make your plot easy to understand.

8. Bubble Chart

A bubble chart is similar to a scatter plot in that it can show distribution or relationship. There is a third data set shown by the size of the bubble or circle.

In the example above, the number of hours spent online isn't just compared to the user's age, as it would be on a scatter plot chart.

Instead, you can also see how the gender of the user impacts time spent online.

This makes bubble charts useful for seeing the rise or fall of trends over time. It also lets you add another option when you're trying to understand relationships between different segments or categories.

For example, if you want to launch a new product, this chart could help you quickly see your new product's cost, risk, and value. This can help you focus your energies on a low-risk new product with a high potential return.

You can also use bubble charts for:

• Top sales by month and location.
• Customer satisfaction surveys.
• Store performance tracking.
• Marketing campaign reviews.

Design Best Practices for Bubble Charts

• Scale bubbles according to area, not diameter.
• Make sure labels are clear and visible.
• Use circular shapes only.

9. Waterfall Chart

Use a waterfall chart to show how an initial value changes with intermediate values — either positive or negative — and results in a final value.

Use this chart to reveal the composition of a number. An example of this would be to showcase how different departments influence overall company revenue and lead to a specific profit number.

The most common use case for a funnel chart is the marketing or sales funnel. But there are many other ways to use this versatile chart.

If you have at least four stages of sequential data, this chart can help you easily see what inputs or outputs impact the final results.

For example, a funnel chart can help you see how to improve your buyer journey or shopping cart workflow. This is because it can help pinpoint major drop-off points.

Other stellar options for these types of charts include:

• Deal pipelines.
• Conversion and retention analysis.
• Bottlenecks in manufacturing and other multi-step processes.
• Marketing campaign performance.
• Website conversion tracking.

Design Best Practices for Funnel Charts

• Scale the size of each section to accurately reflect the size of the data set.
• Use contrasting colors or one color in graduated hues, from darkest to lightest, as the size of the funnel decreases.

11. Heat Map

A heat map shows the relationship between two items and provides rating information, such as high to low or poor to excellent. This chart displays the rating information using varying colors or saturation.

Best Use Cases for Heat Maps

In the example above, the darker the shade of green shows where the majority of people agree.

With enough data, heat maps can make a viewpoint that might seem subjective more concrete. This makes it easier for a business to act on customer sentiment.

There are many uses for these types of charts. In fact, many tech companies use heat map tools to gauge user experience for apps, online tools, and website design .

Another common use for heat map graphs is location assessment. If you're trying to find the right location for your new store, these maps can give you an idea of what the area is like in ways that a visit can't communicate.

Heat maps can also help with spotting patterns, so they're good for analyzing trends that change quickly, like ad conversions. They can also help with:

• Competitor research.
• Customer sentiment.
• Sales outreach.
• Campaign impact.
• Customer demographics.

Design Best Practices for Heat Map

• Use a basic and clear map outline to avoid distracting from the data.
• Use a single color in varying shades to show changes in data.
• Avoid using multiple patterns.

12. Gantt Chart

The Gantt chart is a horizontal chart that dates back to 1917. This chart maps the different tasks completed over a period of time.

Gantt charting is one of the most essential tools for project managers. It brings all the completed and uncompleted tasks into one place and tracks the progress of each.

While the left side of the chart displays all the tasks, the right side shows the progress and schedule for each of these tasks.

This chart type allows you to:

• Break projects into tasks.
• Track the start and end of the tasks.
• Set important events, meetings, and announcements.
• Assign tasks to the team and individuals.

Download the Excel templates mentioned in the video here.

5 Questions to Ask When Deciding Which Type of Chart to Use

1. do you want to compare values.

Charts and graphs are perfect for comparing one or many value sets, and they can easily show the low and high values in the data sets. To create a comparison chart, use these types of graphs:

• Scatter plot

2. Do you want to show the composition of something?

Use this type of chart to show how individual parts make up the whole of something, like the device type used for mobile visitors to your website or total sales broken down by sales rep.

To show composition, use these charts:

• Stacked bar

3. Do you want to understand the distribution of your data?

Distribution charts help you to understand outliers, the normal tendency, and the range of information in your values.

Use these charts to show distribution:

4. Are you interested in analyzing trends in your data set?

If you want more information about how a data set performed during a specific time, there are specific chart types that do extremely well.

You should choose one of the following:

• Dual-axis line

5. Do you want to better understand the relationship between value sets?

Relationship charts can show how one variable relates to one or many different variables. You could use this to show how something positively affects, has no effect, or negatively affects another variable.

When trying to establish the relationship between things, use these charts:

Featured Resource: The Marketer's Guide to Data Visualization

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What is Data Visualization: Unlocking Insights through Visual Representation

‍ Introduction

In the digital age, where we are inundated with vast amounts of information, data visualization emerges as a crucial tool for making sense of the complexity. From business analytics to scientific research, data visualization empowers individuals and organizations to extract valuable insights from their data. In this comprehensive guide for data scientists, we delve into the depths of what data visualization entails, its importance, various methods, and tools, and its impact on decision-making processes.

What is Data Visualization?

At its core, data visualization is the graphical representation of data and information. It transforms raw data into visual formats such as charts, graphs, maps, and dashboards, making complex datasets more accessible, understandable, and actionable all that data alone. Through visual elements like colors, shapes, and sizes, data visualization enables individuals to perceive trends, patterns, and relationships within the data quickly.

Why is Data Visualization Important?

In the era of big data, where organizations are inundated with vast volumes of data from multiple sources, data analyst with the ability to interpret and derive insights from this data is paramount. Here's why data visualization holds such significance:

Facilitates Data Analysis:

Data visualization simplifies the process of analyzing data by presenting it in a visually intuitive manner. It allows analysts and decision-makers to identify trends, correlations, and outliers more efficiently.

Enhances Decision Making:

By providing clear and concise representations of data, visualization aids decision-making processes across various domains. Whether it's predicting sales volumes, monitoring performance metrics, or identifying key insights, visualization enables informed decision-making.

Communicates Complex Concepts:

In fields such as data science, where complex datasets are the norm, visualization serves as a powerful tool for communicating insights to stakeholders who may not have a technical background. Visual representations transcend language barriers and facilitate better understanding.

Encourages Exploration:

Interactive data visualizations empower users to delve deeper into the data , allowing them to manipulate variables, filter information, and uncover hidden patterns. This interactive element fosters exploration and discovery, leading to richer insights.

Drives Data-driven Culture:

In today's data-driven world, organizations that embrace data visualization foster a culture of data-driven decision-making. By making data accessible and understandable to all stakeholders, visualization promotes a deeper understanding of the business landscape and encourages evidence-based strategies.

Types of Data Visualization

Data visualization encompasses a wide array of techniques and methods for visualizing data, each suited to different types of data and analytical tasks. Some common types of data visualization include:

• Bar Charts: Bar charts are one of the most straightforward and commonly used visualization methods . They represent data using rectangular bars, with the length of each bar corresponding to the value it represents. Bar charts are ideal for comparing categorical data or showing changes over time.

2. Line Charts: Line charts are used to visualize trends and patterns over time. They connect data points with lines , making it easy to see how values change continuously. Line charts are particularly useful for tracking performance metrics or analyzing time-series data.

3. Pie Charts: Pie charts represent data as a circle divided into slices, with each slice representing a proportion of the whole. Pie charts are effective for displaying the distribution of categories within a dataset, but they should be used sparingly, as they can be challenging to interpret accurately, especially with multiple categories.

4. Scatter Plots: Scatter plots are used to visualize the relationship between two variables. Each data point is represented by a dot on the graph , with the x-axis and y-axis corresponding to the two variables being compared. Scatter plots are useful for identifying correlations and outliers within the data.

5. Heat Maps: Heat maps use colour gradients to represent the density of data points within a two-dimensional space . They are often used to visualize geographic data or to highlight areas of high or low concentration within a dataset.

6. Histograms: Histograms are graphical representations of the distribution of numerical data . They divide the data into intervals, or bins, and display the frequency of data points within each bin using bars. Histograms are particularly useful for understanding the distribution and central tendencies of continuous data.

7. Box Plots (Box-and-Whisker Plots): Box plots are visual representations that summarize the distribution of numerical data through quartiles. They consist of a box that spans the interquartile range (IQR) of the data, with a line indicating the median. Whiskers extend from the box to show the range of the data, excluding outliers. Box plots are valuable for comparing the distributions of multiple datasets or identifying outliers within a single dataset.

8. Bubble Charts: Bubble charts represent data using circles (or bubbles), where the size of each bubble corresponds to a specific data value. They are often used to visualize three-dimensional data , with the x-axis representing one variable, the y-axis representing another variable, and the bubble size representing a third variable. Bubble charts are useful for highlighting patterns and relationships within multidimensional datasets.

9. Treemaps: Treemaps display hierarchical data structures as nested rectangles, with each rectangle representing a different level of the hierarchy. The size and colour of each rectangle can be used to encode additional information about the data, such as the relative size of categories or the distribution of values within each category. Treemaps are commonly used in areas such as hierarchical data visualization and disk space analysis.

10. Network Diagrams: Network diagrams, also known as graph visualizations, represent relationships between entities as nodes (or vertices) connected by edges (or links). They are used to visualize complex networks , such as social networks, organizational structures, and computer networks. Network diagrams can reveal patterns of connectivity, identify central nodes or clusters, and analyze the flow of information or resources within a network.

The Role of Data Visualization in Various Domains

Data visualization finds applications across a wide range of domains, from business intelligence to scientific research. Here's how it contributes to key areas:

Business Analytics:

In the realm of business analytics , data visualization is instrumental in understanding market trends, customer behavior, and competitive landscapes. It helps businesses identify growth opportunities, optimize operations, and make data-driven decisions to stay ahead in the market.

Healthcare:

In healthcare, data visualization aids in analyzing patient demographics, treatment outcomes, and disease trends. It allows healthcare providers to identify areas for improvement, optimize resource allocation, and ultimately improve patient care and outcomes.

In the financial sector, data visualization is used to monitor market trends , track investment performance, and assess risk. It enables financial analysts and traders to make informed decisions in real-time, based on the latest market data and insights.

Marketing and Advertising:

Data visualization plays a crucial role in marketing and advertising by helping marketers understand customer preferences, track campaign performance, and optimize marketing strategies. It allows marketers to visualize customer journeys, identify target audiences, and personalize marketing efforts for maximum impact.

In education, data visualization is used to track student performance , identify learning trends, and assess the effectiveness of teaching strategies. It enables educators to tailor instruction to individual student needs, monitor progress over time, and make data-driven decisions to improve learning outcomes.

Government and Public Policy:

In the public sector, data visualization is used to analyze demographic trends , track government spending, and monitor public health outcomes. It enables policymakers to make evidence-based decisions, allocate resources effectively, and address pressing social issues.

Challenges and Future Trends

While data visualization offers numerous benefits , it also poses certain challenges, particularly when dealing with large and complex datasets. Some common challenges include:

• Data Quality: Ensuring the accuracy, completeness, and consistency of data is essential for meaningful visualization. Poor data quality can lead to misleading visualizations and erroneous conclusions.
• Interpretation: Interpreting visualizations accurately requires domain knowledge and critical thinking skills. Misinterpretation of visualizations can lead to incorrect assumptions and flawed decision-making.
• Scalability: Visualizing large and complex datasets can be challenging due to limitations in processing power and memory. Scalable visualization techniques are needed to handle increasingly massive volumes of data generated in today's digital world.
• Privacy and Security: Protecting sensitive data from unauthorized access and ensuring compliance with data privacy regulations is critical in data visualization. Secure data handling practices must be implemented to safeguard confidential information.
• Looking ahead, several trends are shaping the future of data visualization :
• Advancements in Technology: Emerging technologies such as machine learning and artificial intelligence are driving innovations in data visualization. These technologies enable automated data analysis, pattern recognition, and predictive analytics, enhancing the capabilities of data visualization tools.
• Real-Time Visualization: With the growing emphasis on real-time data analytics, there is a growing demand for real-time visualization solutions that can provide up-to-the-minute insights into changing data trends and patterns.
• Augmented and Virtual Reality: Augmented reality (AR) and virtual reality (VR) are being increasingly used for immersive data visualization experiences . These technologies offer new ways to interact with data, allowing users to explore complex datasets in three-dimensional space.
• Ethical Considerations: As data visualization becomes more pervasive , there is a growing awareness of the ethical implications of data usage and visualization. Ethical considerations such as data privacy, bias, and transparency are increasingly being incorporated into data visualization practices.

Data Visualization Tools

Data visualization tools are indispensable for transforming raw data into actionable insights, providing intuitive interfaces and robust features for creating and customizing visualizations. Here are some prominent data visualization tools, including Metabase and Superset:

Sprinkle Data:

Sprinkle Data is a comprehensive data visualization platform designed to empower users to explore, analyze, and visualize their data effortlessly. With its user-friendly interface and robust features, Sprinkle Data enables users to create stunning visualizations, dashboards, and reports from various data sources. Its intuitive drag-and-drop interface, coupled with advanced analytics capabilities, allows users to uncover hidden patterns, trends, and correlations within their data. Moreover, Sprinkle Data offers collaborative features, real-time data updates, and seamless integration with popular data sources, making it an ideal choice for businesses seeking to harness the power of data visualization for informed decision-making.

Metabase is an open-source business intelligence tool that enables users to create interactive dashboards and visualizations from their data without requiring any SQL knowledge. With its intuitive interface and simple setup, Metabase allows users to explore data, generate insights, and share findings with ease. It supports a wide range of data sources and offers powerful features such as ad-hoc queries, custom filters, and real-time dashboards, making it a popular choice among small to medium-sized businesses and data-driven teams.

Superset is an open-source data exploration and visualization platform developed by Airbnb. It offers a wide range of visualization options, including charts, graphs, maps, and dashboards, allowing users to analyze and visualize data from multiple sources. With its SQL editor, data exploration capabilities, and integration with popular data warehouses such as Apache Druid and Apache Hive, Superset empowers users to create interactive visualizations and share insights across their organization.

Tableau is a leading data visualization tool known for its powerful analytics capabilities and interactive visualizations. It offers a wide range of visualization options, including charts, graphs, maps, and dashboards, allowing users to explore data from multiple angles. Tableau's intuitive drag-and-drop interface and robust data connectivity make it a popular choice among data analysts, business users, and data scientists.

Microsoft Power BI:

Microsoft Power BI is a cloud-based business analytics tool that enables users to visualize and share insights across their organization. With its rich set of visualization options, data connectors, and collaboration features, Power BI empowers users to create interactive dashboards and reports from diverse data sources, including Excel, SQL Server, and Salesforce.

Google Data Studio:

Google Data Studio is a free data visualization tool that allows users to create interactive dashboards and reports using data from Google Analytics, Google Ads, and other sources. Its intuitive interface and seamless integration with Google products make it an attractive choice for businesses looking to visualize their data and gain actionable insights.

In conclusion, data visualization is a powerful tool for transforming data into actionable insights across various domains. By leveraging visual representations to communicate complex information effectively, data visualization enables informed decision-making, drives innovation, and fosters a deeper understanding of the world around us. As technology continues to evolve and data volumes continue to grow, the importance of effective data visualization will only continue to increase, shaping the way we interact with and derive value from data in the future. ‍

‍ FAQ: Understanding Data Visualization

1. What is data visualization?

Data visualization is the graphical representation of data and information, transforming raw data into visual formats like charts, graphs, and maps for easier understanding and analysis.

2. Why is data visualization important?

Data visualization is crucial in the era of big data as it facilitates data analysis, enhances decision-making processes, communicates complex concepts, encourages exploration, and drives a data-driven culture.

3. What are some common types of data visualization?

Common types include bar charts, line charts, pie charts, scatter plots, heat maps, histograms, box plots, bubble charts, treemaps, network diagrams, word clouds, and Sankey diagrams.

4. How does data visualization contribute to various domains?

In business analytics, healthcare, finance, marketing, education, and government, data visualization aids in understanding trends, optimizing strategies, and making informed decisions.

5. What challenges does data visualization face?

Challenges include ensuring data quality, accurate interpretation, scalability for large datasets, and maintaining privacy and security.

6. What are some future trends in data visualization?

Advancements in technology, real-time visualization, augmented and virtual reality applications, and ethical considerations regarding data usage and visualization.

7. What role does data visualization play in business intelligence?

Data visualization helps businesses understand market trends, customer behaviour, and competitive landscapes, enabling them to make data-driven decisions for growth and optimization.

8. How does data visualization impact healthcare?

In healthcare, data visualization assists in analyzing patient demographics, treatment outcomes, and disease trends, leading to improved resource allocation and patient care.

9. How does data visualization aid in financial analysis?

Data visualization is used in finance to monitor market trends, track investment performance, and assess risk, facilitating informed decision-making for financial analysts and traders.

10. What significance does data visualization hold in marketing and advertising?

In marketing and advertising, data visualization helps marketers understand customer preferences, track campaign performance, and personalize marketing strategies for maximum impact.

11. How does data visualization benefit education?

In education, data visualization is utilized to track student performance, identify learning trends, and improve teaching strategies, leading to enhanced learning outcomes.

12. What role does data visualization play in government and public policy?

In the public sector, data visualization aids in analyzing demographic trends, monitoring government spending, and addressing social issues through evidence-based decision-making.

13. How does data visualization address challenges related to data quality?

Data visualization ensures data accuracy, completeness, and consistency, enabling meaningful representation and analysis of data despite potential quality issues.

14. What are some examples of emerging technologies driving innovations in data visualization?

Examples include machine learning and artificial intelligence, which enable automated analysis, pattern recognition, and predictive analytics, enhancing the capabilities of data visualization tools.

15. How do augmented and virtual reality technologies contribute to data visualization?

Augmented and virtual reality offer immersive visualization experiences, allowing users to explore complex datasets in three-dimensional space, opening up new possibilities for data analysis and interpretation.

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What Is a Growth Curve?

Understanding a growth curve, the bottom line.

• Business Leaders
• Math and Statistics

Growth Curve: Definition, How It's Used, and Example

Adam Hayes, Ph.D., CFA, is a financial writer with 15+ years Wall Street experience as a derivatives trader. Besides his extensive derivative trading expertise, Adam is an expert in economics and behavioral finance. Adam received his master's in economics from The New School for Social Research and his Ph.D. from the University of Wisconsin-Madison in sociology. He is a CFA charterholder as well as holding FINRA Series 7, 55 & 63 licenses. He currently researches and teaches economic sociology and the social studies of finance at the Hebrew University in Jerusalem.

A growth curve is a graphical representation how how something changes over time. An example of a growth curve might be a chart showing a country's population increase over time.

Growth curves are widely used in statistics to determine patterns of growth over time of a quantity—be it linear, exponential, or cubic. Businesses use growth curves to track or predict many factors, including future sales .

Key Takeaways

• A growth curve shows the direction of some phenomena over time, in the past or into the future, or both.
• Growth curves are typically displayed on a set of axes where the x-axis is time and the y-axis shows an amount of growth.
• Growth curves are used in a variety of applications from population biology and ecology to finance and economics.
• Growth curves allow for the monitoring of change over time and what variables may cause this change. Businesses and investors can adjust strategies depending on the growth curve.

The shape of a growth curve can make a big difference when a business determines whether to launch a new product or enter a new market . Slow growth markets are less likely to be appealing because there is less room for profit. Exponential growth is generally positive but could mean that the market will attract a lot of competitors.

Growth curves were initially used in the physical sciences such as biology. Today, they're a common component of social sciences as well.

Digital Enhancements

Advancements in digital technologies and business models now require analysts to account for growth patterns unique to the modern economy. For example, the winner-take-all phenomenon is a fairly recent development brought on by companies such as Amazon, Google, and Apple . Researchers are scrambling to make sense of growth curves that are unique to new business models and platforms.

Growth curves are often associated with biology, allowing biologists to study organisms and how these organisms behave in a specific environment and the changes to that environment in a controlled setting.

Shifts in demographics, the nature of work, and artificial intelligence will further strain conventional ways of analyzing growth curves or trends.

Analysis of growth curves plays an essential role in determining the future success of products, markets, and societies, both at the micro and macro levels.

Example of a Growth Curve

In the image below, the growth curve displayed represents the growth of a population in millions over a span of decades. The shape of this growth curve indicates exponential growth. That is, the growth curve starts slowly, remains nearly flat for some time, and then curves sharply upwards, appearing almost vertical.

This curve follows the general formula:

V = S * (1 + R) t

The current value, V, of an initial starting point subject to exponential growth, can be determined by multiplying the starting value, S, by the sum of one plus the rate of interest, R, raised to the power of t, or the number of periods that have elapsed.

In finance, exponential growth appears most commonly in the context of compound interest.

The power of compounding is one of the most powerful forces in finance. This concept allows investors to create large sums with little initial capital. Savings accounts that carry a compounding interest rate are common examples.

What Are the 2 Types of Growth Curves?

The two types of growth curves are exponential growth curves and logarithmic growth curves. In an exponential growth curve, the slope grows greater and greater as time moves along. In a logarithmic growth curve, the slope grows sharply, and then over time the slope declines until it becomes flat.

Why Use a Growth Curve?

Growth curves are a helpful visual representation of change over time. Growth curves can be used to understand a variety of changes over time, such as developmental and economic. They allow for the understanding of the effect of policies or treatments.

What Is a Business Growth Model?

A business growth model provides a visual representation for businesses to track various metrics and key drivers, allowing businesses to map out growth and adjust the businesses accordingly to foster these metrics.

A growth curve is a graph that represents the way a phenomenon changes over time. It can show both the past and the future. They typically use two axes, where the x-axis is time and the y-axis is growth.

Growth curves are used in many disciplines, including sciences such as biology and ecology. They are also used in finance and economics. Businesses can use growth curves to see how a specific market is changing over time. This can help them decide whether to enter or leave a certain market or adjust their selling strategy to account for changes.

Curran, Patrick J., Obeidat, Khawla, and Losardo, Diane, via National Library of Medicine. " Twelve Frequently Asked Questions About Growth Curve Modeling: Abstract ." Journal of Cognition and Development , vol. 11, no. 2, 2010.

Sigirli, Deniz and Ercan, Ilker. " Examining Growth with Statistical Shape Analysis and Comparison of Growth Models ." Journal of Modern Applied Statistical Methods , vol. 11, no. 2, November 2012, pp. 1.

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Mindfulness

How visualization can benefit your well-being, visualization can help you reach a range of goals..

Updated November 20, 2023 | Reviewed by Gary Drevitch

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Co-written by Kelsey Schultz and Tchiki Davis

Visualization, also called mental imagery , is essentially seeing with the mind’s eye or hearing with the mind’s ear. That is, when visualizing you are having a visual sensory experience without the use of your eyes. In fact, research has shown that visualization recruits the same brain areas that actual seeing does (Pearson et al., 2015).

Humans have evolved to rely heavily on our eyesight, making us highly visually-oriented creatures. Because our brains are adapted to easily process and comprehend visual information, visualization can be a powerful tool for influencing our thoughts, emotions , and behaviors. In fact, research has shown that processing emotions using visualization is more powerful than processing verbally (Blackwell et al., 2019). For example, when research participants listen to descriptions of emotionally valenced situations (i.e., “your boss telling you that they are disappointed with your work”), participants who are instructed to imagine themselves in the situation demonstrate a greater change in mood than those that are instructed only to think about the situation verbally (Blackwell et al., 2019).

There appear to be a number of emotional, cognitive, and behavioral benefits to practicing visualization.

​Emotional. Some forms of visualization have been shown to increase optimism and other positive emotions (Murphy et al., 2015). It has also been shown to be a useful method for regulating negative emotions such as anxiety or overwhelm (Blackwell et al., 2019).

Cognitive. Visualization techniques can be used to facilitate some kinds of decision-making and problem-solving (Blackwell et al., 2019). For example, visualization might be helpful when planning the best route to take on your upcoming road trip. Visualization techniques, such as the mind palace, are also an effective means of improving memory . The mind palace technique involves using a place you are very familiar with, such as your bedroom, and using different locations within that space as mnemonic devices associated with a particular piece of information you are trying to store.

Behavioral. Visualization can also help us achieve our goals by allowing us to determine the appropriate sequences of actions needed to reach our goal and identify any potential obstacles we might encounter as we proceed toward a goal. In other words, we can use visualization as a sort of rough draft for our plans by imagining each step we need to take to reach our goal, what each step might include, what might go wrong, and the ways in which we might need to prepare.

Visualization Tools

Music. Visualization music is music that is specifically intended to facilitate visualization and similar meditative processes. This kind of music can also be described as atmospheric or ambient, as the purpose is not to occupy your attention , but rather to help you focus attention on your visualizations.

Boards. Visualization boards, also called vision boards , are visual representations of your goals , intentions, and desires. Vision boards are typically poster-sized and include a collage-type arrangement of images that symbolize different facets of your goals and intentions. Vision boards are useful for ensuring that your goals remain salient. That is, by creating a visual representation of your goals, you can easily look back at your vision board and remind yourself of the intentions you set. When your intentions are at the forefront of your mind, you are more likely to act in accordance with them.

Guided Imagery

Guided imagery is a visualization exercise in which you engage all of your senses as you imagine yourself in a positive, peaceful environment.

• To begin, find a comfortable position, close your eyes, and begin breathing slowly and deeply as you start to relax.
• Next, visualize a place where you feel calm and content. This can be a place you’ve been before, a place you would like to go, or a place that is wholly the product of your imagination . Engage all of your senses to add depth and detail to the place you are visualizing. Can you feel a soft breeze? Do you hear birds or the sound of water lapping on the shore?
• Reflect on the calm that emerges as you move deeper into your vision.
• As you inhale, imagine peace washing over you and filling your body.
• As you exhale, imagine exhaustion, tension , and stress being washed away.
• Stay in your vision for as long as you like.

Visualization is a simple yet powerful technique that we can use to improve many facets of our lives. We can use visualization to improve our mood, help us remember important information, facilitate problem-solving and decision-making , and boost progress toward our goals. Depending on the purpose, there are many forms of visualization we can practice. For example, if we are trying to regulate our mood we might try visualization meditation , whereas if we are trying to solidify our goals for the new year we might use a vision board or a mind map .

Adapted from a post on visualization published by The Berkeley Well-Being Institute.

Blackwell, S. E. (2019). Mental imagery: From basic research to clinical practice. Journal of Psychotherapy Integration, 29(3), 235.

Murphy, S. E., O’Donoghue, M. C., Drazich, E. H., Blackwell, S. E., Nobre, A. C., & Holmes, E. A. (2015). Imagining a brighter future: the effect of positive imagery training on mood, prospective mental imagery and emotional bias in older adults. Psychiatry Research, 230(1), 36-43.

Pearson, J., Naselaris, T., Holmes, E. A., & Kosslyn, S. M. (2015). Mental imagery: functional mechanisms and clinical applications. Trends in cognitive sciences, 19(10), 590-602.​

Tchiki Davis, Ph.D. , is a consultant, writer, and expert on well-being technology.

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Understanding what emotional intelligence looks like and the steps needed to improve it could light a path to a more emotionally adept world.

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• Published: 19 July 2015

The role of visual representations in scientific practices: from conceptual understanding and knowledge generation to ‘seeing’ how science works

• Maria Evagorou 1 ,
• Sibel Erduran 2 &
• Terhi Mäntylä 3  

International Journal of STEM Education volume  2 , Article number:  11 ( 2015 ) Cite this article

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The use of visual representations (i.e., photographs, diagrams, models) has been part of science, and their use makes it possible for scientists to interact with and represent complex phenomena, not observable in other ways. Despite a wealth of research in science education on visual representations, the emphasis of such research has mainly been on the conceptual understanding when using visual representations and less on visual representations as epistemic objects. In this paper, we argue that by positioning visual representations as epistemic objects of scientific practices, science education can bring a renewed focus on how visualization contributes to knowledge formation in science from the learners’ perspective.

This is a theoretical paper, and in order to argue about the role of visualization, we first present a case study, that of the discovery of the structure of DNA that highlights the epistemic components of visual information in science. The second case study focuses on Faraday’s use of the lines of magnetic force. Faraday is known of his exploratory, creative, and yet systemic way of experimenting, and the visual reasoning leading to theoretical development was an inherent part of the experimentation. Third, we trace a contemporary account from science focusing on the experimental practices and how reproducibility of experimental procedures can be reinforced through video data.

Conclusions

Our conclusions suggest that in teaching science, the emphasis in visualization should shift from cognitive understanding—using the products of science to understand the content—to engaging in the processes of visualization. Furthermore, we suggest that is it essential to design curriculum materials and learning environments that create a social and epistemic context and invite students to engage in the practice of visualization as evidence, reasoning, experimental procedure, or a means of communication and reflect on these practices. Implications for teacher education include the need for teacher professional development programs to problematize the use of visual representations as epistemic objects that are part of scientific practices.

During the last decades, research and reform documents in science education across the world have been calling for an emphasis not only on the content but also on the processes of science (Bybee 2014 ; Eurydice 2012 ; Duschl and Bybee 2014 ; Osborne 2014 ; Schwartz et al. 2012 ), in order to make science accessible to the students and enable them to understand the epistemic foundation of science. Scientific practices, part of the process of science, are the cognitive and discursive activities that are targeted in science education to develop epistemic understanding and appreciation of the nature of science (Duschl et al. 2008 ) and have been the emphasis of recent reform documents in science education across the world (Achieve 2013 ; Eurydice 2012 ). With the term scientific practices, we refer to the processes that take place during scientific discoveries and include among others: asking questions, developing and using models, engaging in arguments, and constructing and communicating explanations (National Research Council 2012 ). The emphasis on scientific practices aims to move the teaching of science from knowledge to the understanding of the processes and the epistemic aspects of science. Additionally, by placing an emphasis on engaging students in scientific practices, we aim to help students acquire scientific knowledge in meaningful contexts that resemble the reality of scientific discoveries.

Despite a wealth of research in science education on visual representations, the emphasis of such research has mainly been on the conceptual understanding when using visual representations and less on visual representations as epistemic objects. In this paper, we argue that by positioning visual representations as epistemic objects, science education can bring a renewed focus on how visualization contributes to knowledge formation in science from the learners’ perspective. Specifically, the use of visual representations (i.e., photographs, diagrams, tables, charts) has been part of science and over the years has evolved with the new technologies (i.e., from drawings to advanced digital images and three dimensional models). Visualization makes it possible for scientists to interact with complex phenomena (Richards 2003 ), and they might convey important evidence not observable in other ways. Visual representations as a tool to support cognitive understanding in science have been studied extensively (i.e., Gilbert 2010 ; Wu and Shah 2004 ). Studies in science education have explored the use of images in science textbooks (i.e., Dimopoulos et al. 2003 ; Bungum 2008 ), students’ representations or models when doing science (i.e., Gilbert et al. 2008 ; Dori et al. 2003 ; Lehrer and Schauble 2012 ; Schwarz et al. 2009 ), and students’ images of science and scientists (i.e., Chambers 1983 ). Therefore, studies in the field of science education have been using the term visualization as “the formation of an internal representation from an external representation” (Gilbert et al. 2008 , p. 4) or as a tool for conceptual understanding for students.

In this paper, we do not refer to visualization as mental image, model, or presentation only (Gilbert et al. 2008 ; Philips et al. 2010 ) but instead focus on visual representations or visualization as epistemic objects. Specifically, we refer to visualization as a process for knowledge production and growth in science. In this respect, modeling is an aspect of visualization, but what we are focusing on with visualization is not on the use of model as a tool for cognitive understanding (Gilbert 2010 ; Wu and Shah 2004 ) but the on the process of modeling as a scientific practice which includes the construction and use of models, the use of other representations, the communication in the groups with the use of the visual representation, and the appreciation of the difficulties that the science phase in this process. Therefore, the purpose of this paper is to present through the history of science how visualization can be considered not only as a cognitive tool in science education but also as an epistemic object that can potentially support students to understand aspects of the nature of science.

Scientific practices and science education

According to the New Generation Science Standards (Achieve 2013 ), scientific practices refer to: asking questions and defining problems; developing and using models; planning and carrying out investigations; analyzing and interpreting data; using mathematical and computational thinking; constructing explanations and designing solutions; engaging in argument from evidence; and obtaining, evaluating, and communicating information. A significant aspect of scientific practices is that science learning is more than just about learning facts, concepts, theories, and laws. A fuller appreciation of science necessitates the understanding of the science relative to its epistemological grounding and the process that are involved in the production of knowledge (Hogan and Maglienti 2001 ; Wickman 2004 ).

The New Generation Science Standards is, among other changes, shifting away from science inquiry and towards the inclusion of scientific practices (Duschl and Bybee 2014 ; Osborne 2014 ). By comparing the abilities to do scientific inquiry (National Research Council 2000 ) with the set of scientific practices, it is evident that the latter is about engaging in the processes of doing science and experiencing in that way science in a more authentic way. Engaging in scientific practices according to Osborne ( 2014 ) “presents a more authentic picture of the endeavor that is science” (p.183) and also helps the students to develop a deeper understanding of the epistemic aspects of science. Furthermore, as Bybee ( 2014 ) argues, by engaging students in scientific practices, we involve them in an understanding of the nature of science and an understanding on the nature of scientific knowledge.

Science as a practice and scientific practices as a term emerged by the philosopher of science, Kuhn (Osborne 2014 ), refers to the processes in which the scientists engage during knowledge production and communication. The work that is followed by historians, philosophers, and sociologists of science (Latour 2011 ; Longino 2002 ; Nersessian 2008 ) revealed the scientific practices in which the scientists engage in and include among others theory development and specific ways of talking, modeling, and communicating the outcomes of science.

Visualization as an epistemic object

Schematic, pictorial symbols in the design of scientific instruments and analysis of the perceptual and functional information that is being stored in those images have been areas of investigation in philosophy of scientific experimentation (Gooding et al. 1993 ). The nature of visual perception, the relationship between thought and vision, and the role of reproducibility as a norm for experimental research form a central aspect of this domain of research in philosophy of science. For instance, Rothbart ( 1997 ) has argued that visualizations are commonplace in the theoretical sciences even if every scientific theory may not be defined by visualized models.

Visual representations (i.e., photographs, diagrams, tables, charts, models) have been used in science over the years to enable scientists to interact with complex phenomena (Richards 2003 ) and might convey important evidence not observable in other ways (Barber et al. 2006 ). Some authors (e.g., Ruivenkamp and Rip 2010 ) have argued that visualization is as a core activity of some scientific communities of practice (e.g., nanotechnology) while others (e.g., Lynch and Edgerton 1988 ) have differentiated the role of particular visualization techniques (e.g., of digital image processing in astronomy). Visualization in science includes the complex process through which scientists develop or produce imagery, schemes, and graphical representation, and therefore, what is of importance in this process is not only the result but also the methodology employed by the scientists, namely, how this result was produced. Visual representations in science may refer to objects that are believed to have some kind of material or physical existence but equally might refer to purely mental, conceptual, and abstract constructs (Pauwels 2006 ). More specifically, visual representations can be found for: (a) phenomena that are not observable with the eye (i.e., microscopic or macroscopic); (b) phenomena that do not exist as visual representations but can be translated as such (i.e., sound); and (c) in experimental settings to provide visual data representations (i.e., graphs presenting velocity of moving objects). Additionally, since science is not only about replicating reality but also about making it more understandable to people (either to the public or other scientists), visual representations are not only about reproducing the nature but also about: (a) functioning in helping solving a problem, (b) filling gaps in our knowledge, and (c) facilitating knowledge building or transfer (Lynch 2006 ).

Using or developing visual representations in the scientific practice can range from a straightforward to a complicated situation. More specifically, scientists can observe a phenomenon (i.e., mitosis) and represent it visually using a picture or diagram, which is quite straightforward. But they can also use a variety of complicated techniques (i.e., crystallography in the case of DNA studies) that are either available or need to be developed or refined in order to acquire the visual information that can be used in the process of theory development (i.e., Latour and Woolgar 1979 ). Furthermore, some visual representations need decoding, and the scientists need to learn how to read these images (i.e., radiologists); therefore, using visual representations in the process of science requires learning a new language that is specific to the medium/methods that is used (i.e., understanding an X-ray picture is different from understanding an MRI scan) and then communicating that language to other scientists and the public.

There are much intent and purposes of visual representations in scientific practices, as for example to make a diagnosis, compare, describe, and preserve for future study, verify and explore new territory, generate new data (Pauwels 2006 ), or present new methodologies. According to Latour and Woolgar ( 1979 ) and Knorr Cetina ( 1999 ), visual representations can be used either as primary data (i.e., image from a microscope). or can be used to help in concept development (i.e., models of DNA used by Watson and Crick), to uncover relationships and to make the abstract more concrete (graphs of sound waves). Therefore, visual representations and visual practices, in all forms, are an important aspect of the scientific practices in developing, clarifying, and transmitting scientific knowledge (Pauwels 2006 ).

Methods and Results: Merging Visualization and scientific practices in science

In this paper, we present three case studies that embody the working practices of scientists in an effort to present visualization as a scientific practice and present our argument about how visualization is a complex process that could include among others modeling and use of representation but is not only limited to that. The first case study explores the role of visualization in the construction of knowledge about the structure of DNA, using visuals as evidence. The second case study focuses on Faraday’s use of the lines of magnetic force and the visual reasoning leading to the theoretical development that was an inherent part of the experimentation. The third case study focuses on the current practices of scientists in the context of a peer-reviewed journal called the Journal of Visualized Experiments where the methodology is communicated through videotaped procedures. The three case studies represent the research interests of the three authors of this paper and were chosen to present how visualization as a practice can be involved in all stages of doing science, from hypothesizing and evaluating evidence (case study 1) to experimenting and reasoning (case study 2) to communicating the findings and methodology with the research community (case study 3), and represent in this way the three functions of visualization as presented by Lynch ( 2006 ). Furthermore, the last case study showcases how the development of visualization technologies has contributed to the communication of findings and methodologies in science and present in that way an aspect of current scientific practices. In all three cases, our approach is guided by the observation that the visual information is an integral part of scientific practices at the least and furthermore that they are particularly central in the scientific practices of science.

Case study 1: use visual representations as evidence in the discovery of DNA

The focus of the first case study is the discovery of the structure of DNA. The DNA was first isolated in 1869 by Friedrich Miescher, and by the late 1940s, it was known that it contained phosphate, sugar, and four nitrogen-containing chemical bases. However, no one had figured the structure of the DNA until Watson and Crick presented their model of DNA in 1953. Other than the social aspects of the discovery of the DNA, another important aspect was the role of visual evidence that led to knowledge development in the area. More specifically, by studying the personal accounts of Watson ( 1968 ) and Crick ( 1988 ) about the discovery of the structure of the DNA, the following main ideas regarding the role of visual representations in the production of knowledge can be identified: (a) The use of visual representations was an important part of knowledge growth and was often dependent upon the discovery of new technologies (i.e., better microscopes or better techniques in crystallography that would provide better visual representations as evidence of the helical structure of the DNA); and (b) Models (three-dimensional) were used as a way to represent the visual images (X-ray images) and connect them to the evidence provided by other sources to see whether the theory can be supported. Therefore, the model of DNA was built based on the combination of visual evidence and experimental data.

An example showcasing the importance of visual representations in the process of knowledge production in this case is provided by Watson, in his book The Double Helix (1968):

…since the middle of the summer Rosy [Rosalind Franklin] had had evidence for a new three-dimensional form of DNA. It occurred when the DNA 2molecules were surrounded by a large amount of water. When I asked what the pattern was like, Maurice went into the adjacent room to pick up a print of the new form they called the “B” structure. The instant I saw the picture, my mouth fell open and my pulse began to race. The pattern was unbelievably simpler than those previously obtained (A form). Moreover, the black cross of reflections which dominated the picture could arise only from a helical structure. With the A form the argument for the helix was never straightforward, and considerable ambiguity existed as to exactly which type of helical symmetry was present. With the B form however, mere inspection of its X-ray picture gave several of the vital helical parameters. (p. 167-169)

As suggested by Watson’s personal account of the discovery of the DNA, the photo taken by Rosalind Franklin (Fig.  1 ) convinced him that the DNA molecule must consist of two chains arranged in a paired helix, which resembles a spiral staircase or ladder, and on March 7, 1953, Watson and Crick finished and presented their model of the structure of DNA (Watson and Berry 2004 ; Watson 1968 ) which was based on the visual information provided by the X-ray image and their knowledge of chemistry.

X-ray chrystallography of DNA

In analyzing the visualization practice in this case study, we observe the following instances that highlight how the visual information played a role:

Asking questions and defining problems: The real world in the model of science can at some points only be observed through visual representations or representations, i.e., if we are using DNA as an example, the structure of DNA was only observable through the crystallography images produced by Rosalind Franklin in the laboratory. There was no other way to observe the structure of DNA, therefore the real world.

Analyzing and interpreting data: The images that resulted from crystallography as well as their interpretations served as the data for the scientists studying the structure of DNA.

Experimenting: The data in the form of visual information were used to predict the possible structure of the DNA.

Modeling: Based on the prediction, an actual three-dimensional model was prepared by Watson and Crick. The first model did not fit with the real world (refuted by Rosalind Franklin and her research group from King’s College) and Watson and Crick had to go through the same process again to find better visual evidence (better crystallography images) and create an improved visual model.

Example excerpts from Watson’s biography provide further evidence for how visualization practices were applied in the context of the discovery of DNA (Table  1 ).

In summary, by examining the history of the discovery of DNA, we showcased how visual data is used as scientific evidence in science, identifying in that way an aspect of the nature of science that is still unexplored in the history of science and an aspect that has been ignored in the teaching of science. Visual representations are used in many ways: as images, as models, as evidence to support or rebut a model, and as interpretations of reality.

Case study 2: applying visual reasoning in knowledge production, the example of the lines of magnetic force

The focus of this case study is on Faraday’s use of the lines of magnetic force. Faraday is known of his exploratory, creative, and yet systemic way of experimenting, and the visual reasoning leading to theoretical development was an inherent part of this experimentation (Gooding 2006 ). Faraday’s articles or notebooks do not include mathematical formulations; instead, they include images and illustrations from experimental devices and setups to the recapping of his theoretical ideas (Nersessian 2008 ). According to Gooding ( 2006 ), “Faraday’s visual method was designed not to copy apparent features of the world, but to analyse and replicate them” (2006, p. 46).

The lines of force played a central role in Faraday’s research on electricity and magnetism and in the development of his “field theory” (Faraday 1852a ; Nersessian 1984 ). Before Faraday, the experiments with iron filings around magnets were known and the term “magnetic curves” was used for the iron filing patterns and also for the geometrical constructs derived from the mathematical theory of magnetism (Gooding et al. 1993 ). However, Faraday used the lines of force for explaining his experimental observations and in constructing the theory of forces in magnetism and electricity. Examples of Faraday’s different illustrations of lines of magnetic force are given in Fig.  2 . Faraday gave the following experiment-based definition for the lines of magnetic forces:

a Iron filing pattern in case of bar magnet drawn by Faraday (Faraday 1852b , Plate IX, p. 158, Fig. 1), b Faraday’s drawing of lines of magnetic force in case of cylinder magnet, where the experimental procedure, knife blade showing the direction of lines, is combined into drawing (Faraday, 1855, vol. 1, plate 1)

A line of magnetic force may be defined as that line which is described by a very small magnetic needle, when it is so moved in either direction correspondent to its length, that the needle is constantly a tangent to the line of motion; or it is that line along which, if a transverse wire be moved in either direction, there is no tendency to the formation of any current in the wire, whilst if moved in any other direction there is such a tendency; or it is that line which coincides with the direction of the magnecrystallic axis of a crystal of bismuth, which is carried in either direction along it. The direction of these lines about and amongst magnets and electric currents, is easily represented and understood, in a general manner, by the ordinary use of iron filings. (Faraday 1852a , p. 25 (3071))

The definition describes the connection between the experiments and the visual representation of the results. Initially, the lines of force were just geometric representations, but later, Faraday treated them as physical objects (Nersessian 1984 ; Pocovi and Finlay 2002 ):

I have sometimes used the term lines of force so vaguely, as to leave the reader doubtful whether I intended it as a merely representative idea of the forces, or as the description of the path along which the power was continuously exerted. … wherever the expression line of force is taken simply to represent the disposition of forces, it shall have the fullness of that meaning; but that wherever it may seem to represent the idea of the physical mode of transmission of the force, it expresses in that respect the opinion to which I incline at present. The opinion may be erroneous, and yet all that relates or refers to the disposition of the force will remain the same. (Faraday, 1852a , p. 55-56 (3075))

He also felt that the lines of force had greater explanatory power than the dominant theory of action-at-a-distance:

Now it appears to me that these lines may be employed with great advantage to represent nature, condition, direction and comparative amount of the magnetic forces; and that in many cases they have, to the physical reasoned at least, a superiority over that method which represents the forces as concentrated in centres of action… (Faraday, 1852a , p. 26 (3074))

For giving some insight to Faraday’s visual reasoning as an epistemic practice, the following examples of Faraday’s studies of the lines of magnetic force (Faraday 1852a , 1852b ) are presented:

(a) Asking questions and defining problems: The iron filing patterns formed the empirical basis for the visual model: 2D visualization of lines of magnetic force as presented in Fig.  2 . According to Faraday, these iron filing patterns were suitable for illustrating the direction and form of the magnetic lines of force (emphasis added):

It must be well understood that these forms give no indication by their appearance of the relative strength of the magnetic force at different places, inasmuch as the appearance of the lines depends greatly upon the quantity of filings and the amount of tapping; but the direction and forms of these lines are well given, and these indicate, in a considerable degree, the direction in which the forces increase and diminish . (Faraday 1852b , p.158 (3237))

Despite being static and two dimensional on paper, the lines of magnetic force were dynamical (Nersessian 1992 , 2008 ) and three dimensional for Faraday (see Fig.  2 b). For instance, Faraday described the lines of force “expanding”, “bending,” and “being cut” (Nersessian 1992 ). In Fig.  2 b, Faraday has summarized his experiment (bar magnet and knife blade) and its results (lines of force) in one picture.

(b) Analyzing and interpreting data: The model was so powerful for Faraday that he ended up thinking them as physical objects (e.g., Nersessian 1984 ), i.e., making interpretations of the way forces act. Of course, he made a lot of experiments for showing the physical existence of the lines of force, but he did not succeed in it (Nersessian 1984 ). The following quote illuminates Faraday’s use of the lines of force in different situations:

The study of these lines has, at different times, been greatly influential in leading me to various results, which I think prove their utility as well as fertility. Thus, the law of magneto-electric induction; the earth’s inductive action; the relation of magnetism and light; diamagnetic action and its law, and magnetocrystallic action, are the cases of this kind… (Faraday 1852a , p. 55 (3174))

(c) Experimenting: In Faraday's case, he used a lot of exploratory experiments; in case of lines of magnetic force, he used, e.g., iron filings, magnetic needles, or current carrying wires (see the quote above). The magnetic field is not directly observable and the representation of lines of force was a visual model, which includes the direction, form, and magnitude of field.

(d) Modeling: There is no denying that the lines of magnetic force are visual by nature. Faraday’s views of lines of force developed gradually during the years, and he applied and developed them in different contexts such as electromagnetic, electrostatic, and magnetic induction (Nersessian 1984 ). An example of Faraday’s explanation of the effect of the wire b’s position to experiment is given in Fig.  3 . In Fig.  3 , few magnetic lines of force are drawn, and in the quote below, Faraday is explaining the effect using these magnetic lines of force (emphasis added):

Picture of an experiment with different arrangements of wires ( a , b’ , b” ), magnet, and galvanometer. Note the lines of force drawn around the magnet. (Faraday 1852a , p. 34)

It will be evident by inspection of Fig. 3 , that, however the wires are carried away, the general result will, according to the assumed principles of action, be the same; for if a be the axial wire, and b’, b”, b”’ the equatorial wire, represented in three different positions, whatever magnetic lines of force pass across the latter wire in one position, will also pass it in the other, or in any other position which can be given to it. The distance of the wire at the place of intersection with the lines of force, has been shown, by the experiments (3093.), to be unimportant. (Faraday 1852a , p. 34 (3099))

In summary, by examining the history of Faraday’s use of lines of force, we showed how visual imagery and reasoning played an important part in Faraday’s construction and representation of his “field theory”. As Gooding has stated, “many of Faraday’s sketches are far more that depictions of observation, they are tools for reasoning with and about phenomena” (2006, p. 59).

Case study 3: visualizing scientific methods, the case of a journal

The focus of the third case study is the Journal of Visualized Experiments (JoVE) , a peer-reviewed publication indexed in PubMed. The journal devoted to the publication of biological, medical, chemical, and physical research in a video format. The journal describes its history as follows:

JoVE was established as a new tool in life science publication and communication, with participation of scientists from leading research institutions. JoVE takes advantage of video technology to capture and transmit the multiple facets and intricacies of life science research. Visualization greatly facilitates the understanding and efficient reproduction of both basic and complex experimental techniques, thereby addressing two of the biggest challenges faced by today's life science research community: i) low transparency and poor reproducibility of biological experiments and ii) time and labor-intensive nature of learning new experimental techniques. ( http://www.jove.com/ )

By examining the journal content, we generate a set of categories that can be considered as indicators of relevance and significance in terms of epistemic practices of science that have relevance for science education. For example, the quote above illustrates how scientists view some norms of scientific practice including the norms of “transparency” and “reproducibility” of experimental methods and results, and how the visual format of the journal facilitates the implementation of these norms. “Reproducibility” can be considered as an epistemic criterion that sits at the heart of what counts as an experimental procedure in science:

Investigating what should be reproducible and by whom leads to different types of experimental reproducibility, which can be observed to play different roles in experimental practice. A successful application of the strategy of reproducing an experiment is an achievement that may depend on certain isiosyncratic aspects of a local situation. Yet a purely local experiment that cannot be carried out by other experimenters and in other experimental contexts will, in the end be unproductive in science. (Sarkar and Pfeifer 2006 , p.270)

We now turn to an article on “Elevated Plus Maze for Mice” that is available for free on the journal website ( http://www.jove.com/video/1088/elevated-plus-maze-for-mice ). The purpose of this experiment was to investigate anxiety levels in mice through behavioral analysis. The journal article consists of a 9-min video accompanied by text. The video illustrates the handling of the mice in soundproof location with less light, worksheets with characteristics of mice, computer software, apparatus, resources, setting up the computer software, and the video recording of mouse behavior on the computer. The authors describe the apparatus that is used in the experiment and state how procedural differences exist between research groups that lead to difficulties in the interpretation of results:

The apparatus consists of open arms and closed arms, crossed in the middle perpendicularly to each other, and a center area. Mice are given access to all of the arms and are allowed to move freely between them. The number of entries into the open arms and the time spent in the open arms are used as indices of open space-induced anxiety in mice. Unfortunately, the procedural differences that exist between laboratories make it difficult to duplicate and compare results among laboratories.

The authors’ emphasis on the particularity of procedural context echoes in the observations of some philosophers of science:

It is not just the knowledge of experimental objects and phenomena but also their actual existence and occurrence that prove to be dependent on specific, productive interventions by the experimenters” (Sarkar and Pfeifer 2006 , pp. 270-271)

The inclusion of a video of the experimental procedure specifies what the apparatus looks like (Fig.  4 ) and how the behavior of the mice is captured through video recording that feeds into a computer (Fig.  5 ). Subsequently, a computer software which captures different variables such as the distance traveled, the number of entries, and the time spent on each arm of the apparatus. Here, there is visual information at different levels of representation ranging from reconfiguration of raw video data to representations that analyze the data around the variables in question (Fig.  6 ). The practice of levels of visual representations is not particular to the biological sciences. For instance, they are commonplace in nanotechnological practices:

Visual illustration of apparatus

Video processing of experimental set-up

Computer software for video input and variable recording

In the visualization processes, instruments are needed that can register the nanoscale and provide raw data, which needs to be transformed into images. Some Imaging Techniques have software incorporated already where this transformation automatically takes place, providing raw images. Raw data must be translated through the use of Graphic Software and software is also used for the further manipulation of images to highlight what is of interest to capture the (inferred) phenomena -- and to capture the reader. There are two levels of choice: Scientists have to choose which imaging technique and embedded software to use for the job at hand, and they will then have to follow the structure of the software. Within such software, there are explicit choices for the scientists, e.g. about colour coding, and ways of sharpening images. (Ruivenkamp and Rip 2010 , pp.14–15)

On the text that accompanies the video, the authors highlight the role of visualization in their experiment:

Visualization of the protocol will promote better understanding of the details of the entire experimental procedure, allowing for standardization of the protocols used in different laboratories and comparisons of the behavioral phenotypes of various strains of mutant mice assessed using this test.

The software that takes the video data and transforms it into various representations allows the researchers to collect data on mouse behavior more reliably. For instance, the distance traveled across the arms of the apparatus or the time spent on each arm would have been difficult to observe and record precisely. A further aspect to note is how the visualization of the experiment facilitates control of bias. The authors illustrate how the olfactory bias between experimental procedures carried on mice in sequence is avoided by cleaning the equipment.

Our discussion highlights the role of visualization in science, particularly with respect to presenting visualization as part of the scientific practices. We have used case studies from the history of science highlighting a scientist’s account of how visualization played a role in the discovery of DNA and the magnetic field and from a contemporary illustration of a science journal’s practices in incorporating visualization as a way to communicate new findings and methodologies. Our implicit aim in drawing from these case studies was the need to align science education with scientific practices, particularly in terms of how visual representations, stable or dynamic, can engage students in the processes of science and not only to be used as tools for cognitive development in science. Our approach was guided by the notion of “knowledge-as-practice” as advanced by Knorr Cetina ( 1999 ) who studied scientists and characterized their knowledge as practice, a characterization which shifts focus away from ideas inside scientists’ minds to practices that are cultural and deeply contextualized within fields of science. She suggests that people working together can be examined as epistemic cultures whose collective knowledge exists as practice.

It is important to stress, however, that visual representations are not used in isolation, but are supported by other types of evidence as well, or other theories (i.e., in order to understand the helical form of DNA, or the structure, chemistry knowledge was needed). More importantly, this finding can also have implications when teaching science as argument (e.g., Erduran and Jimenez-Aleixandre 2008 ), since the verbal evidence used in the science classroom to maintain an argument could be supported by visual evidence (either a model, representation, image, graph, etc.). For example, in a group of students discussing the outcomes of an introduced species in an ecosystem, pictures of the species and the ecosystem over time, and videos showing the changes in the ecosystem, and the special characteristics of the different species could serve as visual evidence to help the students support their arguments (Evagorou et al. 2012 ). Therefore, an important implication for the teaching of science is the use of visual representations as evidence in the science curriculum as part of knowledge production. Even though studies in the area of science education have focused on the use of models and modeling as a way to support students in the learning of science (Dori et al. 2003 ; Lehrer and Schauble 2012 ; Mendonça and Justi 2013 ; Papaevripidou et al. 2007 ) or on the use of images (i.e., Korfiatis et al. 2003 ), with the term using visuals as evidence, we refer to the collection of all forms of visuals and the processes involved.

Another aspect that was identified through the case studies is that of the visual reasoning (an integral part of Faraday’s investigations). Both the verbalization and visualization were part of the process of generating new knowledge (Gooding 2006 ). Even today, most of the textbooks use the lines of force (or just field lines) as a geometrical representation of field, and the number of field lines is connected to the quantity of flux. Often, the textbooks use the same kind of visual imagery than in what is used by scientists. However, when using images, only certain aspects or features of the phenomena or data are captured or highlighted, and often in tacit ways. Especially in textbooks, the process of producing the image is not presented and instead only the product—image—is left. This could easily lead to an idea of images (i.e., photos, graphs, visual model) being just representations of knowledge and, in the worse case, misinterpreted representations of knowledge as the results of Pocovi and Finlay ( 2002 ) in case of electric field lines show. In order to avoid this, the teachers should be able to explain how the images are produced (what features of phenomena or data the images captures, on what ground the features are chosen to that image, and what features are omitted); in this way, the role of visualization in knowledge production can be made “visible” to students by engaging them in the process of visualization.

The implication of these norms for science teaching and learning is numerous. The classroom contexts can model the generation, sharing and evaluation of evidence, and experimental procedures carried out by students, thereby promoting not only some contemporary cultural norms in scientific practice but also enabling the learning of criteria, standards, and heuristics that scientists use in making decisions on scientific methods. As we have demonstrated with the three case studies, visual representations are part of the process of knowledge growth and communication in science, as demonstrated with two examples from the history of science and an example from current scientific practices. Additionally, visual information, especially with the use of technology is a part of students’ everyday lives. Therefore, we suggest making use of students’ knowledge and technological skills (i.e., how to produce their own videos showing their experimental method or how to identify or provide appropriate visual evidence for a given topic), in order to teach them the aspects of the nature of science that are often neglected both in the history of science and the design of curriculum. Specifically, what we suggest in this paper is that students should actively engage in visualization processes in order to appreciate the diverse nature of doing science and engage in authentic scientific practices.

However, as a word of caution, we need to distinguish the products and processes involved in visualization practices in science:

If one considers scientific representations and the ways in which they can foster or thwart our understanding, it is clear that a mere object approach, which would devote all attention to the representation as a free-standing product of scientific labor, is inadequate. What is needed is a process approach: each visual representation should be linked with its context of production (Pauwels 2006 , p.21).

The aforementioned suggests that the emphasis in visualization should shift from cognitive understanding—using the products of science to understand the content—to engaging in the processes of visualization. Therefore, an implication for the teaching of science includes designing curriculum materials and learning environments that create a social and epistemic context and invite students to engage in the practice of visualization as evidence, reasoning, experimental procedure, or a means of communication (as presented in the three case studies) and reflect on these practices (Ryu et al. 2015 ).

Finally, a question that arises from including visualization in science education, as well as from including scientific practices in science education is whether teachers themselves are prepared to include them as part of their teaching (Bybee 2014 ). Teacher preparation programs and teacher education have been critiqued, studied, and rethought since the time they emerged (Cochran-Smith 2004 ). Despite the years of history in teacher training and teacher education, the debate about initial teacher training and its content still pertains in our community and in policy circles (Cochran-Smith 2004 ; Conway et al. 2009 ). In the last decades, the debate has shifted from a behavioral view of learning and teaching to a learning problem—focusing on that way not only on teachers’ knowledge, skills, and beliefs but also on making the connection of the aforementioned with how and if pupils learn (Cochran-Smith 2004 ). The Science Education in Europe report recommended that “Good quality teachers, with up-to-date knowledge and skills, are the foundation of any system of formal science education” (Osborne and Dillon 2008 , p.9).

However, questions such as what should be the emphasis on pre-service and in-service science teacher training, especially with the new emphasis on scientific practices, still remain unanswered. As Bybee ( 2014 ) argues, starting from the new emphasis on scientific practices in the NGSS, we should consider teacher preparation programs “that would provide undergraduates opportunities to learn the science content and practices in contexts that would be aligned with their future work as teachers” (p.218). Therefore, engaging pre- and in-service teachers in visualization as a scientific practice should be one of the purposes of teacher preparation programs.

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Evagorou, M., Erduran, S. & Mäntylä, T. The role of visual representations in scientific practices: from conceptual understanding and knowledge generation to ‘seeing’ how science works. IJ STEM Ed 2 , 11 (2015). https://doi.org/10.1186/s40594-015-0024-x

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• Visual representations
• Epistemic practices
• Science learning

What is visual representation?

In the vast landscape of communication, where words alone may fall short, visual representation emerges as a powerful ally. In a world inundated with information, the ability to convey complex ideas, emotions, and data through visual means is becoming increasingly crucial. But what exactly is visual representation, and why does it hold such sway in our understanding?

Defining Visual Representation:

Visual representation is the act of conveying information, ideas, or concepts through visual elements such as images, charts, graphs, maps, and other graphical forms. It’s a means of translating the abstract into the tangible, providing a visual language that transcends the limitations of words alone.

The Power of Images:

The adage “a picture is worth a thousand words” encapsulates the essence of visual representation. Images have an unparalleled ability to evoke emotions, tell stories, and communicate complex ideas in an instant. Whether it’s a photograph capturing a poignant moment or an infographic distilling intricate data, images possess a unique capacity to resonate with and engage the viewer on a visceral level.

Facilitating Understanding:

One of the primary functions of visual representation is to enhance understanding. Humans are inherently visual creatures, and we often process and retain visual information more effectively than text. Complex concepts that might be challenging to grasp through written explanations can be simplified and clarified through visual aids. This is particularly valuable in fields such as science, where intricate processes and structures can be elucidated through diagrams and illustrations.

Visual representation also plays a crucial role in education. In classrooms around the world, teachers leverage visual aids to facilitate learning, making lessons more engaging and accessible. From simple charts that break down historical timelines to interactive simulations that bring scientific principles to life, visual representation is a cornerstone of effective pedagogy.

Data Visualization:

In an era dominated by big data, the importance of data visualization cannot be overstated. Raw numbers and statistics can be overwhelming and abstract, but when presented visually, they transform into meaningful insights. Graphs, charts, and maps are powerful tools for conveying trends, patterns, and correlations, enabling decision-makers to glean actionable intelligence from vast datasets.

Consider the impact of a well-crafted infographic that distills complex research findings into a visually digestible format. Data visualization not only simplifies information but also allows for more informed decision-making in fields ranging from business and healthcare to social sciences and environmental studies.

Cultural and Artistic Expression:

Visual representation extends beyond the realm of information and education; it is also a potent form of cultural and artistic expression. Paintings, sculptures, photographs, and other visual arts serve as mediums through which individuals can convey their emotions, perspectives, and cultural narratives. Artistic visual representation has the power to transcend language barriers, fostering a shared human experience that resonates universally.

Conclusion:

In a world inundated with information, visual representation stands as a beacon of clarity and understanding. Whether it’s simplifying complex concepts, conveying data-driven insights, or expressing the depth of human emotion, visual elements enrich our communication in ways that words alone cannot. As we navigate an increasingly visual society, recognizing and harnessing the power of visual representation is not just a skill but a necessity for effective communication and comprehension. So, let us embrace the visual language that surrounds us, unlocking a deeper, more nuanced understanding of the world.

• Review article
• Open access
• Published: 11 July 2018

Decision making with visualizations: a cognitive framework across disciplines

• Lace M. Padilla   ORCID: orcid.org/0000-0001-9251-5279 1 , 2 ,
• Sarah H. Creem-Regehr 2 ,
• Mary Hegarty 3 &
• Jeanine K. Stefanucci 2  

Cognitive Research: Principles and Implications volume  3 , Article number:  29 ( 2018 ) Cite this article

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Visualizations—visual representations of information, depicted in graphics—are studied by researchers in numerous ways, ranging from the study of the basic principles of creating visualizations, to the cognitive processes underlying their use, as well as how visualizations communicate complex information (such as in medical risk or spatial patterns). However, findings from different domains are rarely shared across domains though there may be domain-general principles underlying visualizations and their use. The limited cross-domain communication may be due to a lack of a unifying cognitive framework. This review aims to address this gap by proposing an integrative model that is grounded in models of visualization comprehension and a dual-process account of decision making. We review empirical studies of decision making with static two-dimensional visualizations motivated by a wide range of research goals and find significant direct and indirect support for a dual-process account of decision making with visualizations. Consistent with a dual-process model, the first type of visualization decision mechanism produces fast, easy, and computationally light decisions with visualizations. The second facilitates slower, more contemplative, and effortful decisions with visualizations. We illustrate the utility of a dual-process account of decision making with visualizations using four cross-domain findings that may constitute universal visualization principles. Further, we offer guidance for future research, including novel areas of exploration and practical recommendations for visualization designers based on cognitive theory and empirical findings.

Significance

People use visualizations to make large-scale decisions, such as whether to evacuate a town before a hurricane strike, and more personal decisions, such as which medical treatment to undergo. Given their widespread use and social impact, researchers in many domains, including cognitive psychology, information visualization, and medical decision making, study how we make decisions with visualizations. Even though researchers continue to develop a wealth of knowledge on decision making with visualizations, there are obstacles for scientists interested in integrating findings from other domains—including the lack of a cognitive model that accurately describes decision making with visualizations. Research that does not capitalize on all relevant findings progresses slower, lacks generalizability, and may miss novel solutions and insights. Considering the importance and impact of decisions made with visualizations, it is critical that researchers have the resources to utilize cross-domain findings on this topic. This review provides a cognitive model of decision making with visualizations that can be used to synthesize multiple approaches to visualization research. Further, it offers practical recommendations for visualization designers based on the reviewed studies while deepening our understanding of the cognitive processes involved when making decisions with visualizations.

Introduction

Every day we make numerous decisions with the aid of visualizations , including selecting a driving route, deciding whether to undergo a medical treatment, and comparing figures in a research paper. Visualizations are external visual representations that are systematically related to the information that they represent (Bertin, 1983 ; Stenning & Oberlander, 1995 ). The information represented might be about objects, events, or more abstract information (Hegarty, 2011 ). The scope of the previously mentioned examples illustrates the diversity of disciplines that have a vested interest in the influence of visualizations on decision making. While the term decision has a range of meanings in everyday language, here decision making is defined as a choice between two or more competing courses of action (Balleine, 2007 ).

We argue that for visualizations to be most effective, researchers need to integrate decision-making frameworks into visualization cognition research. Reviews of decision making with visual-spatial uncertainty also agree there has been a general lack of emphasis on mental processes within the visualization decision-making literature (Kinkeldey, MacEachren, Riveiro, & Schiewe, 2017 ; Kinkeldey, MacEachren, & Schiewe, 2014 ). The framework that has dominated applied decision-making research for the last 30 years is a dual-process account of decision making. Dual-process theories propose that we have two types of decision processes: one for automatic, easy decisions (Type 1); and another for more contemplative decisions (Type 2) (Kahneman & Frederick, 2002 ; Stanovich, 1999 ). Footnote 1 Even though many research areas involving higher-level cognition have made significant efforts to incorporate dual-process theories (Evans, 2008 ), visualization research has yet to directly test the application of current decision-making frameworks or develop an effective cognitive model for decision making with visualizations. The goal of this work is to integrate a dual-process account of decision making with established cognitive frameworks of visualization comprehension.

In this paper, we present an overview of current decision-making theories and existing visualization cognition frameworks, followed by a proposal for an integrated model of decision making with visualizations, and a selective review of visualization decision-making studies to determine if there is cross-domain support for a dual-process account of decision making with visualizations. As a preview, we will illustrate Type 1 and 2 processing in decision making with visualizations using four cross-domain findings that we observed in the literature review. Our focus here is on demonstrating how dual-processing can be a useful framework for examining visualization decision-making research. We selected the cross-domain findings as relevant demonstrations of Type 1 and 2 processing that were shared across the studies reviewed, but they do not represent all possible examples of dual-processing in visualization decision-making research. The review documents each of the cross-domain findings, in turn, using examples from studies in multiple domains. These cross-domain findings differ in their reliance on Type 1 and Type 2 processing. We conclude with recommendations for future work and implications for visualization designers.

Decision-making frameworks

Decision-making researchers have pursued two dominant research paths to study how humans make decisions under risk. The first assumes that humans make rational decisions, which are based on weighted and ordered probability functions and can be mathematically modeled (e.g. Kunz, 2004 ; Von Neumann, 1953 ). The second proposes that people often make intuitive decisions using heuristics (Gigerenzer, Todd, & ABC Research Group, 2000 ; Kahneman & Tversky, 1982 ). While there is fervent disagreement on the efficacy of heuristics and whether human behavior is rational (Vranas, 2000 ), there is more consensus that we can make both intuitive and strategic decisions (Epstein, Pacini, Denes-Raj, & Heier, 1996 ; Evans, 2008 ; Evans & Stanovich, 2013 ; cf. Keren & Schul, 2009 ). The capacity to make intuitive and strategic decisions is described by a dual-process account of decision making, which suggests that humans make fast, easy, and computationally light decisions (known as Type 1 processing) by default, but can also make slow, contemplative, and effortful decisions by employing Type 2 processing (Kahneman, 2011 ). Various versions of dual-processing theory exist, with the key distinctions being in the attributes associated with each type of process (for a more detailed review of dual-process theories, see Evans & Stanovich, 2013 ). For example, older dual-systems accounts of decision making suggest that each process is associated with specific cognitive or neurological systems. In contrast, dual-process (sometimes termed dual-type) theories propose that the processes are distinct but do not necessarily occur in separate cognitive or neurological systems (hence the use of process over system) (Evans & Stanovich, 2013 ).

Many applied domains have adapted a dual-processing model to explain task- and domain-specific decisions, with varying degrees of success (Evans, 2008 ). For example, when a physician is deciding if a patient should be assigned to a coronary care unit or a regular nursing bed, the doctor can use a heuristic or utilize heart disease predictive instruments to make the decision (Marewski & Gigerenzer, 2012 ). In the case of the heuristic, the doctor would employ a few simple rules (diagrammed in Fig.  1 ) that would guide her decision, such as considering the patient’s chief complaint being chest pain. Another approach is to apply deliberate mental effort to make a more time-consuming and effortful decision, which could include using heart disease predictive instruments (Marewski & Gigerenzer, 2012 ). In a review of how applied domains in higher-level cognition have implemented a dual-processing model for domain-specific decisions, Evans ( 2008 ) argues that prior work has conflicting accounts of Type 1 and 2 processing. Some studies suggest that the two types work in parallel while others reveal conflicts between the Types (Sloman, 2002 ). In the physician example proposed by Marewski and Gigerenzer ( 2012 ), the two types are not mutually exclusive, as doctors can utilize Type 2 to make a more thoughtful decision that is also influenced by some rules of thumb or Type 1. In sum, Evans ( 2008 ) argues that due to the inconsistency of classifying Type 1 and 2, the distinction between only two types is likely an oversimplification. Evans ( 2008 ) suggests that the literature only consistently supports the identification of processes that require a capacity-limited, working memory resource versus those that do not. Evans and Stanovich ( 2013 ) updated their definition based on new behavioral and neuroscience evidence stating, “the defining characteristic of Type 1 processes is their autonomy. They do not require ‘controlled attention,’ which is another way of saying that they make minimal demands on working memory resources” (p. 236). There is also debate on how to define the term working memory (Cowan, 2017 ). In line with prior work on decision making with visualizations (Patterson et al., 2014 ), we adopt the definition that working memory consists of multiple components that maintain a limited amount of information (their capacity) for a finite period (Cowan, 2017 ). Contemporary theories of working memory also stress the ability to engage attention in a controlled manner to suppress automatic responses and maintain the most task-relevant information with limited capacity (Engle, Kane, & Tuholski, 1999 ; Kane, Bleckley, Conway, & Engle, 2001 ; Shipstead, Harrison, & Engle, 2015 ).

Coronary care unit decision tree, which illustrates a sequence of rules that a doctor could use to guide treatment decisions. Redrawn from “Heuristic decision making in medicine” by J. Marewski, and G. Gigerenzer 2012, Dialogues in clinical neuroscience, 14(1) , 77. ST-segment change refers to if certain anomaly appears in the patient’s electrocardiogram. NTG nitroglycerin, MI myocardial infarction, T T-waves with peaking or inversion

Identifying processes that require significant working memory provides a definition of Type 2 processing with observable neural correlates. Therefore, in line with Evans and Stanovich ( 2013 ), in the remainder of this manuscript, we will use significant working memory capacity demands and significant need for cognitive control, as defined above, as the criterion for Type 2 processing. In the context of visualization decision making, processes that require significant working memory are those that depend on the deliberate application of working memory to function. Type 1 processing occurs outside of users’ conscious awareness and may utilize small amounts of working memory but does not rely on conscious processing in working memory to drive the process. It should be noted that Type 1 and 2 processing are not mutually exclusive and many real-world decisions likely incorporate all processes. This review will attempt to identify tasks in visualization decision making that require significant working memory and capacity (Type 2 processing) and those that rely more heavily on Type 1 processing, as a first step to combining decision theory with visualization cognition.

Visualization cognition

Visualization cognition is a subset of visuospatial reasoning, which involves deriving meaning from external representations of visual information that maintain consistent spatial relations (Tversky, 2005 ). Broadly, two distinct approaches delineate visualization cognition models (Shah, Freedman, & Vekiri, 2005 ). The first approach refers to perceptually focused frameworks which attempt to specify the processes involved in perceiving visual information in displays and make predictions about the speed and efficiency of acquiring information from a visualization (e.g. Hollands & Spence, 1992 ; Lohse, 1993 ; Meyer, 2000 ; Simkin & Hastie, 1987 ). The second approach considers the influence of prior knowledge as well as perception. For example, Cognitive Fit Theory (Vessey, 1991), suggests that the user compares a learned graphic convention (mental schema) to the visual depiction. Visualizations that do not match the mental schema require cognitive transformations to make the visualization and mental representation align. For example, Fig.  2 illustrates a fictional relationship between the population growth of Species X and a predator species. At first glance, it may appear that when the predator species was introduced that the population of Species X dropped. However, after careful observation, you may notice that the higher population values are located lower on the Y-axis, which does not match our mental schema for graphs. With some effort, you can mentally reorder the values on the Y-axis to match your mental schema and then you may notice that the introduction of the predator species actually correlates with growth in the population of Species X. When the viewer is forced to mentally transform the visualization to match their mental schema, processing steps are increased, which may increase errors, time to complete a task, and demand on working memory (Vessey, 1991).

Fictional relationship between the population growth of Species X and a predator species, where the Y-axis ordering does not match standard graphic conventions. Notice that the y-axis is reverse ordered. This figure was inspired by a controversial graphic produced by Christine Chan of Reuters, which showed the relationship between Florida’s “Stand Your Ground” law and firearm murders with the Y-axis reversed ordered (Lallanilla, 2014 )

Pinker ( 1990 ) proposed a cognitive model (see Fig.  3 ), which provides an integrative structure that denotes the distinction between top-down and bottom-up encoding mechanisms in understanding data graphs. Researchers have generalized this model to propose theories of comprehension, learning, and memory with visual information (Hegarty, 2011 ; Kriz & Hegarty, 2007 ; Shah & Freedman, 2011 ). The Pinker ( 1990 ) model suggests that from the visual array , defined as the unprocessed neuronal firing in response to visualizations, bottom-up encoding mechanisms are utilized to construct a visual description , which is the mental encoding of the visual stimulus. Following encoding, viewers mentally search long-term memory for knowledge relevant for interpreting the visualization. This knowledge is proposed to be in the form of a graph schema.

Adapted figure from the Pinker ( 1990 ) model of visualization comprehension, which illustrates each process

Then viewers use a match process, where the graph schema that is the most similar to the visual array is retrieved. When a matching graph schema is found, the schema becomes instantiated . The visualization conventions associated with the graph schema can then help the viewer interpret the visualization ( message assembly process). For example, Fig. 3 illustrates comprehension of a bar chart using the Pinker ( 1990 ) model. In this example, the matched graph schema for a bar graph specifies that the dependent variable is on the Y-axis and the independent variable is on the X-axis; the instantiated graph schema incorporates the visual description and this additional information. The conceptual message is the resulting mental representation of the visualization that includes all supplemental information from long-term memory and any mental transformations the viewer may perform on the visualization. Viewers may need to transform their mental representation of the visualization based on their task or conceptual question . In this example, the viewer’s task is to find the average of A and B. To do this, the viewer must interpolate information in the bar chart and update the conceptual message with this additional information. The conceptual question can guide the construction of the mental representation through interrogation , which is the process of seeking out information that is necessary to answer the conceptual question. Top-down encoding mechanisms can influence each of the processes.

The influences of top-down processes are also emphasized in a previous attempt by Patterson et al. ( 2014 ) to extend visualization cognition theories to decision making. The Patterson et al. ( 2014 ) model illustrates how top-down cognitive processing influences encoding, pattern recognition, and working memory, but not decision making or the response. Patterson et al. ( 2014 ) use the multicomponent definition of working memory, proposed by Baddeley and Hitch ( 1974 ) and summarized by Cowan ( 2017 ) as a “multicomponent system that holds information temporarily and mediates its use in ongoing mental activities” (p. 1160). In this conception of working memory, a central executive controls the functions of working memory. The central executive can, among other functions, control attention and hold information in a visuo-spatial temporary store , which is where information can be maintained temporally for decision making without being stored in long-term memory (Baddeley & Hitch, 1974 ).

While incorporating working memory into a visualization decision-making model is valuable, the Patterson et al. ( 2014 ) model leaves some open questions about relationships between components and processes. For example, their model lacks a pathway for working memory to influence decisions based on top-down processing, which is inconsistent with well-established research in decision science (e.g. Gigerenzer & Todd, 1999; Kahneman & Tversky, 1982 ). Additionally, the normal processing pathway, depicted in the Patterson model, is an oversimplification of the interaction between top-down and bottom-up processing that is documented in a large body of literature (e.g. Engel, Fries, & Singer, 2001 ; Mechelli, Price, Friston, & Ishai, 2004 ).

A proposed integrated model of decision making with visualizations

Our proposed model (Fig.  4 ) introduces a dual-process account of decision making (Evans & Stanovich, 2013 ; Gigerenzer & Gaissmaier, 2011 ; Kahneman, 2011 ) into the Pinker ( 1990 ) model of visualization comprehension. A primary addition of our model is the inclusion of working memory, which is utilized to answer the conceptual question and could have a subsequent impact on each stage of the decision-making process, except bottom-up attention. The final stage of our model includes a decision-making process that derives from the conceptual message and informs behavior. In line with a dual-process account (Evans & Stanovich, 2013 ; Gigerenzer & Gaissmaier, 2011 ; Kahneman, 2011 ), the decision step can either be completed with Type 1 processing, which only uses minimal working memory (Evans & Stanovich, 2013 ) or recruit significant working memory, constituting Type 2 processing. Also following Evans and Stanovich ( 2013 ), we argue that people can make a decision with a visualization while using minimal amounts of working memory. We classify this as Type 1 thinking. Lohse ( 1997 ) found that when participants made judgments about budget allocation using profit charts, individuals with less working memory capacity performed equally well compared to those with more working memory capacity, when they only made decisions about three regions (easier task). However, when participants made judgments about nine regions (harder task), individuals with more working memory capacity outperformed those with less working memory capacity. The results of the study reveal that individual differences in working memory capacity only influence performance on complex decision-making tasks (Lohse, 1997 ). Figure  5 (top) illustrates one way that a viewer could make a Type 1 decision about whether the average value of bars A and B is closer to 2 or 2.2. Figure 5 (top) illustrates how a viewer might make a fast and computationally light decision in which she decides that the middle point between the two bars is closer to the salient tick mark of 2 on the Y-axis and answers 2 (which is incorrect). In contrast, Fig.  5 (bottom) shows a second possible method of solving the same problem by utilizing significant working memory (Type 2 processing). In this example, the viewer has recently learned a strategy to address similar problems, uses working memory to guide a top-down attentional search of the visual array, and identifies the values of A and B. Next, she instantiates a different graph schema than in the prior example by utilizing working memory and completes an effortful mental computation of 2.4 + 1.9/2. Ultimately, the application of working memory leads to a different and more effortful decision than in Fig. 5 (top). This example illustrates how significant amounts of working memory can be used at early stages of the decision-making process and produce downstream effects and more considered responses. In the following sections, we provide a selective review of work on decision making with visualizations that demonstrates direct and indirect evidence for our proposed model.

Model of visualization decision making, which emphasizes the influence of working memory. Long-term memory can influence all components and processes in the model either via pre-attentive processes or by conscious application of knowledge

Examples of a fast Type 1 (top) and slow Type 2 (bottom) decision outlined in our proposed model of decision making with visualizations. In these examples, the viewer’s task is to decide if the average value of bars A and B are closer to 2 or 2.2. The thick dotted line denotes significant working memory and the thin dotted line negligible working memory

Empirical studies of visualization decision making

Review method.

To determine if there is cross-domain empirical support for a dual-process account of decision making with visualizations, we selectively reviewed studies of complex decision making with computer-generated two-dimensional (2D) static visualizations. To illustrate the application of a dual-process account of decision making to visualization research, this review highlights representative studies from diverse application areas. Interdisciplinary groups conducted many of these studies and, as such, it is not accurate to classify the studies in a single discipline. However, to help the reader evaluate the cross-domain nature of these findings, Table  1 includes the application area for the specific tasks used in each study.

In reviewing this work, we observed four key cross-domain findings that support a dual-process account of decision making (see Table  2 ). The first two support the inclusion of Type 1 processing, which is illustrated by the direct path for bottom-up attention to guide decision making with the minimal application of working memory (see Fig. 5 top). The first finding is that visualizations direct viewers’ bottom-up attention , which can both help and hinder decision making (see “ Bottom-up attention ”). The second finding is that visual-spatial biases comprise a unique category of bias that is a direct result of the visual encoding technique (see “ Visual-Spatial Biases ”). The third finding supports the inclusion of Type 2 processing in our proposed model and suggests that visualizations vary in cognitive fit between the visual description, graph schema, and conceptual question. If the fit is poor (i.e. there is a mismatch between the visualization and a decision-making component), working memory is used to perform corrective mental transformations (see “ Cognitive fit ”). The final cross-domain finding proposes that knowledge-driven processes may interact with the effects of the visual encoding technique (see “ Knowledge-driven processing ”) and could be a function of either Type 1 or 2 processes. Each of these findings will be detailed at length in the relevant sections. The four cross-domain findings do not represent an exhaustive list of all cross-domain findings that pertain to visualization cognition. However, these were selected as illustrative examples of Type 1 and 2 processing that include significant contributions from multiple domains. Further, some of the studies could fit into multiple sections and were included in a particular section as illustrative examples.

Bottom-up attention

The first cross-domain finding that characterizes Type 1 processing in visualization decision making is that visualizations direct participants’ bottom-up attention to specific visual features, which can be either beneficial or detrimental to decision making. Bottom-up attention consists of involuntary shifts in focus to salient features of a visualization and does not utilize working memory (Connor, Egeth, & Yantis, 2004 ), therefore it is a Type 1 process. The research reviewed in this section illustrates that bottom-up attention has a profound influence on decision making with visualizations. A summary of visual features that studies have used to attract bottom-up attention can be found in Table  3 .

Numerous studies show that salient information in a visualization draws viewers’ attention (Fabrikant, Hespanha, & Hegarty, 2010 ; Hegarty, Canham, & Fabrikant, 2010 ; Hegarty, Friedman, Boone, & Barrett, 2016 ; Padilla, Ruginski, & Creem-Regehr, 2017 ; Schirillo & Stone, 2005 ; Stone et al., 2003 ; Stone, Yates, & Parker, 1997 ). The most common methods for demonstrating that visualizations focus viewers’ attention is by showing that viewers miss non-salient but task-relevant information (Schirillo & Stone, 2005 ; Stone et al., 1997 ; Stone et al., 2003 ), viewers are biased by salient information (Hegarty et al., 2016 ; Padilla, Ruginski et al., 2017 ) or viewers spend more time looking at salient information in a visualization (Fabrikant et al., 2010 ; Hegarty et al., 2010 ). For example, Stone et al. ( 1997 ) demonstrated that when viewers are asked how much they would pay for an improved product using the visualizations in Fig.  6 , they focus on the number of icons while missing the base rate of 5,000,000. If a viewer simply totals the icons, the standard product appears to be twice as dangerous as the improved product, but because the base rate is large, the actual difference between the two products is insignificantly small (0.0000003; Stone et al., 1997 ). In one experiment, participants were willing to pay $125 more for improved tires when viewing the visualizations in Fig. 6 compared to a purely textual representation of the information. The authors also demonstrated the same effect for improved toothpaste, with participants paying $0.95 more when viewing a visual depiction compared to text. The authors’ term this heuristic of focusing on salient information and ignoring other data the foreground effect (Stone et al., 1997 ) (see also Schirillo & Stone, 2005 ; Stone et al., 2003 ).

Icon arrays used to illustrate the risk of standard or improved tires. Participants were tasked with deciding how much they would pay for the improved tires. Note the base rate of 5 M drivers was represented in text. Redrawn from “Effects of numerical and graphical displays on professed risk-taking behavior” by E. R. Stone, J. F. Yates, & A. M. Parker. 1997, Journal of Experimental Psychology: Applied , 3 (4), 243

A more direct test of visualizations guiding bottom-up attention is to examine if salient information biases viewers’ judgments. One method involves identifying salient features using a behaviorally validated saliency model, which predicts the locations that will attract viewers’ bottom-up attention (Harel, 2015 ; Itti, Koch, & Niebur, 1998 ; Rosenholtz & Jin, 2005 ). In one study, researchers compared participants’ judgments with different hurricane forecast visualizations and then, using the Itti et al. ( 1998 ) saliency algorithm, found that the differences in what was salient in the two visualizations correlated with participants’ performance (Padilla, Ruginski et al., 2017 ). Specifically, they suggested that the salient borders of the Cone of Uncertainty (see Fig.  7 , left), which is used by the National Hurricane Center to display hurricane track forecasts, leads some people to incorrectly believe that the hurricane is growing in physical size, which is a misunderstanding of the probability distribution of hurricane paths that the cone is intended to represent (Padilla, Ruginski et al., 2017 ; see also Ruginski et al., 2016 ). Further, they found that when the same data were represented as individual hurricane paths, such that there was no salient boundary (see Fig. 7 , right), viewers intuited the probability of hurricane paths more effectively than the Cone of Uncertainty. However, an individual hurricane path biased viewers’ judgments if it intersected a point of interest. For example, in Fig. 7 (right), participants accurately judged that locations closer to the densely populated lines (highest likelihood of storm path) would receive more damage. This correct judgment changed when a location farther from the center of the storm was intersected by a path, but the closer location was not (see locations a and b in Fig. 7 right). With both visualizations, the researchers found that viewers were negatively biased by the salient features for some tasks (Padilla, Ruginski et al., 2017 ; Ruginski et al., 2016 ).

An example of the Cone of Uncertainty ( left ) and the same data represented as hurricane paths ( right ). Participants were tasked with evaluating the level of damage that would incur to offshore oil rigs at specific locations, based on the hurricane forecast visualization. Redrawn from “Effects of ensemble and summary displays on interpretations of geospatial uncertainty data” by L. M. Padilla, I. Ruginski, and S. H. Creem-Regehr. 2017, Cognitive Research: Principles and Implications , 2 (1), 40

That is not to say that saliency only negatively impacts decisions. When incorporated into visualization design, saliency can guide bottom-up attention to task-relevant information, thereby improving performance (e.g. Fabrikant et al., 2010 ; Fagerlin, Wang, & Ubel, 2005 ; Hegarty et al., 2010 ; Schirillo & Stone, 2005 ; Stone et al., 2003 ; Waters, Weinstein, Colditz, & Emmons, 2007 ). One compelling example using both eye-tracking measures and a saliency algorithm demonstrated that salient features of weather maps directed viewers’ attention to different variables that were visualized on the maps (Hegarty et al., 2010 ) (see also Fabrikant et al., 2010 ). Interestingly, when the researchers manipulated the relative salience of temperature versus pressure (see Fig.  8 ), the salient features captured viewers’ overt attention (as measured by eye fixations) but did not influence performance, until participants were trained on how to effectively interpret the features. Once viewers were trained, their judgments were facilitated when the relevant features were more salient (Hegarty et al., 2010 ). This is an instructive example of how saliency may direct viewers’ bottom-up attention but may not influence their performance until viewers have the relevant top-down knowledge to capitalize on the affordances of the visualization.

Eye-tracking data from Hegarty et al. ( 2010 ). Participants viewed an arrow located in Utah (obscured by eye-tracking data in the figure) and made judgments about whether the arrow correctly identified the wind direction. The black isobars were the task-relevant information. Notice that after instructions, viewers with the pressure-salient visualizations focused on the isobars surrounding Utah, rather than on the legend or in other regions. The panels correspond to the conditions in the original study

In sum, the reviewed studies suggest that bottom-up attention has a profound influence on decision making with visualizations. This is noteworthy because bottom-up attention is a Type 1 process. At a minimum, the work suggests that Type 1 processing influences the first stages of decision making with visualizations. Further, the studies cited in this section provide support for the inclusion of bottom-up attention in our proposed model.

• Visual-spatial biases

A second cross-domain finding that relates to Type 1 processing is that visualizations can give rise to visual-spatial biases that can be either beneficial or detrimental to decision making. We are proposing the new concept of visual-spatial biases and defining this term as a bias that elicits heuristics, which are a direct result of the visual encoding technique. Visual-spatial biases likely originate as a Type 1 process as we suspect they are connected to bottom-up attention, and if detrimental to decision making, have to be actively suppressed by top-down knowledge and cognitive control mechanisms (see Table  4 for summary of biases documented in this section). Visual-spatial biases can also improve decision-making performance. As Card, Mackinlay, and Shneiderman ( 1999 ) point out, we can use vision to think , meaning that visualizations can capitalize on visual perception to interpret a visualization without effort when the visual biases elucidated by the visualization are consistent with the correct interpretation.

Tversky ( 2011 ) presents a taxonomy of visual-spatial communications that are intrinsically related to thought, which are likely the bases for visual-spatial biases (see also Fabrikant & Skupin, 2005 ). One of the most commonly documented visual-spatial biases that we observed across domains is a containment conceptualization of boundary representations in visualizations. Tversky ( 2011 ) makes the analogy, “Framing a picture is a way of saying that what is inside the picture has a different status from what is outside the picture” (p. 522). Similarly, Fabrikant and Skupin ( 2005 ) describe how, “They [boundaries] help partition an information space into zones of relative semantic homogeneity” (p. 673). However, in visualization design, it is common to take continuous data and visually represent them with boundaries (i.e. summary statistics, error bars, isocontours, or regions of interest; Padilla et al., 2015 ; Padilla, Quinan, Meyer, & Creem-Regehr, 2017 ). Binning continuous data is a reasonable approach, particularly when intended to make the data simpler for viewers to understand (Padilla, Quinan, et al., 2017 ). However, it may have the unintended consequence of creating artificial boundaries that can bias users—leading them to respond as if data within a containment is more similar than data across boundaries. For example, McKenzie, Hegarty, Barrett, and Goodchild ( 2016 ) showed that participants were more likely to use a containment heuristic to make decisions about Google Map’s blue dot visualization when the positional uncertainty data were visualized as a bounded circle (Fig.  9 right) compared to a Gaussian fade (Fig. 9 left) (see also Newman & Scholl, 2012 ; Ruginski et al., 2016 ). Recent work by Grounds, Joslyn, and Otsuka ( 2017 ) found that viewers demonstrate a “deterministic construal error” or the belief that visualizations of temperature uncertainty represent a deterministic forecast. However, the deterministic construal error was not observed with textual representations of the same data (see also Joslyn & LeClerc, 2013 ).

Example stimuli from McKenzie et al. ( 2016 ) showing circular semi-transparent overlays used by Google Maps to indicate the uncertainty of the users’ location. Participants compared two versions of these visualizations and determined which represented the most accurate positional location. Redrawn from “Assessing the effectiveness of different visualizations for judgments of positional uncertainty” by G. McKenzie, M. Hegarty, T. Barrett, and M. Goodchild. 2016, International Journal of Geographical Information Science , 30 (2), 221–239

Additionally, some visual-spatial biases follow the same principles as more well-known decision-making biases revealed by researchers in behavioral economics and decision science. In fact, some decision-making biases, such as anchoring , the tendency to use the first data point to make relative judgments, seem to have visual correlates (Belia, Fidler, Williams, & Cumming, 2005 ). For example, Belia et al. ( 2005 ) asked experts with experience in statistics to align two means (representing “Group 1” and “Group 2”) with error bars so that they represented data ranges that were just significantly different (see Fig.  10 for example of stimuli). They found that when the starting position of Group 2 was around 800 ms, participants placed Group 2 higher than when the starting position for Group 2 was at around 300 ms. This work demonstrates that participants used the starting mean of Group 2 as an anchor or starting point of reference, even though the starting position was arbitrary. Other work finds that visualizations can be used to reduce some decision-making biases including anecdotal evidence bias (Fagerlin et al., 2005 ), side effect aversion (Waters et al., 2007 ; Waters, Weinstein, Colditz, & Emmons, 2006 ), and risk aversion (Schirillo & Stone, 2005 ).

Example display and instructions from Belia et al. ( 2005 ). Redrawn from “Researchers misunderstand confidence intervals and standard error bars” by S. Belia, F. Fidler, J. Williams, and G. Cumming. 2005, Psychological Methods, 10 (4), 390. Copyright 2005 by “American Psychological Association”

Additionally, the mere presence of a visualization may inherently bias viewers. For example, viewers find scientific articles with high-quality neuroimaging figures to have greater scientific reasoning than the same article with a bar chart or without a figure (McCabe & Castel, 2008 ). People tend to unconsciously believe that high-quality scientific images reflect high-quality science—as illustrated by work from Keehner, Mayberry, and Fischer ( 2011 ) showing that viewers rate articles with three-dimensional brain images as more scientific than those with 2D images, schematic drawings, or diagrams (See Fig.  11 ). Unintuitively, however, high-quality complex images can be detrimental to performance compared to simpler visualizations (Hegarty, Smallman, & Stull, 2012 ; St. John, Cowen, Smallman, & Oonk, 2001 ; Wilkening & Fabrikant, 2011 ). Hegarty et al. ( 2012 ) demonstrated that novice users prefer realistically depicted maps (see Fig.  12 ), even though these maps increased the time taken to complete the task and focused participants’ attention on irrelevant information (Ancker, Senathirajah, Kukafka, & Starren, 2006 ; Brügger, Fabrikant, & Çöltekin, 2017 ; St. John et al., 2001 ; Wainer, Hambleton, & Meara, 1999 ; Wilkening & Fabrikant, 2011 ). Interestingly, professional meteorologists also demonstrated the same biases as novice viewers (Hegarty et al., 2012 ) (see also Nadav-Greenberg, Joslyn, & Taing, 2008 ).

Image showing participants’ ratings of three-dimensionality and scientific credibility for a given neuroimaging visualization, originally published in grayscale (Keehner et al., 2011 )

Example stimuli from Hegarty et al. ( 2012 ) showing maps with varying levels of realism. Both novice viewers and meteorologists were tasked with selecting a visualization to use and performing a geospatial task. The panels correspond to the conditions in the original study

We argue that visual-spatial biases reflect a Type 1 process, occurring automatically with minimal working memory. Work by Sanchez and Wiley ( 2006 ) provides direct evidence for this assertion using eye-tracking data to demonstrate that individuals with less working memory capacity attend to irrelevant images in a scientific article more than those with greater working memory capacity. The authors argue that we are naturally drawn to images (particularly high-quality depictions) and that significant working memory capacity is required to shift focus away from images that are task-irrelevant. The ease by which visualizations captivate our focus and direct our bottom-up attention to specific features likely increases the impact of these biases, which may be why some visual-spatial biases are notoriously difficult to override using working memory capacity (see Belia et al., 2005 ; Boone, Gunalp, & Hegarty, in press ; Joslyn & LeClerc, 2013 ; Newman & Scholl, 2012 ). We speculate that some visual-spatial biases are intertwined with bottom-up attention—occurring early in the decision-making process and influencing the down-stream processes (see our model in Fig. 4 for reference), making them particularly unremitting.

Cognitive fit

We also observe a cross-domain finding involving Type 2 processing, which suggests that if there is a mismatch between the visualization and a decision-making component, working memory is used to perform corrective mental transformations. Cognitive fit is a term used to describe the correspondence between the visualization and conceptual question or task (see our model for reference; for an overview of cognitive fit, see Vessey, Zhang, & Galletta, 2006 ). Those interested in examining cognitive fit generally attempt to identify and reduce mismatches between the visualization and one of the decision-making components (see Table  5 for a breakdown of the decision-making components that the reviewed studies evaluated). When there is a mismatch produced by the default Type 1 processing, it is argued that significant working memory (Type 2 processing) is required to resolve the discrepancy via mental transformations (Vessey et al., 2006 ). As working memory is capacity limited, the magnitude of mental transformation or amount of working memory required is one predictor of reaction times and errors.

Direct evidence for this claim comes from work demonstrating that cognitive fit differentially influenced the performance of individuals with more and less working memory capacity (Zhu & Watts, 2010 ). The task was to identify which two nodes in a social media network diagram should be removed to disconnect the maximal number of nodes. As predicted by cognitive fit theory, when the visualization did not facilitate the task (Fig.  13 left), participants with less working memory capacity were slower than those with more working memory capacity. However, when the visualization aligned with the task (Fig.  13 right), there was no difference in performance. This work suggests that when there is misalignment between the visualization and a decision-making process, people with more working memory capacity have the resources to resolve the conflict, while those with less resources show performance degradations. Footnote 2 Other work only found a modest relationship between working memory capacity and correct interpretations of high and low temperature forecast visualizations (Grounds et al., 2017 ), which suggests that, for some visualizations, viewers utilize little working memory.

Examples of social media network diagrams from Zhu and Watts ( 2010 ). The authors argue that the figure on the right is more aligned with the task of identifying the most interconnected nodes than the figure on the left

As illustrated in our model, working memory can be recruited to aid all stages of the decision-making process except bottom-up attention. Work that examines cognitive fit theory provides indirect evidence that working memory is required to resolve conflicts in the schema matching and a decision-making component. For example, one way that a mismatch between a viewer’s mental schema and visualization can arise is when the viewer uses a schema that is not optimal for the task. Tversky, Corter, Yu, Mason, and Nickerson ( 2012 ) primed participants to use different schemas by describing the connections in Fig.  14 in terms of either transfer speed or security levels. Participants then decided on the most efficient or secure route for information to travel between computer nodes with either a visualization that encoded data using the thickness of connections, containment, or physical distance (see Fig.  14 ). Tversky et al. ( 2012 ) found that when the links were described based on their information transfer speed, thickness and distance visualizations were the most effective—suggesting that the speed mental schema was most closely matched to the thickness and distance visualizations, whereas the speed schema required mental transformations to align with the containment visualization. Similarly, the thickness and containment visualizations outperformed the distance visualization when the nodes were described as belonging to specific systems with different security levels. This work and others (Feeney, Hola, Liversedge, Findlay, & Metcalf, 2000 ; Gattis & Holyoak, 1996 ; Joslyn & LeClerc, 2013 ; Smelcer & Carmel, 1997 ) provides indirect evidence that gratuitous realignment between mental schema and the visualization can be error-prone and visualization designers should work to reduce the number of transformations required in the decision-making process.

Example of stimuli from Tversky et al. ( 2012 ) showing three types of encoding techniques for connections between nodes (thickness, containment, and distance). Participants were asked to select routes between nodes with different descriptions of the visualizations. Redrawn from “Representing category and continuum: Visualizing thought” by B. Tversky, J. Corter, L. Yu, D. Mason, and J. Nickerson. In Diagrams 2012 (p. 27), P. Cox, P. Rodgers, and B. Plimmer (Eds.), 2012, Berlin Heidelberg: Springer-Verlag

Researchers from multiple domains have also documented cases of misalignment between the task, or conceptual question, and the visualization. For example, Vessey and Galletta ( 1991 ) found that participants completed a financial-based task faster when the visualization they chose (graph or table, see Fig.  15 ) matched the task (spatial or textual). For the spatial task, participants decided which month had the greatest difference between deposits and withdrawals. The textual or symbolic tasks involved reporting specific deposit and withdrawal amounts for various months. The authors argued that when there is a mismatch between the task and visualization, the additional transformation accounts for the increased time taken to complete the task (Vessey & Galletta, 1991 ) (see also Dennis & Carte, 1998 ; Huang et al., 2006 ), which likely takes place in the inference process of our proposed model.

Examples of stimuli from Vessey and Galletta ( 1991 ) depicting deposits and withdraw amounts over the course of a year with a graph ( a ) and table ( b ). Participants completed either a spatial or textual task with the chart or table. Redrawn from “Cognitive fit: An empirical study of information acquisition” by I. Vessey, and D. Galletta. 1991, Information systems research, 2 (1), 72–73. Copyright 1991 by “INFORMS”

The aforementioned studies provide direct (Zhu & Watts, 2010 ) and indirect (Dennis & Carte, 1998 ; Feeney et al., 2000 ; Gattis & Holyoak, 1996 ; Huang et al., 2006 ; Joslyn & LeClerc, 2013 ; Smelcer & Carmel, 1997 ; Tversky et al., 2012 ; Vessey & Galletta, 1991 ) evidence that Type 2 processing recruits working memory to resolve misalignment between decision-making processes and the visualization that arise from default Type 1 processing. These examples of Type 2 processing using working memory to perform effortful mental computations are consistent with the assertions of Evans and Stanovich ( 2013 ) that Type 2 processes enact goal directed complex processing. However, it is not clear from the reviewed work how exactly the visualization and decision-making components are matched. Newman and Scholl ( 2012 ) propose that we match the schema and visualization based on the similarities between the salient visual features, although this proposal has not been tested. Further, work that assesses cognitive fit in terms of the visualization and task only examines the alignment of broad categories (i.e., spatial or semantic). Beyond these broad classifications, it is not clear how to predict if a task and visualization are aligned. In sum, there is not a sufficient cross-disciplinary theory for how mental schemas and tasks are matched to visualizations. However, it is apparent from the reviewed work that Type 2 processes (requiring working memory) can be recruited during the schema matching and inference processes.

Either type 1 and/or 2

Knowledge-driven processing.

In a review of map-reading cognition, Lobben ( 2004 ) states, “…research should focus not only on the needs of the map reader but also on their map-reading skills and abilities” (p. 271). In line with this statement, the final cross-domain finding is that the effects of knowledge can interact with the affordances or biases inherent in the visualization method. Knowledge may be held temporally in working memory (Type 2), held in long-term knowledge but effortfully used (Type 2), or held in long-term knowledge but automatically applied (Type 1). As a result, knowledge-driven processing can involve either Type 1 or Type 2 processes.

Both short- and long-term knowledge can influence visualization affordances and biases. However, it is difficult to distinguish whether Type 2 processing is using significant working memory capacity to temporarily hold knowledge or if participants have stored the relevant knowledge in long-term memory and processing is more automatic. Complicating the issue, knowledge stored in long-term memory can influence decision making with visualizations using both Type 1 and 2 processing. For example, if you try to remember Pythagorean’s Theorem, which you may have learned in high school or middle school, you may recall that a 2  + b 2  = c 2 , where c represents the length of the hypotenuse and a and b represent the lengths of the other two sides of a triangle. Unless you use geometry regularly, you likely had to strenuously search in long-term memory for the equation, which is a Type 2 process and requires significant working memory capacity. In contrast, if you are asked to recall your childhood phone number, the number might automatically come to mind with minimal working memory required (Type 1 processing).

In this section, we highlight cases where knowledge either influenced decision making with visualizations or was present but did not influence decisions (see Table  6 for the type of knowledge examined in each study). These studies are organized based on how much time the viewers had to incorporate the knowledge (i.e. short-term instructions and long-term individual differences in abilities and expertise), which may be indicative of where the knowledge is stored. However, many factors other than time influence the process of transferring knowledge by working memory capacity to long-term knowledge. Therefore, each of the studies cited in this section could be either Type 1, Type 2, or both types of processing.

One example of participants using short-term knowledge to override a familiarity bias comes from work by Bailey, Carswell, Grant, and Basham ( 2007 ) (see also Shen, Carswell, Santhanam, & Bailey, 2012 ). In a complex geospatial task for which participants made judgments about terrorism threats, participants were more likely to select familiar map-like visualizations rather than ones that would be optimal for the task (see Fig.  16 ) (Bailey et al., 2007 ). Using the same task and visualizations, Shen et al. ( 2012 ) showed that users were more likely to choose an efficacious visualization when given training concerning the importance of cognitive fit and effective visualization techniques. In this case, viewers were able to use knowledge-driven processing to improve their performance. However, Joslyn and LeClerc ( 2013 ) found that when participants viewed temperature uncertainty, visualized as error bars around a mean temperature prediction, they incorrectly believed that the error bars represented high and low temperatures. Surprisingly, participants maintained this belief despite a key, which detailed the correct way to interpret each temperature forecast (see also Boone et al., in press ). The authors speculated that the error bars might have matched viewers’ mental schema for high- and low-temperature forecasts (stored in long-term memory) and they incorrectly utilized the high-/low-temperature schema rather than incorporating new information from the key. Additionally, the authors propose that because the error bars were visually represented as discrete values, that viewers may have had difficulty reimagining the error bars as points on a distribution, which they term a deterministic construal error (Joslyn & LeClerc, 2013 ). Deterministic construal visual-spatial biases may also be one of the sources of misunderstanding of the Cone of Uncertainty (Padilla, Ruginski et al., 2017 ; Ruginski et al., 2016 ). A notable difference between these studies and the work of Shen et al. ( 2012 ) is that Shen et al. ( 2012 ) used instructions to correct a familiarity bias, which is a cognitive bias originally documented in the decision-making literature that is not based on the visual elements in the display. In contrast, the biases in Joslyn and LeClerc ( 2013 ) were visual-spatial biases. This provides further evidence that visual-spatial biases may be a unique category of biases that warrant dedicated exploration, as they are harder to influence with knowledge-driven processing.

Example of different types of view orientations used by examined by Bailey et al. ( 2007 ). Participants selected one of these visualizations and then used their selection to make judgments including identifying safe passageways, determining appropriate locations for firefighters, and identifying suspicious locations based on the height of buildings. The panels correspond to the conditions in the original study

Regarding longer-term knowledge, there is substantial evidence that individual differences in knowledge impact decision making with visualizations. For example, numerous studies document the benefit of visualizations for individuals with less health literacy, graph literacy, and numeracy (Galesic & Garcia-Retamero, 2011 ; Galesic, Garcia-Retamero, & Gigerenzer, 2009 ; Keller, Siegrist, & Visschers, 2009 ; Okan, Galesic, & Garcia-Retamero, 2015 ; Okan, Garcia-Retamero, Cokely, & Maldonado, 2012 ; Okan, Garcia-Retamero, Galesic, & Cokely, 2012 ; Reyna, Nelson, Han, & Dieckmann, 2009 ; Rodríguez et al., 2013 ). Visual depictions of health data are particularly useful because health data often take the form of probabilities, which are unintuitive. Visualizations inherently illustrate probabilities (i.e. 10%) as natural frequencies (i.e. 10 out of 100), which are more intuitive (Hoffrage & Gigerenzer, 1998 ). Further, by depicting natural frequencies visually (see example in Fig.  17 ), viewers can make perceptual comparisons rather than mathematical calculations. This dual benefit is likely the reason visualizations produce facilitation for individuals with less health literacy, graph literacy, and numeracy.

Example of stimuli used by Galesic et al. ( 2009 ) in a study demonstrating that natural frequency visualizations can help individuals overcome less numeracy. Participants completed three medical scenario tasks using similar visualizations as depicted here, in which they were asked about the effects of aspirin on risk of stroke or heart attack and about a hypothetical new drug. Redrawn from “Using icon arrays to communicate medical risks: overcoming less numeracy” by M. Galesic, R. Garcia-Retamero, and G. Gigerenzer. 2009, Health Psychology, 28 (2), 210

These studies are good examples of how designers can create visualizations that capitalize on Type 1 processing to help viewers accurately make decisions with complex data even when they lack relevant knowledge. Based on the reviewed work, we speculate that well-designed visualizations that utilize Type 1 processing to intuitively illustrate task-relevant relationships in the data may be particularly beneficial for individuals with less numeracy and graph literacy, even for simple tasks. However, poorly designed visualizations that require superfluous mental transformations may be detrimental to the same individuals. Further, individual differences in expertise, such as graph literacy, which have received more attention in healthcare communication (Galesic & Garcia-Retamero, 2011 ; Nayak et al., 2016 ; Okan et al., 2015 ; Okan, Garcia-Retamero, Cokely, & Maldonado, 2012 ; Okan, Garcia-Retamero, Galesic, & Cokely, 2012 ; Rodríguez et al., 2013 ), may play a large role in how viewers complete even simple tasks in other domains such as map-reading (Kinkeldey et al., 2017 ).

Less consistent are findings on how more experienced users incorporate knowledge acquired over longer periods of time to make decisions with visualizations. Some research finds that students’ decision-making and spatial abilities improved during a semester-long course on Geographic Information Science (GIS) (Lee & Bednarz, 2009 ). Other work finds that experts perform the same as novices (Riveiro, 2016 ), experts can exhibit visual-spatial biases (St. John et al., 2001 ) and experts perform more poorly than expected in their domain of visual expertise (Belia et al., 2005 ). This inconsistency may be due in part to the difficulty in identifying when and if more experienced viewers are automatically applying their knowledge or employing working memory. For example, it is unclear if the students in the GIS course documented by Lee and Bednarz ( 2009 ) developed automatic responses (Type 1) or if they learned the information and used working memory capacity to apply their training (Type 2).

Cheong et al. ( 2016 ) offer one way to gauge how performance may change when one is forced to use Type 1 processing, but then allowed to use Type 2 processing. In a wildfire task using multiple depictions of uncertainty (see Fig.  18 ), Cheong et al. ( 2016 ) found that the type of uncertainty visualization mattered when participants had to make fast Type 1 decisions (5 s) about evacuating from a wildfire. But when given sufficient time to make Type 2 decisions (30 s), participants were not influenced by the visualization technique (see also Wilkening & Fabrikant, 2011 ).

Example of multiple uncertainty visualization techniques for wildfire risk by Cheong et al. ( 2016 ). Participants were presented with a house location (indicated by an X), and asked if they would stay or leave based on one of the wildfire hazard communication techniques shown here. The panels correspond to the conditions in the original study

Interesting future work could limit experts’ time to complete a task (forcing Type 1 processing) and then determine if their judgments change when given more time to complete the task (allowing for Type 2 processing). To test this possibility further, a dual-task paradigm could be used such that experts’ working memory capacity is depleted by a difficult secondary task that also required working memory capacity. Some examples of secondary tasks in a dual-task paradigm include span tasks that require participants to remember or follow patterns of information, while completing the primary task, then report the remembered or relevant information from the pattern (for a full description of theoretical bases for a dual-task paradigm see Pashler, 1994 ). To our knowledge, only one study has used a dual-task paradigm to evaluate cognitive load of a visualization decision-making task (Bandlow et al., 2011 ). However, a growing body of research on other domains, such as wayfinding and spatial cognition, demonstrates the utility of using dual-task paradigms to understand the types of working memory that users employ for a task (Caffò, Picucci, Di Masi, & Bosco, 2011 ; Meilinger, Knauff, & Bülthoff, 2008 ; Ratliff & Newcombe, 2005 ; Trueswell & Papafragou, 2010 ).

Span tasks are examples of spatial or verbal secondary tasks, which include remembering the orientations of an arrow (taxes visual-spatial memory, (Shah & Miyake, 1996 ) or counting backward by 3 s (taxes verbal processing and short-term memory) (Castro, Strayer, Matzke, & Heathcote, 2018 ). One should expect more interference if the primary and secondary tasks recruit the same processes (i.e. visual-spatial primary task paired with a visual-spatial memory span task). An example of such an experimental design is illustrated in Fig.  19 . In the dual-task trial illustrated in Fig.  19 , if participants responses are as fast and accurate as the baseline trial then participants are likely not using significant amounts of working memory capacity for that task. If the task does require significant working memory capacity, then the inclusion of the secondary task should increase the time taken to complete the primary task and potentially produce errors in both the secondary and primary tasks. In visualization decision-making research, this is an open area of exploration for researchers and designers that are interested in understanding how working memory capacity and a dual-process account of decision making applies to their visualizations and application domains.

A diagram of a dual-tasking experiment is shown using the same task as in Fig. 5 . Responses resulting from Type 1 and 2 processing are illustrated. The dual-task trial illustrates how to place additional load on working memory capacity by having the participant perform a demanding secondary task. The impact of the secondary task is illustrated for both time and accuracy. Long-term memory can influence all components and processes in the model either via pre-attentive processes or by conscious application of knowledge

In sum, this section documents cases where knowledge-driven processing does and does not influence decision making with visualizations. Notably, we describe numerous studies where well-designed visualizations (capitalizing on Type 1 processing) focus viewers’ attention on task-relevant relationships in the data, which improves decision accuracy for individuals with less developed health literacy, graph literacy, and numeracy. However, the current work does not test how knowledge-driven processing maps on to the dual-process model of decision making. Knowledge may be held temporally by working memory capacity (Type 2), held in long-term knowledge but strenuously utilized (Type 2), or held in long-term knowledge but automatically applied (Type 1). More work is needed to understand if a dual-process account of decision making accurately describes the influence of knowledge-driven processing on decision making with visualizations. Finally, we detailed an example of a dual-task paradigm as one way to evaluate if viewers are employing Type 1 processing.

Review summary

Throughout this review, we have provided significant direct and indirect evidence that a dual-process account of decision making effectively describes prior findings from numerous domains interested in visualization decision making. The reviewed work provides support for specific processes in our proposed model including the influences of working memory, bottom-up attention, schema matching, inference processes, and decision making. Further, we identified key commonalities in the reviewed work relating to Type 1 and Type 2 processing, which we added to our proposed visualization decision-making model. The first is that utilizing Type 1 processing, visualizations serve to direct participants’ bottom-up attention to specific information, which can be either beneficial or detrimental for decision making (Fabrikant et al., 2010 ; Fagerlin et al., 2005 ; Hegarty et al., 2010 ; Hegarty et al., 2016 ; Padilla, Ruginski et al., 2017 ; Ruginski et al., 2016 ; Schirillo & Stone, 2005 ; Stone et al., 1997 ; Stone et al., 2003 ; Waters et al., 2007 ). Consistent with assertions from cognitive science and scientific visualization (Munzner, 2014 ), we propose that visualization designers should identify the critical information needed for a task and use a visual encoding technique that directs participants’ attention to this information. We encourage visualization designers who are interested in determining which elements in their visualizations will likely attract viewers’ bottom-up attention, to see the Itti et al. ( 1998 ) saliency model, which has been validated with eye-tracking measures (for implementation of this model along with Matlab code see Padilla, Ruginski et al., 2017 ). If deliberate effort is not made to capitalize on Type 1 processing by focusing the viewer’s attention on task-relevant information, then the viewer will likely focus on distractors via Type 1 processing, resulting in poor decision outcomes.

A second cross-domain finding is the introduction of a new concept, visual-spatial biases , which can also be both beneficial and detrimental to decision making. We define this term as a bias that elicits heuristics, which is a direct result of the visual encoding technique. We provide numerous examples of visual-spatial biases across domains (for implementation of this model along with Matlab code, see Padilla, Ruginski et al., 2017 ). The novel utility of identifying visual-spatial biases is that they potentially arise early in the decision-making process during bottom-up attention, thus influencing the entire downstream process, whereas standard heuristics do not exclusively occur at the first stage of decision making. This possibly accounts for the fact that visual-spatial biases have proven difficult to overcome (Belia et al., 2005 ; Grounds et al., 2017 ; Joslyn & LeClerc, 2013 ; Liu et al., 2016 ; McKenzie et al., 2016 ; Newman & Scholl, 2012 ; Padilla, Ruginski et al., 2017 ; Ruginski et al., 2016 ). Work by Tversky ( 2011 ) presents a taxonomy of visual-spatial communications that are intrinsically related to thought, which are likely the bases for visual-spatial biases.

We have also revealed cross-domain findings involving Type 2 processing, which suggest that if there is a mismatch between the visualization and a decision-making component, working memory is used to perform corrective mental transformations. In scenarios where the visualization is aligned with the mental schema and task, performance is fast and accurate (Joslyn & LeClerc, 2013 ). The types of mismatches observed in the reviewed literature are likely both domain-specific and domain-general. For example, situations where viewers employ the correct graph schema for the visualization, but the graph schema does not align with the task, are likely domain-specific (Dennis & Carte, 1998 ; Frownfelter-Lohrke, 1998 ; Gattis & Holyoak, 1996 ; Huang et al., 2006 ; Joslyn & LeClerc, 2013 ; Smelcer & Carmel, 1997 ; Tversky et al., 2012 ). However, other work demonstrates cases where viewers employ a graph schema that does not match the visualization, which is likely domain-general (e.g. Feeney et al., 2000 ; Gattis & Holyoak, 1996 ; Tversky et al., 2012 ). In these cases, viewers could accidentally use the wrong graph schema because it appears to match the visualization or they might not have learned a relevant schema. The likelihood of viewers making attribution errors because they do not know the corresponding schema increases when the visualization is less common, such as with uncertainty visualizations. When there is a mismatch, additional working memory is required resulting in increased time taken to complete the task and in some cases errors (e.g. Joslyn & LeClerc, 2013 ; McKenzie et al., 2016 ; Padilla, Ruginski et al., 2017 ). Based on these findings, we recommend that visualization designers should aim to create visualizations that most closely align with a viewer’s mental schema and task. However, additional empirical research is required to understand the nature of the alignment processes, including the exact method we use to mentally select a schema and the classifications of tasks that match visualizations.

The final cross-domain finding is that knowledge-driven processes can interact or override effects of visualization methods. We find that short-term (Dennis & Carte, 1998 ; Feeney et al., 2000 ; Gattis & Holyoak, 1996 ; Joslyn & LeClerc, 2013 ; Smelcer & Carmel, 1997 ; Tversky et al., 2012 ) and long-term knowledge acquisition (Shen et al., 2012 ) can influence decision making with visualizations. However, there are also examples of knowledge having little influence on decisions, even when prior knowledge could be used to improve performance (Galesic et al., 2009 ; Galesic & Garcia-Retamero, 2011 ; Keller et al., 2009 ; Lee & Bednarz, 2009 ; Okan et al., 2015 ; Okan, Garcia-Retamero, Cokely, & Maldonado, 2012 ; Okan, Garcia-Retamero, Galesic, & Cokely, 2012 ; Reyna et al., 2009 ; Rodríguez et al., 2013 ). We point out that prior knowledge seems to have more of an effect on non-visual-spatial biases, such as a familiarity bias (Belia et al., 2005 ; Joslyn & LeClerc, 2013 ; Riveiro, 2016 ; St. John et al., 2001 ), which suggests that visual-spatial biases may be closely related to bottom-up attention. Further, it is unclear from the reviewed work when knowledge switches from relying on working memory capacity for application to automatic application. We argue that Type 1 and 2 processing have unique advantages and disadvantages for visualization decision making. Therefore, it is valuable to understand which process users are applying for specific tasks in order to make visualizations that elicit optimal performance. In the case of experts and long-term knowledge, we propose that one interesting way to test if users are utilizing significant working memory capacity is to employ a dual-task paradigm (illustrated in Fig.  19 ). A dual-task paradigm can be used to evaluate the amount of working memory required and compare the relative working memory required between competing visualization techniques.

We have also proposed a variety of practical recommendations for visualization designers based on the empirical findings and our cognitive framework. Below is a summary list of our recommendations along with relevant section numbers for reference:

Identify the critical information needed for a task and use a visual encoding technique that directs participants’ attention to this information (“ Bottom-up attention ” section);

To determine which elements in a visualization will likely attract viewers’ bottom-up attention try employing a saliency algorithm (see Padilla, Quinan, et al., 2017 ) (see “ Bottom-up attention ”);

Aim to create visualizations that most closely align with a viewer’s mental schema and task demands (see “ Visual-Spatial Biases ”);

Work to reduce the number of transformations required in the decision-making process (see " Cognitive fit ");

To understand if a viewer is using Type 1 or 2 processing employ a dual-task paradigm (see Fig.  19 );

Consider evaluating the impact of individual differences such as graphic literacy and numeracy on visualization decision making.

Conclusions

We use visual information to inform many important decisions. To develop visualizations that account for real-life decision making, we must understand how and why we come to conclusions with visual information. We propose a dual-process cognitive framework expanding on visualization comprehension theory that is supported by empirical studies to describe the process of decision making with visualizations. We offer practical recommendations for visualization designers that take into account human decision-making processes. Finally, we propose a new avenue of research focused on the influence of visual-spatial biases on decision making.

Change history

02 september 2018.

The original article (Padilla et al., 2018) contained a formatting error in Table 2; this has now been corrected with the appropriate boxes marked clearly.

Dual-process theory will be described in greater detail in next section.

It should be noted that in some cases the activation of Type 2 processing should improve decision accuracy. More research is needed that examines cases where Type 2 could improve decision performance with visualizations.

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LMP is a Ph.D. student at the University of Utah in the Cognitive Neural Science department. LMP is a member of the Visual Perception and Spatial Cognition Research Group directed by Sarah Creem-Regehr, Ph.D., Jeanine Stefanucci, Ph.D., and William Thompson, Ph.D. Her work focuses on graphical cognition, decision making with visualizations, and visual perception. She works on large interdisciplinary projects with visualization scientists and anthropologists.

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Padilla, L.M., Creem-Regehr, S.H., Hegarty, M. et al. Decision making with visualizations: a cognitive framework across disciplines. Cogn. Research 3 , 29 (2018). https://doi.org/10.1186/s41235-018-0120-9

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The development of growth references and growth charts

De Montbeillard produced the first growth chart in the late 18 th century. Since then, growth assessment has developed to become an essential component of child health practice.

To provide a brief history of i) anthropometry, i.e. growth measurements; ii) growth references, the statistical summary of anthropometry, and iii) growth charts, the visual representation of growth references for clinical use.

The major contributors in the three categories over the past 200 years were identified, and their historical contributions put in context with more recent developments.

Anthropometry was originally collected for administrative or public health purposes, its medical role emerging at the end of the 19 th century. Growth reference data were collected in earnest from the 19 th century, during which time the familiar summary statistics – mean, SD, centiles – were developed. More advanced statistical methods emerged much later. Growth charts first appeared in the late 19 th century, and Tanner and Whitehouse later popularised the concepts of velocity and conditional references for growth in puberty. The recent WHO growth standard has been adopted by many countries including the UK, where the UK-WHO charts have pioneered many design features to improve usability and accuracy.

Growth charts have come a long way in 200 years, and they represent an impressive synthesis of anthropometry, statistical summary and chart design.

Introduction

The idea of plotting a child’s body measurements on a chart to illustrate their pattern of growth is generally attributed to Count Philibert de Montbeillard (1720-1785), who plotted his son’s height every six months from birth to age 18 years, and George Buffon (1707-1788) then published the chart in his Histoire Naturelle, thus producing the first height growth curve ( Tanner 1962 ). A growth curve is a powerful graphical tool, as it displays both the size of the child at a series of ages, and at the same time their growth rate or growth velocity over time, based on the slope of the curve.

Since it first appearance in the 18 th century the use of the growth chart has expanded to include displaying the growth pattern of groups of children as well as individuals, and the chart has become an important tool in child health screening and paediatric clinical workup.

To describe the development of growth references and growth charts it is useful to start with some definitions. A growth reference is a statistical summary of anthropometry in a reference group of children, usually presented as the frequency distribution at different ages. The reference group is often representative of some geographic region at a particular time, e.g. Great Britain in 1990 ( Freeman et al. 1995 ). The statistical summary involves the mean and standard deviation or alternatively the median and selected centiles, conditioned (usually) on age and sex. Growth references describe how children grow, and the references can be applied to other children to establish whether or not their measurements are typical of the reference group. A growth standard is essentially the same as a growth reference except that the underlying reference sample is selected on health grounds. Thus it represents a healthy pattern of growth, and the standard shows how children ought to grow rather than how they do grow.

A growth chart is a growth reference presented as a visual display for clinical use, and in this sense it is a graphic design. Many aspects of the design can be varied to make the chart more or less effective as a clinical tool. A growth chart is also a ‘road to health’. Figure 1 is an example of a chart based on a growth reference, here the UK-WHO boys weight reference ( Wright et al. 2010 ), consisting of a series of nine centile curves. By plotting individuals on the chart their measurements can be expressed as centiles . The centile for an individual indicates his or her size, be it height, weight or body mass index etc. The centile indicates the distance they have travelled along the growth road up to that age. The growth chart quantifies size/distance in terms of the centile.

Furthermore, individuals whose growth curve tracks along the centiles over time are growing at average velocity , while if the curve crosses centiles up or down the individual is growing faster or slower than average – centile crossing is a measure of relative velocity. A growth chart visualises growth velocity, but it does not quantify it – centile crossing is uncalibrated. The combination of growth charts and growth references involves three distinct disciplines: the collection of anthropometry data, the statistical summary of the data, and the graphic design of the chart. The purpose of this paper is to sketch out developments in these three areas since the time of de Montbeillard.

Anthropometry

Anthropometry means the measurement of man. Hence it is a collective term for all the measurements that might appear on a growth chart, including most obviously height and weight (and ratio indices like body mass index – BMI), plus limb lengths and circumferences, skinfold thicknesses etc. Historically height has been the main focus, and James Tanner’s A History of the Study of Human Growth ( Tanner 1981 ) impressively documents its changing role over the centuries.

Prior to the 19 th century the main purpose of anthropometry was administrative, to identify, classify and screen individuals. For example, extensive documentation exists on the heights and weights of American slaves, which were useful as markers of their age, maturity and capacity for work, and hence value in the marketplace. Similarly army conscripts were routinely weighed and measured for screening to ensure a minimum level of fitness. Both sets of statistics have subsequently become useful for tracking the secular trend in height over time ( Cole 2003 ), see for example the 150 year trends in Dutch conscript height ( Van Wieringen 1972 ).

In the 19 th century there was increasing awareness of the inequalities in British society, highlighted by the excesses of child labour, and the subsequent debate led to the Factory Acts and the regulation of children’s working conditions. During this time, driven by campaigners like Villermé (1782-1863) and Edwin Chadwick (1800-1890), the discipline of auxological epidemiology developed, defined by Tanner as “the use of growth data to search out and later to define suboptimal conditions of health”. (Auxology is Tanner’s term for the study of human growth.)

This trend was reflected by the increasing numbers of anthropometry surveys of schoolchildren undertaken from the mid-19 th century onwards. Adolphe Quetelet (1796-1874) took the lead here, and was the first to investigate the statistical properties of anthropometry – discussed later. Charles Roberts (d. 1901) and Henry Bowditch (1840-1911) amassed large datasets of child anthropometry, and published them summarised in large tables.

Around the same time Francis Galton (1822-1911) was developing his ideas on eugenics, and he was keen to quantify physical differences between individuals and across families and generations. Anthropometry proved the ideal medium, particularly height with its strong hereditary component and its links to social class. Galton’s keenness to obtain data led him to set up an Anthropometric Laboratory at the 1884 International Health Exhibition in London, where the public could come and pay 3d (1p) to receive 17 measurements of sight, hearing, strength, speed, breathing capacity, arm-span, height and weight, summarised on a card. Some 9337 individuals obliged, including 2954 children. See Figure 3 for Galton’s own set of measurements, where his occupation is recorded as “private gentleman” ( Johnson et al. 1985 ). Galton’s interest in anthropometry differed from that of his contemporaries, or indeed anyone else preceding or following him. He wanted the data to test his ideas and to develop statistical concepts, which are described later.

The motivation for collecting anthropometry altered again around the turn of the 20 th century, when it was recognised that such measurements were useful for clinical assessment in the individual. This was the time when growth charts were first developed, both for weight in babies and height in children. In 1929 the Fels Growth Study was set up in the USA, the first of many such studies where anthropometry data were collected longitudinally over time, and the Fels continues to this day. In 1946 the UK National Study of Health and Development was initiated, the first of many such birth cohort studies, where individuals were recruited around the time of birth and followed up through life. Anthropometry was collected alongside other information, allowing the recent discipline of life course epidemiology to be developed. The 1946 Birth Cohort was followed by similar but larger cohorts in 1958, 1970, 2000 (the Millennium Cohort) and most recently the New Birth Cohort Study, which is planned to recruit in excess of 100,000 children. Many similar cohorts have been set up in other countries, so that the collection of anthropometry data for research purposes is now on a scale undreamt of at the time of de Montbeillard.

The growth reference that underlies the growth chart is a statistical summary of the anthropometry of the reference sample. The summary statistics that are now used routinely for this purpose, the mean, standard deviation and distribution centiles, have themselves emerged since the time of de Montbeillard.

The normal distribution

The concept of the normal distribution, or “the law of frequency of error” as it was then called, was developed quite independently by Carl Friedrich Gauss (1777-1855) in 1809 and Pierre Simon Laplace (1749-1827) in 1810. Its discovery allowed data from a group of individuals to be summarised by their mean and probable error * , so long as they followed a normal distribution. This was a major step forward in reducing large numbers of measurements to just two summary statistics.

One of the first people to apply it to anthropometry was Adolphe Quetelet (1796-1874), an influential and energetic Belgian statistician who among many other things helped to found the Royal Statistical Society in 1834 and of whom Florence Nightingale was a great admirer. He introduced the concept of l’homme moyen , the average man who was representative of a particular group in society ( Quetelet 1869 ). The status of this mean man was obtained from the mean and probable error of the group’s anthropometry, which he collected in many social surveys. His focus was on the mean and not the probable error, which he viewed as representing measurement error rather than true variability.

Galton’s percentile grades

Francis Galton was well aware of Quetelet’s work, and he also latched onto the summary value of the normal distribution, in papers such as his “Notes on the Marlborough School statistics” ( Galton 1874 ), which contained a table of the mean and probable error of height in annual age groups of boys from Marlborough School. However he was also aware of the need for the data to be normally distributed, and he recognised that this often did not apply. So it was that he introduced his concept of percentiles, which he claimed were “much simpler in conception, and of incomparably wider applicability” ( Galton 1875 ). They were based on the ogive or cumulative distribution function, as shown in Figure 4 . He described the ogive curve as follows, assuming 100 boys were arrayed against a wall in order of increasing height: “This line or curve would just touch the heads of all the 100 boys, and would give an exact, natural, and permanent record of the distribution of heights throughout the school.” ( Galton 1876 ). The mean and probable error of the distribution were simple to estimate from the median and quartiles. The percentiles were obtained as the 99 cut-points splitting the ogive into 100 sections or grades , so that the median corresponded to the 50 th percentile and the upper quartile to the 75 th percentile. In addition for normally distributed data the mean would equal the median, and the probable error would be the distance from the 50 th to the 75 th percentile.

At this point it’s worth discussing terminology. Galton chose to call his cut-points percentiles, yet nowadays they are often called centiles. Galton himself called them centiles in at least one of his papers, where the word “centiles” appears in the title and text ( Galton 1899 ). The Wikipedia entry for quantiles lists many terms like tertiles, quartiles, deciles etc, and the only ones whose names start with “per” are percentiles and permilliles (thousandths). So the case for using percentiles is not strong, and the preference here is to use centiles instead.

Centile spacing

To summarise the distribution of anthropometry on a chart one needs to display a subset of the available centiles. Generally the mean or median is provided along with a set of centiles symmetric about the median such as the 3 rd , 10 th and 25 th below and the 75 th , 90 th and 97 th above ( Tanner et al. 1966 ). The 5 th /95 th centiles are sometimes preferred to the 3 rd /97 th ( Hamill et al. 1977 ). Alternatively standard deviation spacings can be used, with zero SDs for the mean and −1, −2 and −3 SDs below and +1, +2 and +3 SDs above ( WHO Multicentre Growth Reference Study Group 2006 ). A compromise between the two formats is provided by Cole’s two-thirds SD spacing, where centiles spaced two-thirds of an SD apart correspond to the (approximate) 2.3 th , 9 th , 25 th , 50 th , 75 th , 91 st and 97.7 th centiles, i.e. close to the conventional set ( Cole 1994 ). Note that the nine centiles in Figure 1 are two-thirds SD spaced. In addition, for a normal distribution the distance between the median and 75 th centile, which corresponds to the probable error, is 0.6745 SDs, i.e. very close to two-thirds or 0.6667 SDs. In this sense the two-thirds SD spacing harks back to the beginning of summary statistics and the probable error.

Calculating centiles

The one remaining statistical issue is how to calculate the selected centiles for the measurement. This is most simply done by splitting the data into age groups, then sorting and counting the data in each group to obtain the centiles. (Nowadays there are several different ways of doing this, the quantile function in the statistical program R for example offering six alternatives ( R Development Core Team 2010 ).) Alternatively if the data are known to be normally distributed, the centiles can be calculated from the mean and probable error (or later, SD). These could then be plotted and a smooth curve drawn through the points using either a French curve or a lead spline.

But jump forward 100 years, to the end of the 20 th century when several new methods had become available, and it was hard to know which method to use. The World Health Organization, as part of its development of the WHO growth standard ( WHO Multicentre Growth Reference Study Group 2006 ) carried out a review of all available methods for constructing growth centiles ( Borghi et al. 2006 ), a total of 30 methods, and its recommendation was Generalized Additive Models for Location, Scale and Shape (GAMLSS) ( Rigby and Stasinopoulos 2005 ). This is a generalisation of an earlier technique called the LMS method ( Cole and Green 1992 ), which assumes that the measurement at each age can be transformed to a normal distribution using a Box-Cox transformation, and just three parameters, the Box-Cox power λ, the median μ, and the coefficient of variation σ, summarise the distribution. The three quantities are allowed to change smoothly with age, reflecting the changing underlying distribution, and the corresponding curves are called the L curve, M curve and S curve respectively. The M curve is the conventional median curve, the S curve shows the fractional SD as it changes with age, and the L curve indicates the age-changing skewness. Together they allow any centiles to be constructed, using the equation:

where z α is the normal equivalent deviate for the required centile, and the LMS values are over a series of ages. Inverting [1] allows a measurement X to be converted to an SD score (z-score):

where here the LMS values are for the child’s age and sex. Based on the reference population, the SD score has mean 0 and SD 1.

GAMLSS goes beyond the LMS method in several respects, but its main advantage over the LMS method is that it can adjust for kurtosis as well as skewness in the distribution. In the end the WHO growth standard was fitted without any adjustment for kurtosis, as its effect on the centiles was minimal, so that in practice the LMS method was used ( WHO 2006 ).

Thus in summary, normally distributed anthropometric data could be summarised by the mean and probable error (or later the SD). Non-normal data were summarised initially with Galton’s centiles and latterly by the LMS method, which effectively added a third skewness summary statistic to the mean and SD.

Growth chart development

The first growth chart.

Suppose we have anthropometry in a reference group of children over a range of ages. How exactly is this information to be presented on a chart? Henry Bowditch (1840-1911) set himself this task when describing the growth of Massachusetts children in 1891 ( Bowditch 1891 ). The information to be presented is in three parts: the age groups into which the data are split (e.g. 11 years, 12 years etc), the selected centiles (e.g. 3 rd , 10 th etc), and the measurement values (e.g. height) corresponding to the centiles in each age group.

These three quantities can be presented on a conventional graph as curves of one variable plotted against another, with separate curves for each category of the third variable. Bowditch’s report demonstrated three alternative layouts for the chart: the first was height plotted against centile for each age group, where each curve corresponded in shape to Galton’s ogive – see Figure 5A . The second was age versus centile for different height categories, which gives a series of falling curves showing how the centile for a given height falls with increasing age – Figure 5B . The third format, which is the one that has endured, was curves of height versus age for each centile, as shown in Figure 6 . This format had the advantage of allowing both the girls’ and boys’ curves to be displayed on the one chart.

Bowditch’s was an enormously significant publication, stimulated by the concept of Galton’s percentile grades, and his third alternative ( Figure 6 ) has stood the test of time to become the standard format of growth chart. Virtually all subsequent growth charts have adopted it, see for example the US NCHS 1977, British 1990 and WHO 2006 charts ( Freeman et al. 1995 , Hamill et al. 1977 , WHO Multicentre Growth Reference Study Group 2006 ). Its appeal is that the centile curves are broadly the same shape as growth curves, and like growth curves they display both distance (position) and velocity (slope) on the one chart.

For much of childhood individual growth curves tend to track along a particular centile, which encourages users to think that the chart is designed to monitor growth over time, hence the name growth chart. But remember that the chart was constructed from cross-sectional data - Bowditch had just one measurement per child - so it can measure distance as a centile, but it cannot measure velocity. It contains no information on whether a given rate of centile crossing is common or uncommon.

Charting growth velocity

To assess velocity a velocity growth chart needed to be invented, based on child measurements collected serially over time. The first velocity chart, published by Leona Bayer and Nancy Bayley ( Bayer and Bayley 1959 ), was designed to monitor height in puberty. The timing of puberty is very variable, with an SD of around 1 year, so that the growth curves of individuals with early and late puberty are very different in shape. Tanner used the term growth tempo for pubertal timing, where tempo is an important phenomenon reflecting the fact that individuals grow according to their developmental age not their chronological age. Thus in puberty the growth chart needs to be interpreted in the light of the individual’s tempo. The chart (see Figure 7 for girls) included an “increment curve” which showed the annual height velocity for children of average tempo, with a peak of 8 cm/year at 11.5 years.

The rest of the chart consists of high and low centiles labelled “accelerated case” and “retarded case”. But the labels are confusing as the curves lead to tall and short final heights respectively, and hence are just as much to do with differences in height as differences in tempo. There are also three median curves labelled “accelerated 1 S.D.”, “average rate of maturation” and “retarded 1 S.D.” respectively, all ending at the same final height but showing their height spurts at different ages. In current notation these correspond to curves for advanced, average and delayed tempo.

The chart also provided height scales both in cm and inch units. A good idea in principle, it was let down by the grid above and to the left of the curves being 5 cm spacing, while below and to the right the grid was 1 inch spacing – quite confusing to use.

Growth assessment in puberty

James Tanner worked with Nancy Bayley during the 1950s and developed his particular interest in pubertal growth during that time. He published his Growth at Adolescence in 1955, and later a greatly expanded 2 nd edition ( Tanner 1962 ). According to Google Scholar it has been cited some 6000 times. He soon followed this up with a major paper on the design of growth charts, published in two parts ( Tanner et al. 1966 ). Interestingly the paper’s title does not mention puberty, but its underlying theme is the impact of pubertal tempo on growth, and how the chart should address it.

At one level the paper is a simple tutorial in the development of distance and velocity references for height and weight. Height is treated as normally distributed, and its centiles by age are calculated from the mean and SD, both of which are tabulated with the centiles. For weight, which is recognised to be skew, there is no tabulated SD just the centiles including the median. These centiles, and corresponding ones for velocity references, are tabulated by age, sex and measurement in a series of no fewer than 18 tables.

But the key message is in the paper’s Figure 1 (see Figure 8 here), height velocity curves for five individuals whose timing of puberty varies. Figure 8A shows the curves plotted against chronological age, where age at peak velocity varies between 12 and 16 years, while in Figure 8B the curves are plotted relative to age at peak velocity and hence are synchronised. In each case the average of the curves appears as a dashed line, and in Figure 8A it is widened and flattened compared to the individual curves. In Figure 8B the phase shift has been removed, and the average curve is the same shape as the individual curves. This bias in the average curve attributable to the age shift was first demonstrated formally for a logistic function growth curve ( Merrell 1931 ), and more recently for a quite general growth function ( Cole et al. 2008 ).

The mean velocity curve in each case is the dashed line.

What it means is that distance curves based on cross-sectional measurements are less steep around the mean age of peak velocity than curves based on individual growth patterns. Tanner distinguishes between the two by calling them “cross-sectional” and “individual-type” curves. Figure 9 shows the contrast between them, two individual curves with relatively early and late peaks respectively ( Figure 9A ), and a smoothed individual-type curve ( Figure 9B ), superimposed on cross-sectional centiles. The curves show marked centile crossing around the time of the peak, so that the cross-sectional centiles give the misleading impression that the growth pattern is other than normal.

Tanner was keen to come up with a form of chart that minimised centile crossing in puberty, the aim being to optimise longitudinal growth assessment. To this end his paper included individual-type curves for height and weight during puberty, both for distance and for velocity, and Figure 10 shows a worked example for a healthy boy’s height from age 4 to adult. In terms of design these combined charts are a tour de force , though they are also complex for regular use. The cross-sectional (single time) centiles appear as lines, while the longitudinal (repeated visit) centiles are shaded. The velocity chart in particular highlights the difference between the two forms, with a narrow pointed longitudinal velocity curve and a wide flat cross-sectional velocity curve. Height is plotted against both chronological age and skeletal age, the latter providing an estimate of chronological age adjusted for puberty tempo.

The Tanner-Whitehouse charts proved to be extremely popular, with two revised versions appearing during the next twenty years ( Tanner and Whitehouse 1976 , Tanner and Davies 1985 ). But there were three problems with them that led people to explore other ways to assess growth in puberty. The first was that height velocity is hard to interpret in clinical practice. At the annual visit the doctor sees how fast the patient has grown in the previous year, and plots it on the velocity chart. But the clinical value of the chart is limited – it fails to highlight age at peak velocity until one or two years after it has happened, which is far too late for therapeutic intervention.

The second problem is that longitudinal centiles are designed to greatly reduce centile crossing, yet in fact individual growth curves still cross centiles up and down – see Figure 10 for example, where the child’s growth curve follows the cross-sectional centiles just as closely as the longitudinal centiles. So the advantage of the longitudinal centiles has been overstated. And the third problem is a shift in ethical attitudes since the 1960s, when skeletal age in children was routinely assessed with a hand-wrist x-ray. Since then there has been a movement against this practice, owing to the radiation dose, and as a result skeletal age is not now routinely measured. The absence of bone age means that there is no simple way to plot an individual growth curve adjusted for puberty, except after the event of peak height velocity, when then tempo effect can be obtained from the velocity curve.

Charting growth velocity as centile crossing – thrive lines

A completely different way of assessing velocity is to base it on centile crossing, as mentioned at the start of the paper. Velocity is conventionally measured in units of measurement per time, e.g. cm/year for height velocity. But if instead it is based on centile crossing the measurement units are SD scores rather than cm or kg (note not centiles – centiles are on a nonlinear bounded scale that is inappropriate for statistical summary). The properties of SD scores (mean 0, SD 1 in the reference population) make the variability of centile-crossing-based velocity particularly simple to calculate ( Cole 1998 ). In addition one can incorporate an adjustment for regression to the mean, which is an important and often neglected consideration in assessing growth velocity. The effect of regression to the mean is that on average small children tend to grow relatively fast, and large children relatively slowly, and adjusting for regression to the mean allows velocity in small and large children to be compared directly.

The underlying algebra is as follows, where Z 1 and Z 2 are measurement SD scores on two occasions t 1 and t 2 from which velocity is to be calculated, and where the correlation between Z 1 and Z 2 is r 1 . The unconditional increment is given by Z 2 – Z 1 (i.e. the change in SD score), and its SD is 2 ( 1 − r 1 ) . This allows the increment to be expressed as an SD score Z u ∗ where

Note that the velocity does not depend on t 1 and t 2 , only on the SD scores and correlation.

For the conditional increment (i.e. adjusted for regression to the mean) the corresponding values are Z – r with SD 1 − r 1 2 , and the conditional increment as an SD score is Z c ∗ where

Note that [3] and [4] are similar, and they only differ materially if r 1 << 1.

In the same way as for a centile curve C 100α and the LMS method, one can obtain a series of SD scores Z i and corresponding measurements X i to plot against equally spaced ages t i that reflect a constant specified unconditional or conditional velocity. Z * = z α . The constant conditional velocity formula is

where z α is the normal equivalent deviate for the required velocity centile, and i is the correlation between Z i and Z i +1 . The required series of SD scores is then obtained by daisy-chaining – use [5] to define Z 2 from Z 1 , and then Z 3 from Z 2 etc. In words, given a starting SD score, a series of SD scores is calculated such that the conditional velocity Z c ∗ between pairs of SD scores is z α . These SD scores can be converted back to measurements X i to plot on the distance chart using [1] . For the simplest case, starting on the median and growing at median velocity, i.e. Z 1 = 0 and z α =0, later SD scores Z 1 are also all zero. Thus a child whose growth follows the median curve on the distance chart is growing at median conditional velocity, as one would expect.

For other choices of z α , positive or negative, the derived series of SD scores back-transformed to the measurement scale represents a “growth curve” with a consistent pattern of centile crossing on the distance chart. This “growth curve” is termed a thrive line , as it quantifies failure to thrive. The slope of the thrive lines, i.e. the degree of centile crossing, depends in a complex way on the initial SD score and the correlation, which in turn depends on the corresponding ages of measurement.

For assessment purposes a series of thrive lines is necessary, with different starting points, so that individual growth curves can be compared in slope with the nearest thrive line. The thrive lines can be printed on a transparent overlay to be superimposed on the chart. The assessment of velocity then involves comparing the slope of the child’s growth curve with the slope of the nearest thrive line. Figure 11A shows the British 1990 weight chart for boys 0-1 years, with the growth curve of a boy measured at 3, 4 and 5 months, over which time he falls from the median to the 9 th centile. Clearly he is growing more slowly than average as he is crossing centiles downwards. But the Figure gives no clue as to whether his velocity is slightly low or very low. Figure 11B shows thrive lines for 5 th centile weight velocity measured over a four-week period. This is designed as a transparent overlay to be placed over Figure 11A , so the growth curve can be compared directly with the thrive lines. It is clear that the growth curve is crossing thrive lines downwards, and hence the boy is growing appreciably more slowly than the 5 th weight velocity centile. In addition he shows the same pattern over two successive months, which indicates a considerably lower velocity centile than the 5 th ( Cole 1998 ).

See text for details.

So in summary, thrive lines provide a way to quantify centile crossing and hence velocity on the distance chart, without the need to calculate or plot velocity. In principle one could have a sheaf of overlays for different velocity centiles, and thrive lines could be applied to height velocity in puberty as well as weight velocity in infancy. It is worth pointing out that as a technology thrive lines are ideally suited to the computer screen, where they can be added to or removed from the chart at the touch of a button.

WHO growth standard

An important milestone in international health occurred in 2006 with the publication of the World Health Organization child growth standard ( WHO Multicentre Growth Reference Study Group 2006 ). The study had a complex design involving infants and children from sites in six countries, selected to be free of constraints to growth and hence growing optimally. Data for the first two years were collected longitudinally, with up to 21 measurement occasions per child, and from 18-71 months the children were measured cross-sectionally. WHO also systematically reviewed the literature on the statistical construction of growth references ( Borghi et al. 2006 ), and carefully documented the process of constructing the centiles ( WHO 2006 ). As the pattern of growth was felt to be optimal, and linear growth in the six countries was similar, WHO has presented the growth standard as being of universal applicability. It has since been endorsed by over 150 countries of the world, and many countries have made it an integral part of their own growth assessment, e.g. the UK-WHO growth reference, see below ( Wright et al. 2010 ).

It should be acknowledged that there has also been controversy surrounding the growth standard. For reasons that are unclear, weight on the WHO growth standard is low at birth and rises rapidly in the early weeks, a growth pattern viewed as unhelpful for encouraging breastfeeding ( Binns et al. 2008 ). Also the WHO standard children are relatively light and with small head circumferences, which means that they differ materially from North European children ( Juliusson et al. 2011 ). But since they were chosen as a growth standard rather than a growth reference, with a lower plane of nutrition ( Cole 2008 ), it is perhaps not too surprising that they are relatively thin, and in a time of rising childhood obesity it is an important message that children growing healthily are thin children.

Chart design with the UK-WHO charts

The final stage in this brief and selective history of growth references and growth charts is to highlight recent work developing the UK-WHO growth charts as a synthesis of the British 1990 reference ( Freeman et al. 1995 ) and the WHO growth standard ( WHO Multicentre Growth Reference Study Group 2006 ). When the WHO standard was first published the British Government Department of Health caused a child growth expert group to be set up under the leadership of Professor Charlotte Wright (University of Glasgow) to develop a British version of the WHO charts. The result was a set of charts from birth to 4 years with evidence-based instructions, several innovative chart design features to simplify plotting and improve plotting accuracy, and they were fully trialled before launch ( Wright et al. 2010 ). As an example Figure 1 illustrates the 0-1 year weight chart for girls, where the centiles start at age 2 weeks rather than at birth. This is for three reasons: i) growth assessment in the first two weeks should be relative to the individual’s own birthweight rather than weight centiles (i.e. has the infant regained birthweight?), so the early centiles are omitted; ii) the break in centiles between birth and 2 weeks reminds the user that the birth centiles (shown on the age 0 axis) are based on the British 1990 reference while those from 2 weeks are from the WHO standard, and iii) as stated earlier, WHO birthweight is very low compared to British 1990 birthweight and for this reason the first two weeks of WHO weight centiles are omitted (see ( Cole et al. 2011 ) for a fuller explanation). The charts, instructions and training materials are all available at http://www.growthcharts.rcpch.ac.uk .

Conclusions

This whistle stop tour has shown how the process of growth assessment has developed and matured in the 200 years since de Montbeillard’s son’s growth curve was drawn. The process has involved an interesting synthesis of three distinct disciplines: anthropology for the collection of anthropometry, statistics to summarise the anthropometry for the growth reference, and graphic design to represent the growth reference as a growth chart. In fact there are other relevant disciplines too, including politics, psychology and ergonomics, where the aim is to encourage individuals to make the best use of the chart. Future developments in chart design are likely to be primarily electronic, exploiting computer and smartphone screen technology, which will free the design from its longstanding two-dimensional straitjacket.

* The probable error, the distance from the median to the third quartile, is approximately twothirds of the standard deviation.

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Shift mindset & attitude with visualization

Visualization can help you to shift your mindset and bring it into your day. Experience improved motivation and focus, and set yourself for success whilst showing up as your best self.

Learn how visualization can support your health and fitness journey

Learn how visualization can help to change your mindset and attitude.

Visualization is a success practice used by people who want to grow and achieve their goals. It is not just daydreaming or wishful thinking. When used correctly, it is a scientific process that allows you to shift your state and tap into more of your inner resources. By state we mean our mental, emotional and physical state. Said another way, it’s our mindset and how we’re showing up to things. When we use effective visualization to shift our state into an empowered one, we can better focus on what’s important, take more dynamic action and more easily overcome challenges. It also allows us to mentally prepare, so that we can show up at our best at the most critical moments.

Visualization can help us with stress in two significant ways. It can help to create a state of deep relaxation after the body is triggered by stress. And it can help us to prevent stress by preventing us from triggering the stress response in the first place. An example of this is swimmer Missy Franklin.

Franklin, who won four gold medals at the London Games, uses visualization as a way of reducing anxiety of the unknown. Says Franklin, “When I get there, I’ve already pictured what’s going to happen a million times so I don’t actually have to think about it.” Like that, visualization can reduce stress and help us relax more. It provides not only a method of creating relaxation after stress has occurred, but it can also help us prevent it. And that makes it an invaluable tool. Visualization is an Effective Way to Create a Positive Mindset and Attitude Objective: Answer the question, “What is visualization?”

When most people think of visualization, they think of a mental practice. Visualization with EnVision goes way beyond that. We recognize that the mind affects the emotions and the body, and all of these are components of setting a winning attitude. In other words, the most effective approach to visualization has a profound effect on how we feel. It changes our attitude and helps us to create a positive mindset. And it is our daily mindset and attitude that propel us rapidly towards our goals. They accelerate our progress and efficiency. They can make all the difference. And visualization can be the key that unlocks the winning mindset and attitude.

Visualization is a versatile tool. We can use it to set attitude and develop a positive mindset. We can use it to rehearse important steps towards our success. One of the most effective uses of visualization is to create a vision for our lives that is so inspiring it compels us to act. At EnVision we call this your compelling future. We help you to define your compelling future and to represent that future visually with a vision board. We help you to know how to best visualize this future so that you feel motivated and inspired. And we help you to know what actions to take in order to achieve it.

What is the value of being able to show up as your best self, each and every day? Visualization is a tool that can be used to shift our internal mental/emotional state. Why? Because when we visualize the subconscious mind reacts as if what we are visualizing is real. That means we can utilize visualization to prime ourselves for the day so that we can show up as the version of ourselves that we want to be. This is the power of visualization. Being able to create our lives in a way that matches our vision. And this is the power of using a visualization app. It can guide you to have the most effective state shift so that you show up as your best self. So why not give it a try?

One of the things that using a visualization app can help with is creating the best habits. This is especially true when it comes to the habit of visualization. While you might be able to find guided visualizations elsewhere, when it comes to practicing visualization for success, EnVision has got everything organized for you. Connecting to your vision, using visualization to set your mindset and attitude for the day, setting powerful intentions and getting key actions done — these are all part of the EnVision daily habit. We help you to create the best future possible.

Success is built one day at a time. Showing up to each day with a positive mindset and attitude makes all the difference in having a productive day moves you closer to your goals. Visualization is a powerful tool for shifting mindset. That is one of the things we focus on with EnVision. Shifting your mindset, your attitude, or what we call “state,” is effectively done with the style of visualization we offer. If you want to create the mindset for success, then check out the EnVision app.

How do you create an unstoppable mindset? With effective visualization. You see, effective visualization goes beyond just picturing what you want. It is about creating that deeply felt emotional state that can inspire you. It is also about rehearsing for the obstacles that you will encounter along your way. When you see yourself overcoming these and coming up with creative solutions to problems, you begin to know that you will succeed. You feel the passion and know that you are unstoppable. And that is part of the benefit of using a visualization app.

Franklin, who won four gold medals at the London Games, uses visualization as a way of reducing anxiety of the unknown. Says Franklin, “When I get there, I’ve already pictured what’s going to happen a million times so I don’t actually have to think about it.” Like that, visualization can reduce stress and help us relax more. It provides not only a method of creating relaxation after stress has occurred, but it can also help us prevent it. And that makes it an invaluable tool.

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How to Represent Linear Data Visually for Information Visualization

Linear data sets come in three varieties – univariate, bivariate and trivariate. A univariate data set has a single dependent variable which varies compared to the independent attributes of that data. A bivariate set has two dependent variables and a trivariate set has three.

Representing data sets of these types is a very common task for the information visualization designer. Choosing the right form of visualization will depend on the requirements of the user of the visualization as much as the data set itself.

Univariate Data Sets

Univariate data sets are very simple to represent visually. There are many different forms for showing univariate data and one of the most common is tabulating the data itself. For example you might want to show the relationship between types of car and their top speed.

Note: According to Automoblog.net these were the 10 fastest cars in the world in 2007.

Stephen Few, the information visualization consultant said; “Numbers have an important story to tell. They rely on you to give them a clear and convincing voice.” There is nothing intrinsically wrong with presenting this data in a tabulated format. It may be exactly what the user needs . Certainly, you can fairly quickly determine which car is the fastest (the Hennessey Venom GT) from the table – even if it’s not immediately obvious which is the fastest at first glance.

However, it might be better to represent the data graphically which would enable an easier comparison between all the cars.

There are many different graphical representations that can be used to show univariate data. They include pie charts, histograms, scatter plots, bar graphs, etc. The precise nature of the representation chosen will depend on the data set.

For example here’s the speed data shown as a pie chart:

Not very useful is it? There’s too much data of a similar nature and the color key is equally confusing. You can’t tell very much about the cars and their relative speeds from a pie chart.

Whereas here’s the same data set represent as a bar graph:

It is instantly clear from the bar graph which vehicle is the fastest and which is the slowest and how each compares to every other vehicle.

Bivariate Data Sets

Bivariate data sets have two sets of dependent variables that we wish to compare against the independent variable(s).

So let’s take our original data set and expand it to include the horsepower of each vehicle.

Now we might want to examine the relationship between the speed of each vehicle and the horsepower that powers the vehicle. Does an increase in horsepower automatically mean an increase in the speed of the vehicle? Are they proportionate to each other?

Again, there are many different ways to represent the data. We’ve chosen a an area driven graph with the two data sets imposed on top of each other.

From this graph it’s very easy to conclude that while the speeds of the vehicles don’t vary dramatically – the horse power of each vehicle does. Yes, there’s definitely a case to be made that large amounts of horsepower do correlate with speed but it’s only a weak correlation. The McLaren F1 is faster than the Aston Martin One-77 but carries markedly less horsepower, for example.

It’s worth noting that caution must be taken when choosing bivariate representations. In this graph, we have focused our attention on the horsepower of the vehicles and the similarity between the top speeds of the vehicles. However, there is greater variation in the speeds than you can tell by glancing at the graph – it serves our purpose for analysis but is not necessarily the perfect representation for other purposes.

It could also be argued that the third-dimension, in our representation, adds little value to the viewer and could be eliminated in favor of a flatter representation.

Trivariate Data Sets

A trivariate data set includes a third dependent variable that can be represented against the independent variable(s).

For example we might want to include a stopping distance within our car data set (please note that these distances were created for this example and are not likely to be the actual stopping distances of these vehicles) :

Once again trivariate data can be represented in any number of ways. However, a common methodology is the 3D scatter plot as shown above.

Again, caution must be taken when choosing the representation for trivariate data sets. Two common problems with models here are occlusion (where one item in a data set is obscured by another – so you cannot see its actual place in the model) and the fact that it can be hard to determine where, exactly, along any given axis the data point lays.

It’s for this reason that trivariate models are often interactive and can be manipulated by the user to be viewed from different angles in order to gain a better understanding of the data.

A Practical Tip

There is no usual reason to create your models by hand; most spreadsheet packages (such as Excel) can create univariate and bivariate models with ease from tabulated data. There are also specialist software modeling packages for more complex models including trivariate data sets.

You may decide to create the model in one package and then, for reasons of aesthetics , recreate the model in a graphic design package as the design elements in Excel, for example, are somewhat limited.

The Take Away

The key to creating visual representations of linear data is to ensure the usability of the final representation. Fortunately, you do not have to create these models “from scratch” but can use computer tools to do the job for you. This allows you to quickly switch between models until you find one that is fit for purpose.

References & Where to Learn More:

10 Fastest cars in the world.

Stephen Few – Show Me Numbers Designing Tables and Graphs to Enlighten – Analytics Press, ISB 978-0970601971

Hero Image: Author/Copyright holder: Eric Fischer. Copyright terms and licence: CC BY 2.0

Perception and Memory in HCI and UX

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35 Inspiring Symbols of Growth: Unleash Your Inner Potential

• October 19, 2023

In today’s fast-paced world, harnessing the power of symbols of growth can be transformative in achieving personal and professional success. In this comprehensive guide, we’ll delve into the significance of these symbols and how you can use them to optimize your potential.

By understanding and incorporating these Symbols of Growth , you’ll be well on your way to thriving in all aspects of your life.

Key Takeaways:

• Symbols of growth have profound psychological and emotional impact, influencing our mindset, goals, and actions. They inspire us to adopt a growth mindset and continuously improve.
• Surrounding ourselves with symbols of growth creates an environment conducive to personal development. These symbols serve as motivational reminders to stay focused on growth.
• Incorporating symbols into goal-setting and visualization exercises can help us actualize our aspirations and stay committed to transformation.
• There are countless symbols representing growth across cultures and spiritual traditions. Understanding their significance provides deeper insight into human nature and our shared desire for self-improvement.
• The journey of growth requires resilience, adaptability, and determination. By internalizing the essence of these symbolic representations, we can unlock our potential.

The Importance of Symbols of Growth

Symbols of growth hold immense power in shaping our thoughts, attitudes, and actions. By leveraging these symbols, we can not only identify areas of personal and professional growth but also create an environment conducive to success.

In this section, we’ll delve deeper into the significance of symbols of growth, exploring the psychological impact of symbols, how they influence our behavior and mindset, and the role they play in goal-setting and achievement.

The Psychological Impact of Symbols

Symbols have been an essential part of human communication and culture throughout history. They serve as visual representations of abstract ideas, beliefs, and values, allowing us to communicate complex concepts in a simplified form. Our minds are naturally drawn to symbols, and they often hold a profound emotional resonance.

In the context of growth, symbols serve as powerful reminders of our potential for development and transformation. They can inspire us, motivate us, and help us overcome challenges by evoking feelings of hope, resilience, and determination.

Influencing Behavior and Mindset

Symbols of growth can have a direct impact on our behavior and mindset. When we surround ourselves with symbols that represent growth and development, we are more likely to adopt a growth mindset – a belief in our capacity for change and improvement.

This mindset can have far-reaching effects on our lives, increasing our motivation, resilience, and willingness to take on challenges. It can also lead to greater self-awareness, as we become more attuned to our strengths, weaknesses, and areas for growth.

Symbolism in Goal-Setting and Achievement

Utilizing symbols of growth in the goal-setting process can be an effective way to foster a growth-oriented mindset. By incorporating these symbols into our personal and professional goals, we create a visual representation of the growth and transformation we hope to achieve.

This process can help clarify our intentions, making it easier to develop a plan of action and stay focused on our goals.

Additionally, the visual nature of symbols can serve as a constant reminder of our commitment to growth, helping us maintain motivation and overcome obstacles along the way.

Top 30 Symbols of Growth:

1. the tree of life.

The Tree of Life represents the interconnectedness of all living things and the cycle of life, growth, and renewal. It is a symbol of stability, strength, and wisdom, signifying the potential for continuous growth and transformation. This ancient symbol is found in various cultures and spiritual traditions, reminding us of our deep-rooted connection to nature and the importance of nurturing our personal growth to reach our full potential.

2. The Phoenix

The Phoenix is a mythical bird that symbolizes rebirth, renewal, and transformation. It represents the ability to rise from the ashes and overcome adversity, embodying resilience and the power of personal growth. The Phoenix teaches us that life’s challenges can serve as opportunities for self-discovery and reinvention. By embracing the Phoenix’s energy, we can face our difficulties with courage and emerge stronger and wiser.

3. The Lotus Flower

The Lotus Flower is a symbol of purity, enlightenment, and spiritual growth. It grows in muddy water, yet it rises above the surface to bloom, untouched by its surroundings. This remarkable process symbolizes our ability to rise above adversity and transform ourselves into something beautiful and pure. The Lotus Flower encourages us to seek wisdom and self-awareness, inspiring us to connect with our inner strength and resilience.

4. The Butterfly

The Butterfly represents transformation, metamorphosis, and personal growth. Its journey from a caterpillar to a butterfly is an inspiring metaphor for the potential within each of us to evolve and change. The Butterfly reminds us that we must embrace change and let go of the past to reach our full potential. By embodying the Butterfly’s spirit, we can face life’s transitions with grace and emerge stronger and more vibrant.

5. The Celtic Spiral

The Celtic Spiral is a symbol of growth, evolution, and the cycles of life. Found in ancient Celtic art, it represents the ever-changing nature of existence and the continuous journey of personal and spiritual development. The Celtic Spiral reminds us of the interconnectedness of all things and the importance of embracing change and growth in our lives.

6. The Seed

The Seed is a symbol of potential, growth, and new beginnings. It represents the power within each of us to nurture our dreams, ideas, and aspirations, transforming them into reality. The Seed encourages us to cultivate our passions and talents, reminding us that even the smallest efforts can yield great results. By embodying the Seed’s spirit, we can approach life with a sense of curiosity and wonder, planting the seeds for a brighter future.

7. The Bamboo

The Bamboo is a symbol of flexibility, resilience, and growth. It is known for its incredible strength and ability to bend without breaking, even in the most challenging conditions. This remarkable quality serves as a metaphor for our capacity to adapt and persevere in the face of adversity. The Bamboo teaches us the importance of maintaining a growth mindset, embracing change, and staying rooted in our values and beliefs.

8. The Acorn

The Acorn is a symbol of potential, strength, and growth. It represents the promise of new life, reminding us that even the smallest beginnings can lead to great achievements. The Acorn encourages us to embrace our unique gifts and talents, nurturing them to fruition with patience and perseverance. By embodying the Acorn’s spirit, we can approach our personal and professional growth with confidence and determination.

9. The Mountain

The Mountain is a symbol of strength, wisdom, and spiritual growth. It represents the challenges we face in life and our ability to overcome them, reaching new heights of self-discovery and understanding. The Mountain teaches us the importance of perseverance and inner strength, reminding us that we can conquer our obstacles and achieve our goals.

10. The Yggdrasil 

The Yggdrasil is a sacred tree in Norse mythology, representing the universe and the interconnectedness of all things. It symbolizes growth, wisdom, and the eternal cycle of life, death, and rebirth. By embracing the energy of the Yggdrasil, we can cultivate a deeper understanding of our place in the cosmos and our capacity for personal and spiritual growth.

11. Ingwaz Rune

The Ingwaz Rune is a symbol of fertility, growth, and inner transformation in Norse mythology. It represents the potential within each of us to develop and nurture our talents and aspirations. Ingwaz encourages us to embrace change and growth, reminding us that we have the power to shape our destiny and manifest our dreams.

12. Jera Rune

The Jera Rune is a symbol of cycles, harvest, and positive change in Norse mythology. It represents the natural progression of growth, transformation, and the rewards that come from hard work and perseverance. Jera encourages us to maintain a growth mindset, trust in the process of personal development, and celebrate our achievements.

13. The Sunflower

The Sunflower is a symbol of vitality, happiness, and personal growth. It follows the path of the sun, always seeking the light, representing our innate desire for growth and self-improvement. The Sunflower teaches us the importance of staying positive and focused on our goals, even in challenging times.

14. The Oak Tree

The Oak Tree is a symbol of strength, endurance, and growth. It has deep roots and a solid foundation, signifying stability and resilience in the face of adversity. The Oak Tree encourages us to cultivate inner strength and patience, reminding us that true growth takes time and perseverance.

15. Infinity Symbol

The Infinity Symbol is a symbol of limitless potential, eternity, and personal growth. It represents the boundless nature of the universe and the endless possibilities available to us. The continuous, flowing shape of the symbol signifies the never-ending journey of self-discovery and improvement. By embracing the concept of infinity, we are encouraged to approach our personal and spiritual growth with an open heart and mind, understanding that there are no limits to what we can achieve and become.

16. The Koi Fish

The Koi Fish is a symbol of perseverance, transformation, and personal growth. It is known for its ability to swim upstream, overcoming obstacles and challenges in pursuit of its goals. The Koi Fish teaches us the importance of determination and persistence, reminding us that we have the power to overcome adversity and achieve our dreams.

17. The Egg

The Egg is a symbol of new beginnings, potential, and growth. It represents the promise of life and the potential for transformation that lies within each of us. The Egg encourages us to embrace change and growth, nurturing our dreams and aspirations with patience and care.

18. The Green Man

The Green Man is a symbol of fertility, renewal, and growth. Often depicted as a face made of leaves and vines, the Green Man represents the cyclical nature of life and our connection to the natural world. Embracing the energy of the Green Man can help us cultivate a deeper appreciation for the cycles of growth and transformation in our own lives.

19. The Stag

The Stag is a symbol of strength, wisdom, and personal growth. It represents our ability to navigate life’s challenges with grace and confidence, embodying the qualities of leadership and resilience. The Stag encourages us to stand tall in the face of adversity and embrace our inner strength, reminding us that we have the power to overcome obstacles and achieve our goals.

20. The Vine

The Vine is a symbol of growth, expansion, and adaptability. It represents our ability to navigate life’s twists and turns, reaching out and embracing new opportunities for growth and learning. The Vine teaches us the importance of adaptability, encouraging us to stay open to change and cultivate a growth mindset.

21. The Garden

The Garden is a symbol of cultivation, growth, and nurturing. It represents the care and attention we give to our personal and spiritual development, fostering an environment that encourages growth and self-discovery. The Garden reminds us of the importance of tending to our inner world, nurturing our dreams and aspirations, and cultivating a life that reflects our true values and passions.

22. The Labyrinth

The Labyrinth is a symbol of personal growth, self-discovery, and transformation. It represents the journey we take through life, exploring our inner world and seeking deeper understanding and wisdom. The Labyrinth encourages us to embrace the twists and turns of our personal journey, trusting that we will find our way to the center of our true selves.

23. The Waterfall

The Waterfall is a symbol of rejuvenation, cleansing, and growth. It represents the power of water to transform and renew, both physically and emotionally. The Waterfall teaches us the importance of letting go of the past and embracing the flow of life, allowing ourselves to grow and change with the currents of our experiences.

24. The Arrow

The Arrow is a symbol of direction, focus, and personal growth. It represents our ability to set our sights on our goals and aspirations, propelling ourselves forward with determination and precision. The Arrow encourages us to aim high, stay focused on our targets, and embrace the journey of self-improvement and growth.

25. The Snake

26. The Lighthouse

The Lighthouse is a symbol of guidance, hope, and personal growth. It represents our ability to find our way through life’s storms and challenges, seeking the light of wisdom and understanding. The Lighthouse encourages us to trust our inner compass, cultivate self-awareness, and embrace the journey of self-discovery.

27. The River

The River is a symbol of flow, movement, and personal growth. It represents our ability to adapt and change as we navigate life’s currents, embracing new experiences and opportunities for growth. The River teaches us the importance of staying open to change and trusting in the natural flow of life.

28. The Rainbow

The Rainbow is a symbol of hope, renewal, and personal growth. It represents the promise of new beginnings and the potential for transformation that follows life’s storms. The Rainbow encourages us to stay hopeful and optimistic, trusting that brighter days lie ahead and that we have the power to create a life of joy and fulfillment.

29. The Scarab

The Scarab is a symbol of transformation, renewal, and personal growth. In ancient Egyptian culture, it represents the cycle of the sun and the idea of rebirth, signifying the potential for new beginnings and self-improvement. The Scarab encourages us to embrace change, let go of the past, and continuously evolve as we journey through life.

30. The Merkaba

The Merkaba is a symbol of spiritual growth, energy, and higher consciousness. It represents the balance and union of opposites, embodying the potential for deep personal transformation and spiritual awakening. The Merkaba encourages us to seek self-awareness, explore the depths of our inner world, and unlock our full potential.

31. The Dharma Wheel

The Dharma Wheel is a symbol of spiritual growth, enlightenment, and the path to self-realization in Buddhism. It represents the teachings of the Buddha and the journey towards inner peace and liberation from suffering. The Dharma Wheel encourages us to seek wisdom, cultivate mindfulness, and embrace the principles of compassion and loving-kindness in our lives.

32. The Hourglass

The Hourglass is a symbol of time, change, and personal growth. It represents the fleeting nature of our lives, reminding us of the importance of making the most of each moment and embracing opportunities for growth and self-improvement. The Hourglass encourages us to be mindful of the passage of time and to prioritize our personal development, cultivating a life that aligns with our deepest values and passions.

33. The Spider

The Spider is a symbol of creativity, patience, and personal growth. It represents our ability to weave the web of our own lives, taking an active role in shaping our destiny and manifesting our dreams. The Spider encourages us to approach life with a sense of curiosity and wonder, exploring the threads that connect us to our passions and purpose.

34. The Chakra

The Chakra is a symbol of energy, balance, and personal growth in Hinduism and various spiritual traditions. Chakras are energy centers located throughout the body, representing different aspects of our physical, emotional, and spiritual well-being. The concept of Chakra encourages us to cultivate self-awareness, work on balancing our energies, and align our inner world with our outer actions. By focusing on the Chakra system, we can foster holistic growth, achieve harmony in our lives, and unlock our full potential.

35 The Nautilus Shell

The Nautilus Shell is a symbol of growth, evolution, and the interconnectedness of life. It represents the natural beauty and mathematical perfection found in nature, embodying the concept of continuous expansion and self-improvement. The Nautilus Shell encourages us to embrace the journey of personal growth, seeking wisdom and understanding as we navigate the ever-changing currents of life.

The Evolution of Symbols of Growth

While ancient cultures relied heavily on nature-based symbols of growth, modern abstract designs and conceptual imagery are emerging. For instance, spirals and fractals representing evolution are gaining popularity.

As humanity progresses, our representations of growth adapt to our changing lifestyles and philosophies. However, the core desire for guidance and inspiration persists regardless of the symbols’ form. Our shared need for growth endures across generations.

Symbols of Growth – FAQs

Why are symbols of growth important in our personal journeys?

Symbols of growth serve as inspiring reminders of our potential for improvement. They motivate us to overcome challenges, foster a growth mindset, and continuously expand our horizons. These symbols provide direction and hope, especially during difficult transitions.

How can symbols of growth help us achieve professional success?

A: Incorporating symbolic representations into vision boards, goal journals, or office décor creates an empowering workspace. These symbols instill confidence, clarity, and determination to excel. They also remind us to embrace opportunities for continuous learning and skill-building.

What role do symbols play in spiritual or inner growth?

Symbols representing spiritual growth, like the lotus or yin-yang, remind us to look inward and nurture our inner wisdom. They teach timeless lessons about resilience, harmony, and enlightenment. Regular reflection on their essence can guide us toward self-realization.

Why is nature an important source of symbols of growth?

Natural symbols, like trees, seeds, and mountains, reflect the cycles and interconnectedness of life. They represent concepts like resilience, potential, and determination. Connecting with nature’s transformative power through these symbols cultivates inner strength.

Do symbols of growth have any downsides?

Over-reliance on external symbols can sometimes distract us from inner work. Their impact depends on how mindfully we engage with them. However, used positively, they provide guidance through life’s complexities. Moderation and self-awareness are key.

How can parents and teachers foster growth mindsets using symbols?

Incorporating symbolic illustrations and stories about growth into educational materials and activities can inspire children. Positive symbols plant seeds to approach challenges proactively and confidently. However, flexibility based on age is important.

What role do symbols of growth play in healing and rehabilitation?

Symbols of transformation and renewal, like the phoenix and the butterfly, provide hope during recovery. They represent our capacity to overcome adversity and instill faith in the rehabilitation process. Support groups often leverage them for motivation.

How can couples use symbolic imagery to nurture relational growth?

Shared symbols like infinity signs or intertwined vines represent commitment, resilience, and adaptation. They remind couples to actively nurture their bond through challenges. Displaying joint artwork also reinforces shared growth and teamwork.

What is a contemporary example of a popular symbol of growth?

Many people today get tree of life tattoos, representing interconnectedness and the cycles of growth. This enduring symbol has been modernized across artistic genres but retains its essence. Its resurgence reveals our timeless need for growth symbols.

Symbols of growth have been an essential part of human culture and spirituality, transcending time and geography. These powerful symbols represent growth, renewal, and transformation in various aspects of our lives, including personal, spiritual, and physical growth.

As we embark on our journey of personal transformation and growth, it’s essential to remember that growth and change are inherent in the nature of life.

The potential for growth lies within each of us, and it is through embracing this potential that we unlock our true strength and resilience.

From ancient Egyptian symbols to popular tattoo designs, these symbols of growth have become universal, guiding us towards a brighter, more enlightened future.

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The Power of Visualization in Math

Creating visual representations for math students can open up understanding. We have resources you can use in class tomorrow.

When do you know it’s time to try something different in your math lesson?

For me, I knew the moment I read this word problem to my fifth-grade summer school students: “On average, the sun’s energy density reaching Earth’s upper atmosphere is 1,350 watts per square meter. Assume the incident, monochromatic light has a wavelength of 800 nanometers (each photon has an energy of 2.48 × 10 -19 joules at this wavelength). How many photons are incident on the Earth’s upper atmosphere in one second?”

My students couldn’t get past the language, the sizes of the different numbers, or the science concepts addressed in the question. In short, I had effectively shut them down, and I needed a new approach to bring them back to their learning. So I started drawing on the whiteboard and created something with a little whimsy, a cartoon photon asking how much energy a photon has.

Immediately, students started yelling out, “2.48 × 10 -19 joules,” and they could even cite the text where they had learned the information. I knew I was on to something, so the next thing I drew was a series of boxes with our friend the photon.

If all of the photons in the image below were to hit in one second, how much energy is represented in the drawing?

Students realized that we were just adding up all the individual energy from each photon and then quickly realized that this was multiplication. And then they knew that the question we were trying to answer was just figuring out the number of photons, and since we knew the total energy in one second, we could compute the number of photons by division.

The point being, we reached a place where my students were able to process the learning. The power of the visual representation made all the difference for these students, and being able to sequence through the problem using the visual supports completely changed the interactions they were having with the problem.

If you’re like me, you’re thinking, “So the visual representations worked with this problem, but what about other types of problems? Surely there isn’t a visual model for every problem!”

The power of this moment, the change in the learning environment, and the excitement of my fifth graders as they could not only understand but explain to others what the problem was about convinced me it was worth the effort to pursue visualization and try to answer these questions: Is there a process to unlock visualizations in math? And are there resources already available to help make mathematics visual?

I realized that the first step in unlocking visualization as a scaffold for students was to change the kind of question I was asking myself. A powerful question to start with is: “How might I represent this learning target in a visual way?” This reframing opens a world of possible representations that we might not otherwise have considered. Thinking about many possible visual representations is the first step in creating a good one for students.

The Progressions published in tandem with the Common Core State Standards for mathematics are one resource for finding specific visual models based on grade level and standard. In my fifth-grade example, what I constructed was a sequenced process to develop a tape diagram—a type of visual model that uses rectangles to represent the parts of a ratio. I didn’t realize it, but to unlock my thinking I had to commit to finding a way to represent the problem in a visual way. Asking yourself a very simple series of questions leads you down a variety of learning paths, and primes you for the next step in the sequence—finding the right resources to complete your visualization journey.

Posing the question of visualization readies your brain to identify the right tool for the desired learning target and your students. That is, you’ll more readily know when you’ve identified the right tool for the job for your students. There are many, many resources available to help make this process even easier, and I’ve created a matrix of clickable tools, articles, and resources .

The process to visualize your math instruction is summarized at the top of my Visualizing Math graphic; below that is a mix of visualization strategies and resources you can use tomorrow in your classroom.

Our job as educators is to set a stage that maximizes the amount of learning done by our students, and teaching students mathematics in this visual way provides a powerful pathway for us to do our job well. The process of visualizing mathematics tests your abilities at first, and you’ll find that it makes both you and your students learn.

Harness the Power Within: With Effective Visualization Exercises

The power of visualization.

Visualization is a powerful technique that taps into the mind’s ability to create vivid mental images. It is the process of using your imagination to create a visual representation of a desired outcome or experience. By engaging in visualization exercises, individuals can harness the power of their minds to manifest their goals and aspirations.

Understanding Visualization

Visualization is a technique that has been used for centuries across various cultures and disciplines. It involves creating detailed mental images and engaging the senses to make the experience as real as possible. When visualizing, individuals can imagine themselves in specific situations, interacting with their environment, and achieving their desired outcomes.

Visualization is based on the principle that the mind and body are interconnected. By vividly imagining a desired outcome, individuals can activate the same neural pathways as if they were actually experiencing it. This process can have a profound impact on one’s thoughts, emotions, and behaviors.

Benefits of Visualization Exercises

There are numerous benefits to incorporating visualization exercises into your daily routine. Here are some of the key advantages:

• Clarifies Goals:  Visualization helps individuals gain clarity on their goals and desires. By visualizing the end result, individuals can define what they truly want and set a clear direction for their actions.
• Boosts Motivation:  When individuals visualize their goals, they tap into their inner motivation and drive. Visualizing the desired outcome can ignite a sense of purpose and determination, making it easier to stay committed to their goals.
• Increases Self-Confidence:  Visualization exercises can enhance self-confidence by creating a mental image of success. By visualizing themselves overcoming challenges and achieving their goals, individuals build a positive self-image and develop the belief that they can succeed.
• Improves Performance:  Visualization is a valuable tool for enhancing performance in various areas of life. Athletes, public speakers, and performers often use visualization techniques to mentally rehearse their actions and prepare for success.
• Reduces Stress and Anxiety:  Engaging in visualization exercises can help individuals reduce stress and anxiety. By visualizing calming and peaceful scenes, individuals can activate the relaxation response and promote a sense of calmness.
• Enhances Problem-Solving Skills:  Visualization can stimulate creativity and innovative thinking. By visualizing different scenarios and potential solutions, individuals can expand their problem-solving capabilities.

To fully reap the benefits of visualization exercises, it is important to practice regularly and consistently. By integrating visualization into your daily routine, you can tap into the power of your mind and unlock your full potential.

In the next sections, we will explore specific visualization techniques, such as creating a vision board and mental rehearsal, that can further enhance personal growth and performance. Stay tuned!

Note: If you’re looking for more tools and resources to support personal growth and self-improvement, check out our collection of  life coaching worksheets  on various topics, including goal setting, self-esteem, mindfulness, and more.

Guided Visualization Exercise

Visualization exercises are powerful tools that can help individuals tap into their inner potential and manifest their goals and desires. By engaging the mind’s eye and imagination, guided visualization exercises can create a vivid and detailed mental experience that enhances focus, motivation, and overall well-being. In this section, we will explore a step-by-step guide to a basic visualization exercise and how to visualize your goals and desires effectively.

Step-by-Step Guide to a Basic Visualization Exercise

Follow these steps to embark on a basic visualization exercise:

• Find a quiet and comfortable space : Choose a space where you can relax and focus without distractions. It could be a quiet room, a peaceful outdoor spot, or anywhere that brings you calmness.
• Get into a relaxed state : Sit or lie down in a comfortable position. Take a few deep breaths, inhaling slowly and exhaling fully. Allow your body to relax, releasing any tension or stress.
• Create a mental image : Close your eyes and start creating a mental image of a place or scenario that brings you a sense of peace and tranquility. It could be a serene beach, a lush forest, or any location that resonates with you.
• Engage your senses : Dive into the details of your mental image. Engage all your senses to make it as vivid as possible. Notice the colors, textures, sounds, and scents in your visualization. Immerse yourself in the experience.
• Experience positive emotions : As you continue visualizing, focus on evoking positive emotions associated with your mental image. Feel the joy, serenity, or excitement that arises within you. Allow these emotions to fill you up.
• Stay in the visualization : Remain in this visualization for a few minutes, allowing yourself to fully experience the positive emotions and sensations. Embrace the sense of calmness and fulfillment that it brings.
• Gradually return to the present moment : When you are ready to end the exercise, slowly bring your awareness back to the present moment. Take a few deep breaths and gently open your eyes. Reflect on the experience and the emotions it evoked.

Visualizing Your Goals and Desires

Visualization can be a powerful tool for manifesting your goals and desires. By visualizing your goals with clarity and intention, you can enhance your focus and motivation, making it easier to take the necessary steps towards achieving them. Here are some tips for visualizing your goals effectively:

• Be specific : Clearly define your goals and desires. The more specific you are, the easier it is to visualize them with detail and clarity.
• Use present tense : Visualize your goals as if they have already been achieved. This helps create a sense of belief and certainty in your mind, making it easier to manifest them into reality.
• Engage your emotions : As you visualize your goals, tap into the emotions associated with achieving them. Feel the joy, excitement, and fulfillment that come with accomplishing what you desire.
• Visualize the process : While it’s important to visualize the end result, also visualize the journey towards your goals. See yourself taking the necessary steps, overcoming challenges, and growing along the way.
• Revisit your visualization regularly : Make it a habit to incorporate visualization into your daily routine. Spend a few minutes each day visualizing your goals and desires, reinforcing your belief in their attainment.

By incorporating guided visualization exercises and visualizing your goals and desires regularly, you can harness the power within and create a positive mindset that propels you towards success. Remember, visualization is just one tool in the journey towards achieving your goals. Combine it with other practices such as  journaling prompts  and  goal setting worksheets  to enhance your personal growth and self-improvement journey.

Creative Visualization Techniques

When it comes to harnessing the power of visualization, there are various techniques you can employ to enhance your practice. In this section, we will explore two effective creative visualization techniques:  creating a vision board  and  mental rehearsal and future pacing .

Creating a Vision Board

A vision board is a powerful visual representation of your goals, dreams, and aspirations. It serves as a tangible reminder of what you want to manifest in your life. Creating a vision board involves gathering images, words, and symbols that represent your desired outcomes and arranging them on a board or a digital collage.

To create a vision board, follow these steps:

• Set your intentions : Determine the specific areas of your life you want to focus on, such as career, relationships, health, or personal growth.
• Gather visual material : Look for images, quotes, and phrases that resonate with your goals. You can find these in magazines, books, or online sources.
• Arrange and customize : Arrange the collected material on a board or create a digital collage using software or apps. Be creative and arrange the images in a way that feels inspiring and meaningful to you.
• Display your vision board : Place your vision board in a location where you will see it frequently, such as your bedroom, office, or as your computer or phone wallpaper. Regularly engage with your vision board by taking a few moments each day to visualize yourself already living your desired reality.

A vision board acts as a constant visual reminder of your goals and helps reinforce positive thoughts and emotions. It can inspire and motivate you to take action towards manifesting your dreams. For more self-reflection and goal-setting tools, you may also find  goal-setting worksheets  useful.

Mental Rehearsal and Future Pacing

Mental rehearsal and future pacing are visualization techniques that involve vividly imagining yourself successfully achieving your desired outcomes. By mentally rehearsing the steps and experiences leading up to your goals, you can enhance your confidence and increase the likelihood of success.

To practice mental rehearsal and future pacing, follow these steps:

• Set a specific goal : Clearly define the goal you want to achieve, whether it’s acing a presentation, winning a sports competition, or delivering a captivating speech.
• Create a mental picture : Close your eyes and vividly imagine yourself in the situation where you have achieved your goal. Engage all your senses to make the visualization as detailed and realistic as possible.
• Embrace positive emotions : As you visualize your success, immerse yourself in the positive emotions associated with achieving your goal. Feel the excitement, joy, and fulfillment that comes with accomplishing what you set out to do.
• Repeat and reinforce : Practice mental rehearsal and future pacing regularly to reinforce your positive mental images and emotions. This repetition helps to rewire your brain, strengthening the neural pathways associated with success and creating a positive mindset.

By engaging in mental rehearsal and future pacing, you are priming your mind and body for success. These techniques can boost your confidence, reduce anxiety, and improve your overall performance. For additional tools to enhance personal growth and self-confidence, consider exploring  self-esteem worksheets  and  mindfulness worksheets .

Incorporating these creative visualization techniques into your practice can amplify the effectiveness of your visualization exercises. Whether you choose to create a vision board or engage in mental rehearsal and future pacing, these techniques empower you to tap into the power of your imagination and manifest your dreams into reality.

Visualization for Personal Growth

Visualization exercises are powerful tools that can be used for personal growth and development. By harnessing the power of visualization, individuals can enhance their self-confidence, boost their self-esteem, and overcome fears and limiting beliefs. Let’s explore these aspects in detail.

Enhancing Self-Confidence and Self-Esteem

Visualization exercises can play a significant role in enhancing self-confidence and self-esteem. By visualizing yourself in situations where you feel confident, successful, and empowered, you can create a mental blueprint of what you want to embody in real life.

One technique to boost self-confidence is to visualize yourself accomplishing goals and achieving success. Close your eyes and vividly imagine yourself confidently taking action, overcoming obstacles, and celebrating your achievements. By repeatedly visualizing these scenarios, you reinforce positive beliefs about your abilities and cultivate a strong sense of self-confidence.

Another way to enhance self-esteem through visualization is to focus on self-love and self-acceptance. Visualize yourself accepting and loving who you are, embracing your strengths, and appreciating your unique qualities. This practice helps to cultivate a positive self-image and fosters self-compassion, which are essential components of healthy self-esteem.

Overcoming Fears and Limiting Beliefs

Visualization exercises can also be effective in overcoming fears and limiting beliefs that hold us back from reaching our full potential. By visualizing ourselves successfully facing and overcoming our fears, we can reframe our mindset and build resilience.

To overcome fears, start by visualizing yourself in a situation that triggers your fear. Imagine yourself remaining calm and composed, gradually facing and conquering your fear. Visualize every detail, including your emotions, actions, and the positive outcome you desire. This process helps to desensitize your fear response and rewires your brain to associate the situation with feelings of confidence and empowerment.

Similarly, to overcome limiting beliefs, visualize yourself challenging and reframing those beliefs. Imagine yourself confidently taking on new challenges, pushing past self-imposed limitations, and achieving success. By repeatedly visualizing these scenarios, you can reprogram your subconscious mind, replacing limiting beliefs with empowering ones.

By incorporating visualization exercises into your personal growth journey, you can strengthen your self-confidence, boost your self-esteem, and overcome fears and limiting beliefs. Remember to combine visualization techniques with other supportive practices such as journaling, using  journaling prompts , and utilizing relevant worksheets like  self-esteem worksheets . Embrace the power of visualization as a valuable tool for personal transformation and watch as it positively impacts your life.

Visualization for Performance Enhancement

Visualization is a powerful tool that can be utilized to enhance various aspects of performance. Whether you’re an athlete aiming to improve sports performance or an individual looking to enhance public speaking skills, incorporating visualization exercises into your routine can significantly impact your performance.

Improving Sports Performance

Visualization can be a game-changer for athletes looking to take their performance to the next level. By vividly imagining themselves successfully executing their desired movements, athletes can mentally rehearse and refine their skills. This technique helps to activate the neural pathways associated with the specific movements, enhancing muscle memory and coordination.

When visualizing sports performance, it’s essential to engage all the senses. Athletes can mentally recreate the sights, sounds, and even the feelings they experience during their sport. By doing so, they can effectively simulate the actual performance and prepare themselves mentally and emotionally.

For example, a basketball player can visualize shooting free throws with perfect form, hearing the sound of the ball swishing through the net and feeling the satisfaction of a successful shot. By repeating these mental rehearsals consistently, athletes can improve their focus, confidence, and overall performance on the field or court.

Enhancing Public Speaking Skills

Public speaking can be a nerve-wracking experience for many individuals. Visualization exercises can help ease anxiety, boost confidence, and improve overall public speaking skills. By visualizing themselves delivering a compelling and engaging speech, individuals can mentally prepare for the challenges they may face during a public speaking engagement.

When using visualization for public speaking, individuals can imagine themselves confidently standing on stage, speaking clearly and articulately, and captivating their audience. They can visualize the positive reactions from the listeners, such as nodding heads and engaged expressions. By repeatedly visualizing successful speaking engagements, individuals can reduce anxiety, increase self-assurance, and improve their overall delivery.

Visualization can also be used to mentally rehearse specific aspects of public speaking, such as maintaining eye contact, using gestures effectively, or managing stage fright. By incorporating these mental rehearsals into their preparation routine, individuals can enhance their performance and deliver impactful speeches with greater ease.

By harnessing the power of visualization, athletes can enhance their sports performance, and individuals can improve their public speaking skills. These visualization exercises provide an opportunity to mentally rehearse and prepare for success, boosting confidence and improving overall performance. Remember to incorporate visualization into your routine consistently to reap the full benefits.

Incorporating Visualization into Your Daily Routine

To truly harness the power of visualization, it’s important to make it a consistent part of your daily routine. By finding the right time and space and making visualization a habit, you can maximize the benefits of this powerful practice.

Finding the Right Time and Space

To engage in effective visualization exercises, it’s crucial to find a quiet and comfortable space where you can focus without distractions. Choose a location where you feel at ease and can fully immerse yourself in the visualization process.

The right time for visualization may vary for each individual. Some may find it beneficial to start their day with visualization exercises to set a positive tone for the day ahead. Others may prefer to incorporate visualization into their evening routine to unwind and relax. Experiment with different times of the day to determine what works best for you.

Consider using props or creating a dedicated space for visualization. For example, you could use soft lighting, calming scents, or soothing music to enhance the ambiance and create a conducive environment for visualization. Find what resonates with you and helps you enter a state of deep focus and relaxation.

Making Visualization a Habit

To truly reap the benefits of visualization, it’s important to make it a consistent habit. Here are some tips to help you incorporate visualization into your daily routine:

• Set aside dedicated time : Schedule a specific time slot each day for your visualization practice. Treat it as a non-negotiable appointment with yourself.
• Start small : Begin with shorter visualization sessions, gradually increasing the duration as you become more comfortable and experienced. Even just a few minutes of focused visualization can make a difference.
• Use reminders : Set reminders or alarms on your phone or use visual cues, such as sticky notes or symbols, to prompt yourself to engage in visualization.
• Combine visualization with other practices : Integrate visualization into other daily activities, such as meditation, journaling, or goal-setting exercises. This can help reinforce the habit and create a synergistic effect.
• Track your progress : Keep a visualization journal or use a habit tracker to monitor your consistency. Celebrate each small milestone and use it as motivation to continue your practice.

By making visualization a regular part of your routine, you will strengthen your ability to manifest your goals and desires. Visualization can become a powerful tool for personal growth and transformation.

Remember to check out our other articles on  journaling prompts ,  self-esteem worksheets ,  goal-setting worksheets , and other resources that can complement your visualization practice and support your personal development journey.

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7 Visual Frameworks for Strategy Analysis Presentation

Last Updated on March 4, 2024 by Rosemary

There are dozens of frameworks you can use for strategy analysis, from the classical SWOT model to the BCG matrix. The question is which one to choose and how to illustrate the strategy engagingly and understandably for your audience. As usual, the simplest way is the best 🙂

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Frameworks for Strategy Analysis and Planning

Below is the list of key tools used for strategic management. Starting with techniques for analyzing the current business situation and market opportunities and finishing with methods for planning the next company moves:

• SWOT analysis
• Porter’s Five Forces
• Business Review
• PEST and PESTEL analysis
• SMART goals
• Roadmaps for strategy planning

Choose the strategy model that fits your market and situation. We used those models in our business, however, we are not management consultants ourselves. But as presentation designers, we can advise you on how to present the selected model using simple diagrams .

Check out those books for entrepreneurs and managers , they will help you define the strategy you need and the tools to use.

In this article, you will find various ways to show and illustrate these strategy frameworks.

1. Business Review – visual summarizing KPIs and results

Have you ever thought that financial data can be interesting and not boring? 🙂 There is a way to make financial results more interesting, show sales, production, accounting data, and other KPIs in eye-catching visual form. What is more, the solution is simple: just add a few simple shapes and change plain numbers to colorful, simple infographics. Example of  business review visual slides

If you want to find more inspiration on making similar diagrams, check this blog article “ How to Make Attractive Annual Company Review “.

2. SWOT Analysis – diagrams for understanding strong and weak points

A SWOT analysis is a useful tool for brainstorming and strategic planning. You’ll get more value from a SWOT analysis if you conduct it with a specific objective or question in mind. The crucial step is to move away from usually busy SWOT findings notes to clean and eye-catchy slides presenting all SWOT areas. Illustration of  SWOT one-pager 

Do you need to add more details to your SWOT presentation? Reuse the same graphics. A slide costs you nothing so don’t be afraid to split busy slides into several ones. You can assign a color and symbol to each of the 4 SWOT areas to identify them in your presentation.

For more inspiration on using SWOT check this article with examples of how to grab attention to all issues of SWOT presentation.  If you prefer conducting your SWOT analysis online, there are also a bunch of mobile and cloud apps for personal or company SWOT as well.

3. PEST Analysis – testing your external environment

PEST analysis is commonly used in strategic and marketing planning or product development. If you are looking for more PEST visualizations, read our article on How to create a great PEST slide or presentation.

4. Porter’s Five Forces – a framework for identifying a company’s environment

Porter’s Five Forces is a simple but powerful tool for understanding where power lies in a business situation. This model helps you understand both the strength of your current competitive position and the strength of a position you’re considering moving into.

Here are some ideas on how to present Porter’s 5 forces creatively . You may also search for a more detailed explanation of how to analyze the competitive environment in this  article.

5. BCG Matrix – identifying customer segments

BCG matrix is designed to help a business consider growth opportunities by reviewing its portfolio of products to decide where to invest, discontinue, or develop products. More ideas on how to present the BCG matrix.

6. SMART Goals – ensuring  your objectives are clear and reachable

To set effective goals, use the S.M.A.R.T. method of defining them. If you present the goals in nice eye-catching ways, you can reach better engagement by your audience. Design templates of  SMART goals  benchmark tables

If you write your plans and targets in text only, people will not be eager to read and remind them often. On the other side, if you present them in a clear aesthetic way, people will remember them longer (we wrote more about it in this blog How to make SMART goals visually engaging).

7. Roadmaps – presenting a long-term vision

A well-designed strategic roadmap is like a GPS for your business . It’s one of the best tools to lift the fog and make your vision clear for everyone on the team.

Roadmap slide deck illustration for project planning

I recommend using those five steps  (Forbes article) to create an effective long-term or short-term strategy:

• Check where you are
• Prioritize what’s important
• What to achieve
• Who will do it, who’s accountable

Once you have it, it’s time to pack it into a nice engaging presentation design. See the blog  Three Creative Ways to Do a Roadmap slide .

Whatever your planning level and context are, the visual roadmap can be one of the best weapons in your communication arsenal.

Those are seven essential tools for strategic planning and implementation. Check specific framework graphics in the infoDiagram business diagrams collection to find what you need.

You may want to create your own slides and use more models than we suggested. For this purpose, we recently created an infographics do-it-yourself collection:  Flat Infographic Presentation Templates.

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Explore our blog to get ideas for Strategic Planning Presentations.

Conclusion – Make Your Strategy Visual

As you can see, all those strategy tools can be pretty easily visualized. Even if using plain simple PowerPoint shapes – 4 colorful rectangles for the matrix or a wide arrow for roadmaps.

Here’s what a professional management consultancy principal told us about using such visual frameworks in her work:

“As a management consultant, it is important for me to visually display my slides in a way that not only appeals to my clients, but also sets the quality of my work apart and gives more life to my message.”

Astrid Malval-Beharry from StratMaven Operations Consulting Firm

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What tool do you use the most in the strategic analysis? Drop us a line in the comments 🙂