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Understanding Data Presentations (Guide + Examples)

In this age of overwhelming information, the skill to effectively convey data has become extremely valuable. Initiating a discussion on data presentation types involves thoughtful consideration of the nature of your data and the message you aim to convey. Different types of visualizations serve distinct purposes. Whether you’re dealing with how to develop a report or simply trying to communicate complex information, how you present data influences how well your audience understands and engages with it. This extensive guide leads you through the different ways of data presentation.

Table of Contents

What is a Data Presentation?

What should a data presentation include, line graphs, treemap chart, scatter plot, how to choose a data presentation type, recommended data presentation templates, common mistakes done in data presentation.

A data presentation is a slide deck that aims to disclose quantitative information to an audience through the use of visual formats and narrative techniques derived from data analysis, making complex data understandable and actionable. This process requires a series of tools, such as charts, graphs, tables, infographics, dashboards, and so on, supported by concise textual explanations to improve understanding and boost retention rate.

Data presentations require us to cull data in a format that allows the presenter to highlight trends, patterns, and insights so that the audience can act upon the shared information. In a few words, the goal of data presentations is to enable viewers to grasp complicated concepts or trends quickly, facilitating informed decision-making or deeper analysis.

Data presentations go beyond the mere usage of graphical elements. Seasoned presenters encompass visuals with the art of data storytelling , so the speech skillfully connects the points through a narrative that resonates with the audience. Depending on the purpose – inspire, persuade, inform, support decision-making processes, etc. – is the data presentation format that is better suited to help us in this journey.

To nail your upcoming data presentation, ensure to count with the following elements:

• Clear Objectives: Understand the intent of your presentation before selecting the graphical layout and metaphors to make content easier to grasp.
• Engaging introduction: Use a powerful hook from the get-go. For instance, you can ask a big question or present a problem that your data will answer. Take a look at our guide on how to start a presentation for tips & insights.
• Structured Narrative: Your data presentation must tell a coherent story. This means a beginning where you present the context, a middle section in which you present the data, and an ending that uses a call-to-action. Check our guide on presentation structure for further information.
• Visual Elements: These are the charts, graphs, and other elements of visual communication we ought to use to present data. This article will cover one by one the different types of data representation methods we can use, and provide further guidance on choosing between them.
• Insights and Analysis: This is not just showcasing a graph and letting people get an idea about it. A proper data presentation includes the interpretation of that data, the reason why it’s included, and why it matters to your research.
• Conclusion & CTA: Ending your presentation with a call to action is necessary. Whether you intend to wow your audience into acquiring your services, inspire them to change the world, or whatever the purpose of your presentation, there must be a stage in which you convey all that you shared and show the path to staying in touch. Plan ahead whether you want to use a thank-you slide, a video presentation, or which method is apt and tailored to the kind of presentation you deliver.
• Q&A Session: After your speech is concluded, allocate 3-5 minutes for the audience to raise any questions about the information you disclosed. This is an extra chance to establish your authority on the topic. Check our guide on questions and answer sessions in presentations here.

Bar charts are a graphical representation of data using rectangular bars to show quantities or frequencies in an established category. They make it easy for readers to spot patterns or trends. Bar charts can be horizontal or vertical, although the vertical format is commonly known as a column chart. They display categorical, discrete, or continuous variables grouped in class intervals [1] . They include an axis and a set of labeled bars horizontally or vertically. These bars represent the frequencies of variable values or the values themselves. Numbers on the y-axis of a vertical bar chart or the x-axis of a horizontal bar chart are called the scale.

Real-Life Application of Bar Charts

Let’s say a sales manager is presenting sales to their audience. Using a bar chart, he follows these steps.

Step 1: Selecting Data

The first step is to identify the specific data you will present to your audience.

The sales manager has highlighted these products for the presentation.

• Product A: Men’s Shoes
• Product B: Women’s Apparel
• Product C: Electronics
• Product D: Home Decor

Step 2: Choosing Orientation

Opt for a vertical layout for simplicity. Vertical bar charts help compare different categories in case there are not too many categories [1] . They can also help show different trends. A vertical bar chart is used where each bar represents one of the four chosen products. After plotting the data, it is seen that the height of each bar directly represents the sales performance of the respective product.

It is visible that the tallest bar (Electronics – Product C) is showing the highest sales. However, the shorter bars (Women’s Apparel – Product B and Home Decor – Product D) need attention. It indicates areas that require further analysis or strategies for improvement.

Step 3: Colorful Insights

Different colors are used to differentiate each product. It is essential to show a color-coded chart where the audience can distinguish between products.

• Men’s Shoes (Product A): Yellow
• Women’s Apparel (Product B): Orange
• Electronics (Product C): Violet
• Home Decor (Product D): Blue

Bar charts are straightforward and easily understandable for presenting data. They are versatile when comparing products or any categorical data [2] . Bar charts adapt seamlessly to retail scenarios. Despite that, bar charts have a few shortcomings. They cannot illustrate data trends over time. Besides, overloading the chart with numerous products can lead to visual clutter, diminishing its effectiveness.

For more information, check our collection of bar chart templates for PowerPoint .

Line graphs help illustrate data trends, progressions, or fluctuations by connecting a series of data points called ‘markers’ with straight line segments. This provides a straightforward representation of how values change [5] . Their versatility makes them invaluable for scenarios requiring a visual understanding of continuous data. In addition, line graphs are also useful for comparing multiple datasets over the same timeline. Using multiple line graphs allows us to compare more than one data set. They simplify complex information so the audience can quickly grasp the ups and downs of values. From tracking stock prices to analyzing experimental results, you can use line graphs to show how data changes over a continuous timeline. They show trends with simplicity and clarity.

Real-life Application of Line Graphs

To understand line graphs thoroughly, we will use a real case. Imagine you’re a financial analyst presenting a tech company’s monthly sales for a licensed product over the past year. Investors want insights into sales behavior by month, how market trends may have influenced sales performance and reception to the new pricing strategy. To present data via a line graph, you will complete these steps.

First, you need to gather the data. In this case, your data will be the sales numbers. For example:

• January: $45,000
• February: $55,000
• March: $45,000
• April: $60,000
• May: $ 70,000
• June: $65,000
• July: $62,000
• August: $68,000
• September: $81,000
• October: $76,000
• November: $87,000
• December: $91,000

After choosing the data, the next step is to select the orientation. Like bar charts, you can use vertical or horizontal line graphs. However, we want to keep this simple, so we will keep the timeline (x-axis) horizontal while the sales numbers (y-axis) vertical.

Step 3: Connecting Trends

After adding the data to your preferred software, you will plot a line graph. In the graph, each month’s sales are represented by data points connected by a line.

Step 4: Adding Clarity with Color

If there are multiple lines, you can also add colors to highlight each one, making it easier to follow.

Line graphs excel at visually presenting trends over time. These presentation aids identify patterns, like upward or downward trends. However, too many data points can clutter the graph, making it harder to interpret. Line graphs work best with continuous data but are not suitable for categories.

For more information, check our collection of line chart templates for PowerPoint and our article about how to make a presentation graph .

A data dashboard is a visual tool for analyzing information. Different graphs, charts, and tables are consolidated in a layout to showcase the information required to achieve one or more objectives. Dashboards help quickly see Key Performance Indicators (KPIs). You don’t make new visuals in the dashboard; instead, you use it to display visuals you’ve already made in worksheets [3] .

Keeping the number of visuals on a dashboard to three or four is recommended. Adding too many can make it hard to see the main points [4]. Dashboards can be used for business analytics to analyze sales, revenue, and marketing metrics at a time. They are also used in the manufacturing industry, as they allow users to grasp the entire production scenario at the moment while tracking the core KPIs for each line.

Real-Life Application of a Dashboard

Consider a project manager presenting a software development project’s progress to a tech company’s leadership team. He follows the following steps.

Step 1: Defining Key Metrics

To effectively communicate the project’s status, identify key metrics such as completion status, budget, and bug resolution rates. Then, choose measurable metrics aligned with project objectives.

Step 2: Choosing Visualization Widgets

After finalizing the data, presentation aids that align with each metric are selected. For this project, the project manager chooses a progress bar for the completion status and uses bar charts for budget allocation. Likewise, he implements line charts for bug resolution rates.

Step 3: Dashboard Layout

Key metrics are prominently placed in the dashboard for easy visibility, and the manager ensures that it appears clean and organized.

Dashboards provide a comprehensive view of key project metrics. Users can interact with data, customize views, and drill down for detailed analysis. However, creating an effective dashboard requires careful planning to avoid clutter. Besides, dashboards rely on the availability and accuracy of underlying data sources.

For more information, check our article on how to design a dashboard presentation , and discover our collection of dashboard PowerPoint templates .

Treemap charts represent hierarchical data structured in a series of nested rectangles [6] . As each branch of the ‘tree’ is given a rectangle, smaller tiles can be seen representing sub-branches, meaning elements on a lower hierarchical level than the parent rectangle. Each one of those rectangular nodes is built by representing an area proportional to the specified data dimension.

Treemaps are useful for visualizing large datasets in compact space. It is easy to identify patterns, such as which categories are dominant. Common applications of the treemap chart are seen in the IT industry, such as resource allocation, disk space management, website analytics, etc. Also, they can be used in multiple industries like healthcare data analysis, market share across different product categories, or even in finance to visualize portfolios.

Real-Life Application of a Treemap Chart

Let’s consider a financial scenario where a financial team wants to represent the budget allocation of a company. There is a hierarchy in the process, so it is helpful to use a treemap chart. In the chart, the top-level rectangle could represent the total budget, and it would be subdivided into smaller rectangles, each denoting a specific department. Further subdivisions within these smaller rectangles might represent individual projects or cost categories.

Step 1: Define Your Data Hierarchy

While presenting data on the budget allocation, start by outlining the hierarchical structure. The sequence will be like the overall budget at the top, followed by departments, projects within each department, and finally, individual cost categories for each project.

• Top-level rectangle: Total Budget
• Second-level rectangles: Departments (Engineering, Marketing, Sales)
• Third-level rectangles: Projects within each department
• Fourth-level rectangles: Cost categories for each project (Personnel, Marketing Expenses, Equipment)

Step 2: Choose a Suitable Tool

It’s time to select a data visualization tool supporting Treemaps. Popular choices include Tableau, Microsoft Power BI, PowerPoint, or even coding with libraries like D3.js. It is vital to ensure that the chosen tool provides customization options for colors, labels, and hierarchical structures.

Here, the team uses PowerPoint for this guide because of its user-friendly interface and robust Treemap capabilities.

Step 3: Make a Treemap Chart with PowerPoint

After opening the PowerPoint presentation, they chose “SmartArt” to form the chart. The SmartArt Graphic window has a “Hierarchy” category on the left.  Here, you will see multiple options. You can choose any layout that resembles a Treemap. The “Table Hierarchy” or “Organization Chart” options can be adapted. The team selects the Table Hierarchy as it looks close to a Treemap.

Step 5: Input Your Data

After that, a new window will open with a basic structure. They add the data one by one by clicking on the text boxes. They start with the top-level rectangle, representing the total budget.  

Step 6: Customize the Treemap

By clicking on each shape, they customize its color, size, and label. At the same time, they can adjust the font size, style, and color of labels by using the options in the “Format” tab in PowerPoint. Using different colors for each level enhances the visual difference.

Treemaps excel at illustrating hierarchical structures. These charts make it easy to understand relationships and dependencies. They efficiently use space, compactly displaying a large amount of data, reducing the need for excessive scrolling or navigation. Additionally, using colors enhances the understanding of data by representing different variables or categories.

In some cases, treemaps might become complex, especially with deep hierarchies.  It becomes challenging for some users to interpret the chart. At the same time, displaying detailed information within each rectangle might be constrained by space. It potentially limits the amount of data that can be shown clearly. Without proper labeling and color coding, there’s a risk of misinterpretation.

A heatmap is a data visualization tool that uses color coding to represent values across a two-dimensional surface. In these, colors replace numbers to indicate the magnitude of each cell. This color-shaded matrix display is valuable for summarizing and understanding data sets with a glance [7] . The intensity of the color corresponds to the value it represents, making it easy to identify patterns, trends, and variations in the data.

As a tool, heatmaps help businesses analyze website interactions, revealing user behavior patterns and preferences to enhance overall user experience. In addition, companies use heatmaps to assess content engagement, identifying popular sections and areas of improvement for more effective communication. They excel at highlighting patterns and trends in large datasets, making it easy to identify areas of interest.

We can implement heatmaps to express multiple data types, such as numerical values, percentages, or even categorical data. Heatmaps help us easily spot areas with lots of activity, making them helpful in figuring out clusters [8] . When making these maps, it is important to pick colors carefully. The colors need to show the differences between groups or levels of something. And it is good to use colors that people with colorblindness can easily see.

Check our detailed guide on how to create a heatmap here. Also discover our collection of heatmap PowerPoint templates .

Pie charts are circular statistical graphics divided into slices to illustrate numerical proportions. Each slice represents a proportionate part of the whole, making it easy to visualize the contribution of each component to the total.

The size of the pie charts is influenced by the value of data points within each pie. The total of all data points in a pie determines its size. The pie with the highest data points appears as the largest, whereas the others are proportionally smaller. However, you can present all pies of the same size if proportional representation is not required [9] . Sometimes, pie charts are difficult to read, or additional information is required. A variation of this tool can be used instead, known as the donut chart , which has the same structure but a blank center, creating a ring shape. Presenters can add extra information, and the ring shape helps to declutter the graph.

Pie charts are used in business to show percentage distribution, compare relative sizes of categories, or present straightforward data sets where visualizing ratios is essential.

Real-Life Application of Pie Charts

Consider a scenario where you want to represent the distribution of the data. Each slice of the pie chart would represent a different category, and the size of each slice would indicate the percentage of the total portion allocated to that category.

Step 1: Define Your Data Structure

Imagine you are presenting the distribution of a project budget among different expense categories.

• Column A: Expense Categories (Personnel, Equipment, Marketing, Miscellaneous)
• Column B: Budget Amounts ($40,000, $30,000, $20,000, $10,000) Column B represents the values of your categories in Column A.

Step 2: Insert a Pie Chart

Using any of the accessible tools, you can create a pie chart. The most convenient tools for forming a pie chart in a presentation are presentation tools such as PowerPoint or Google Slides.  You will notice that the pie chart assigns each expense category a percentage of the total budget by dividing it by the total budget.

For instance:

• Personnel: $40,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 40%
• Equipment: $30,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 30%
• Marketing: $20,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 20%
• Miscellaneous: $10,000 / ($40,000 + $30,000 + $20,000 + $10,000) = 10%

You can make a chart out of this or just pull out the pie chart from the data.

3D pie charts and 3D donut charts are quite popular among the audience. They stand out as visual elements in any presentation slide, so let’s take a look at how our pie chart example would look in 3D pie chart format.

Step 03: Results Interpretation

The pie chart visually illustrates the distribution of the project budget among different expense categories. Personnel constitutes the largest portion at 40%, followed by equipment at 30%, marketing at 20%, and miscellaneous at 10%. This breakdown provides a clear overview of where the project funds are allocated, which helps in informed decision-making and resource management. It is evident that personnel are a significant investment, emphasizing their importance in the overall project budget.

Pie charts provide a straightforward way to represent proportions and percentages. They are easy to understand, even for individuals with limited data analysis experience. These charts work well for small datasets with a limited number of categories.

However, a pie chart can become cluttered and less effective in situations with many categories. Accurate interpretation may be challenging, especially when dealing with slight differences in slice sizes. In addition, these charts are static and do not effectively convey trends over time.

For more information, check our collection of pie chart templates for PowerPoint .

Histograms present the distribution of numerical variables. Unlike a bar chart that records each unique response separately, histograms organize numeric responses into bins and show the frequency of reactions within each bin [10] . The x-axis of a histogram shows the range of values for a numeric variable. At the same time, the y-axis indicates the relative frequencies (percentage of the total counts) for that range of values.

Whenever you want to understand the distribution of your data, check which values are more common, or identify outliers, histograms are your go-to. Think of them as a spotlight on the story your data is telling. A histogram can provide a quick and insightful overview if you’re curious about exam scores, sales figures, or any numerical data distribution.

Real-Life Application of a Histogram

In the histogram data analysis presentation example, imagine an instructor analyzing a class’s grades to identify the most common score range. A histogram could effectively display the distribution. It will show whether most students scored in the average range or if there are significant outliers.

Step 1: Gather Data

He begins by gathering the data. The scores of each student in class are gathered to analyze exam scores.

After arranging the scores in ascending order, bin ranges are set.

Step 2: Define Bins

Bins are like categories that group similar values. Think of them as buckets that organize your data. The presenter decides how wide each bin should be based on the range of the values. For instance, the instructor sets the bin ranges based on score intervals: 60-69, 70-79, 80-89, and 90-100.

Step 3: Count Frequency

Now, he counts how many data points fall into each bin. This step is crucial because it tells you how often specific ranges of values occur. The result is the frequency distribution, showing the occurrences of each group.

Here, the instructor counts the number of students in each category.

• 60-69: 1 student (Kate)
• 70-79: 4 students (David, Emma, Grace, Jack)
• 80-89: 7 students (Alice, Bob, Frank, Isabel, Liam, Mia, Noah)
• 90-100: 3 students (Clara, Henry, Olivia)

Step 4: Create the Histogram

It’s time to turn the data into a visual representation. Draw a bar for each bin on a graph. The width of the bar should correspond to the range of the bin, and the height should correspond to the frequency.  To make your histogram understandable, label the X and Y axes.

In this case, the X-axis should represent the bins (e.g., test score ranges), and the Y-axis represents the frequency.

The histogram of the class grades reveals insightful patterns in the distribution. Most students, with seven students, fall within the 80-89 score range. The histogram provides a clear visualization of the class’s performance. It showcases a concentration of grades in the upper-middle range with few outliers at both ends. This analysis helps in understanding the overall academic standing of the class. It also identifies the areas for potential improvement or recognition.

Thus, histograms provide a clear visual representation of data distribution. They are easy to interpret, even for those without a statistical background. They apply to various types of data, including continuous and discrete variables. One weak point is that histograms do not capture detailed patterns in students’ data, with seven compared to other visualization methods.

A scatter plot is a graphical representation of the relationship between two variables. It consists of individual data points on a two-dimensional plane. This plane plots one variable on the x-axis and the other on the y-axis. Each point represents a unique observation. It visualizes patterns, trends, or correlations between the two variables.

Scatter plots are also effective in revealing the strength and direction of relationships. They identify outliers and assess the overall distribution of data points. The points’ dispersion and clustering reflect the relationship’s nature, whether it is positive, negative, or lacks a discernible pattern. In business, scatter plots assess relationships between variables such as marketing cost and sales revenue. They help present data correlations and decision-making.

Real-Life Application of Scatter Plot

A group of scientists is conducting a study on the relationship between daily hours of screen time and sleep quality. After reviewing the data, they managed to create this table to help them build a scatter plot graph:

In the provided example, the x-axis represents Daily Hours of Screen Time, and the y-axis represents the Sleep Quality Rating.

The scientists observe a negative correlation between the amount of screen time and the quality of sleep. This is consistent with their hypothesis that blue light, especially before bedtime, has a significant impact on sleep quality and metabolic processes.

There are a few things to remember when using a scatter plot. Even when a scatter diagram indicates a relationship, it doesn’t mean one variable affects the other. A third factor can influence both variables. The more the plot resembles a straight line, the stronger the relationship is perceived [11] . If it suggests no ties, the observed pattern might be due to random fluctuations in data. When the scatter diagram depicts no correlation, whether the data might be stratified is worth considering.

Choosing the appropriate data presentation type is crucial when making a presentation . Understanding the nature of your data and the message you intend to convey will guide this selection process. For instance, when showcasing quantitative relationships, scatter plots become instrumental in revealing correlations between variables. If the focus is on emphasizing parts of a whole, pie charts offer a concise display of proportions. Histograms, on the other hand, prove valuable for illustrating distributions and frequency patterns. 

Bar charts provide a clear visual comparison of different categories. Likewise, line charts excel in showcasing trends over time, while tables are ideal for detailed data examination. Starting a presentation on data presentation types involves evaluating the specific information you want to communicate and selecting the format that aligns with your message. This ensures clarity and resonance with your audience from the beginning of your presentation.

1. Fact Sheet Dashboard for Data Presentation

Convey all the data you need to present in this one-pager format, an ideal solution tailored for users looking for presentation aids. Global maps, donut chats, column graphs, and text neatly arranged in a clean layout presented in light and dark themes.

Use This Template

2. 3D Column Chart Infographic PPT Template

Represent column charts in a highly visual 3D format with this PPT template. A creative way to present data, this template is entirely editable, and we can craft either a one-page infographic or a series of slides explaining what we intend to disclose point by point.

3. Data Circles Infographic PowerPoint Template

An alternative to the pie chart and donut chart diagrams, this template features a series of curved shapes with bubble callouts as ways of presenting data. Expand the information for each arch in the text placeholder areas.

4. Colorful Metrics Dashboard for Data Presentation

This versatile dashboard template helps us in the presentation of the data by offering several graphs and methods to convert numbers into graphics. Implement it for e-commerce projects, financial projections, project development, and more.

5. Animated Data Presentation Tools for PowerPoint & Google Slides

A slide deck filled with most of the tools mentioned in this article, from bar charts, column charts, treemap graphs, pie charts, histogram, etc. Animated effects make each slide look dynamic when sharing data with stakeholders.

6. Statistics Waffle Charts PPT Template for Data Presentations

This PPT template helps us how to present data beyond the typical pie chart representation. It is widely used for demographics, so it’s a great fit for marketing teams, data science professionals, HR personnel, and more.

7. Data Presentation Dashboard Template for Google Slides

A compendium of tools in dashboard format featuring line graphs, bar charts, column charts, and neatly arranged placeholder text areas. 

8. Weather Dashboard for Data Presentation

Share weather data for agricultural presentation topics, environmental studies, or any kind of presentation that requires a highly visual layout for weather forecasting on a single day. Two color themes are available.

9. Social Media Marketing Dashboard Data Presentation Template

Intended for marketing professionals, this dashboard template for data presentation is a tool for presenting data analytics from social media channels. Two slide layouts featuring line graphs and column charts.

10. Project Management Summary Dashboard Template

A tool crafted for project managers to deliver highly visual reports on a project’s completion, the profits it delivered for the company, and expenses/time required to execute it. 4 different color layouts are available.

11. Profit & Loss Dashboard for PowerPoint and Google Slides

A must-have for finance professionals. This typical profit & loss dashboard includes progress bars, donut charts, column charts, line graphs, and everything that’s required to deliver a comprehensive report about a company’s financial situation.

Overwhelming visuals

One of the mistakes related to using data-presenting methods is including too much data or using overly complex visualizations. They can confuse the audience and dilute the key message.

Inappropriate chart types

Choosing the wrong type of chart for the data at hand can lead to misinterpretation. For example, using a pie chart for data that doesn’t represent parts of a whole is not right.

Lack of context

Failing to provide context or sufficient labeling can make it challenging for the audience to understand the significance of the presented data.

Inconsistency in design

Using inconsistent design elements and color schemes across different visualizations can create confusion and visual disarray.

Failure to provide details

Simply presenting raw data without offering clear insights or takeaways can leave the audience without a meaningful conclusion.

Lack of focus

Not having a clear focus on the key message or main takeaway can result in a presentation that lacks a central theme.

Visual accessibility issues

Overlooking the visual accessibility of charts and graphs can exclude certain audience members who may have difficulty interpreting visual information.

In order to avoid these mistakes in data presentation, presenters can benefit from using presentation templates . These templates provide a structured framework. They ensure consistency, clarity, and an aesthetically pleasing design, enhancing data communication’s overall impact.

Understanding and choosing data presentation types are pivotal in effective communication. Each method serves a unique purpose, so selecting the appropriate one depends on the nature of the data and the message to be conveyed. The diverse array of presentation types offers versatility in visually representing information, from bar charts showing values to pie charts illustrating proportions. 

Using the proper method enhances clarity, engages the audience, and ensures that data sets are not just presented but comprehensively understood. By appreciating the strengths and limitations of different presentation types, communicators can tailor their approach to convey information accurately, developing a deeper connection between data and audience understanding.

[1] Government of Canada, S.C. (2021) 5 Data Visualization 5.2 Bar Chart , 5.2 Bar chart .  https://www150.statcan.gc.ca/n1/edu/power-pouvoir/ch9/bargraph-diagrammeabarres/5214818-eng.htm

[2] Kosslyn, S.M., 1989. Understanding charts and graphs. Applied cognitive psychology, 3(3), pp.185-225. https://apps.dtic.mil/sti/pdfs/ADA183409.pdf

[3] Creating a Dashboard . https://it.tufts.edu/book/export/html/1870

[4] https://www.goldenwestcollege.edu/research/data-and-more/data-dashboards/index.html

[5] https://www.mit.edu/course/21/21.guide/grf-line.htm

[6] Jadeja, M. and Shah, K., 2015, January. Tree-Map: A Visualization Tool for Large Data. In GSB@ SIGIR (pp. 9-13). https://ceur-ws.org/Vol-1393/gsb15proceedings.pdf#page=15

[7] Heat Maps and Quilt Plots. https://www.publichealth.columbia.edu/research/population-health-methods/heat-maps-and-quilt-plots

[8] EIU QGIS WORKSHOP. https://www.eiu.edu/qgisworkshop/heatmaps.php

[9] About Pie Charts.  https://www.mit.edu/~mbarker/formula1/f1help/11-ch-c8.htm

[10] Histograms. https://sites.utexas.edu/sos/guided/descriptive/numericaldd/descriptiven2/histogram/ [11] https://asq.org/quality-resources/scatter-diagram

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Present Your Data Like a Pro

• Joel Schwartzberg

Demystify the numbers. Your audience will thank you.

While a good presentation has data, data alone doesn’t guarantee a good presentation. It’s all about how that data is presented. The quickest way to confuse your audience is by sharing too many details at once. The only data points you should share are those that significantly support your point — and ideally, one point per chart. To avoid the debacle of sheepishly translating hard-to-see numbers and labels, rehearse your presentation with colleagues sitting as far away as the actual audience would. While you’ve been working with the same chart for weeks or months, your audience will be exposed to it for mere seconds. Give them the best chance of comprehending your data by using simple, clear, and complete language to identify X and Y axes, pie pieces, bars, and other diagrammatic elements. Try to avoid abbreviations that aren’t obvious, and don’t assume labeled components on one slide will be remembered on subsequent slides. Every valuable chart or pie graph has an “Aha!” zone — a number or range of data that reveals something crucial to your point. Make sure you visually highlight the “Aha!” zone, reinforcing the moment by explaining it to your audience.

With so many ways to spin and distort information these days, a presentation needs to do more than simply share great ideas — it needs to support those ideas with credible data. That’s true whether you’re an executive pitching new business clients, a vendor selling her services, or a CEO making a case for change.

• JS Joel Schwartzberg oversees executive communications for a major national nonprofit, is a professional presentation coach, and is the author of Get to the Point! Sharpen Your Message and Make Your Words Matter and The Language of Leadership: How to Engage and Inspire Your Team . You can find him on LinkedIn and X. TheJoelTruth

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Unit 2: Displaying and comparing quantitative data

About this unit.

Can you measure it with numbers? Then it's quantitative data! This unit covers some basic methods for graphing distributions of quantitative data like dot plots, histograms, and stem and leaf plots. We'll also explore how to use those displays to compare the features of different distributions.

Displaying quantitative data with graphs

• Representing data (Opens a modal)
• Frequency tables & dot plots (Opens a modal)
• Dot plots and frequency tables review (Opens a modal)
• Creating a histogram (Opens a modal)
• Histograms (Opens a modal)
• Interpreting a histogram (Opens a modal)
• Histograms review (Opens a modal)
• Stem-and-leaf plots (Opens a modal)
• Reading stem and leaf plots (Opens a modal)
• Stem and leaf plots review (Opens a modal)
• Creating frequency tables Get 3 of 4 questions to level up!
• Creating dot plots Get 3 of 4 questions to level up!
• Reading dot plots & frequency tables Get 3 of 4 questions to level up!
• Create histograms Get 3 of 4 questions to level up!
• Read histograms Get 3 of 4 questions to level up!
• Reading stem and leaf plots Get 3 of 4 questions to level up!

Describing and comparing distributions

• Shapes of distributions (Opens a modal)
• Clusters, gaps, peaks & outliers (Opens a modal)
• Comparing distributions with dot plots (example problem) (Opens a modal)
• Comparing dot plots, histograms, and box plots (Opens a modal)
• Example: Comparing distributions (Opens a modal)
• Shape of distributions Get 3 of 4 questions to level up!
• Clusters, gaps, & peaks in data distributions Get 5 of 7 questions to level up!
• Comparing distributions Get 3 of 4 questions to level up!
• Comparing data displays Get 3 of 4 questions to level up!
• Comparing data distributions Get 3 of 4 questions to level up!
• Comparing center and spread Get 5 of 7 questions to level up!

More on data displays

• Reading line graphs (Opens a modal)
• Misleading line graphs (Opens a modal)

Quantitative Data Analysis 101

The lingo, methods and techniques, explained simply.

By: Derek Jansen (MBA)  and Kerryn Warren (PhD) | December 2020

Quantitative data analysis is one of those things that often strikes fear in students. It’s totally understandable – quantitative analysis is a complex topic, full of daunting lingo , like medians, modes, correlation and regression. Suddenly we’re all wishing we’d paid a little more attention in math class…

The good news is that while quantitative data analysis is a mammoth topic, gaining a working understanding of the basics isn’t that hard , even for those of us who avoid numbers and math . In this post, we’ll break quantitative analysis down into simple , bite-sized chunks so you can approach your research with confidence.

Overview: Quantitative Data Analysis 101

• What (exactly) is quantitative data analysis?
• When to use quantitative analysis
• How quantitative analysis works

The two “branches” of quantitative analysis

• Descriptive statistics 101
• Inferential statistics 101
• How to choose the right quantitative methods
• Recap & summary

What is quantitative data analysis?

Despite being a mouthful, quantitative data analysis simply means analysing data that is numbers-based – or data that can be easily “converted” into numbers without losing any meaning.

For example, category-based variables like gender, ethnicity, or native language could all be “converted” into numbers without losing meaning – for example, English could equal 1, French 2, etc.

This contrasts against qualitative data analysis, where the focus is on words, phrases and expressions that can’t be reduced to numbers. If you’re interested in learning about qualitative analysis, check out our post and video here .

What is quantitative analysis used for?

Quantitative analysis is generally used for three purposes.

• Firstly, it’s used to measure differences between groups . For example, the popularity of different clothing colours or brands.
• Secondly, it’s used to assess relationships between variables . For example, the relationship between weather temperature and voter turnout.
• And third, it’s used to test hypotheses in a scientifically rigorous way. For example, a hypothesis about the impact of a certain vaccine.

Again, this contrasts with qualitative analysis , which can be used to analyse people’s perceptions and feelings about an event or situation. In other words, things that can’t be reduced to numbers.

How does quantitative analysis work?

Well, since quantitative data analysis is all about analysing numbers , it’s no surprise that it involves statistics . Statistical analysis methods form the engine that powers quantitative analysis, and these methods can vary from pretty basic calculations (for example, averages and medians) to more sophisticated analyses (for example, correlations and regressions).

Sounds like gibberish? Don’t worry. We’ll explain all of that in this post. Importantly, you don’t need to be a statistician or math wiz to pull off a good quantitative analysis. We’ll break down all the technical mumbo jumbo in this post.

Need a helping hand?

As I mentioned, quantitative analysis is powered by statistical analysis methods . There are two main “branches” of statistical methods that are used – descriptive statistics and inferential statistics . In your research, you might only use descriptive statistics, or you might use a mix of both , depending on what you’re trying to figure out. In other words, depending on your research questions, aims and objectives . I’ll explain how to choose your methods later.

So, what are descriptive and inferential statistics?

Well, before I can explain that, we need to take a quick detour to explain some lingo. To understand the difference between these two branches of statistics, you need to understand two important words. These words are population and sample .

First up, population . In statistics, the population is the entire group of people (or animals or organisations or whatever) that you’re interested in researching. For example, if you were interested in researching Tesla owners in the US, then the population would be all Tesla owners in the US.

However, it’s extremely unlikely that you’re going to be able to interview or survey every single Tesla owner in the US. Realistically, you’ll likely only get access to a few hundred, or maybe a few thousand owners using an online survey. This smaller group of accessible people whose data you actually collect is called your sample .

So, to recap – the population is the entire group of people you’re interested in, and the sample is the subset of the population that you can actually get access to. In other words, the population is the full chocolate cake , whereas the sample is a slice of that cake.

So, why is this sample-population thing important?

Well, descriptive statistics focus on describing the sample , while inferential statistics aim to make predictions about the population, based on the findings within the sample. In other words, we use one group of statistical methods – descriptive statistics – to investigate the slice of cake, and another group of methods – inferential statistics – to draw conclusions about the entire cake. There I go with the cake analogy again…

With that out the way, let’s take a closer look at each of these branches in more detail.

Branch 1: Descriptive Statistics

Descriptive statistics serve a simple but critically important role in your research – to describe your data set – hence the name. In other words, they help you understand the details of your sample . Unlike inferential statistics (which we’ll get to soon), descriptive statistics don’t aim to make inferences or predictions about the entire population – they’re purely interested in the details of your specific sample .

When you’re writing up your analysis, descriptive statistics are the first set of stats you’ll cover, before moving on to inferential statistics. But, that said, depending on your research objectives and research questions , they may be the only type of statistics you use. We’ll explore that a little later.

So, what kind of statistics are usually covered in this section?

Some common statistical tests used in this branch include the following:

• Mean – this is simply the mathematical average of a range of numbers.
• Median – this is the midpoint in a range of numbers when the numbers are arranged in numerical order. If the data set makes up an odd number, then the median is the number right in the middle of the set. If the data set makes up an even number, then the median is the midpoint between the two middle numbers.
• Mode – this is simply the most commonly occurring number in the data set.
• In cases where most of the numbers are quite close to the average, the standard deviation will be relatively low.
• Conversely, in cases where the numbers are scattered all over the place, the standard deviation will be relatively high.
• Skewness . As the name suggests, skewness indicates how symmetrical a range of numbers is. In other words, do they tend to cluster into a smooth bell curve shape in the middle of the graph, or do they skew to the left or right?

Feeling a bit confused? Let’s look at a practical example using a small data set.

On the left-hand side is the data set. This details the bodyweight of a sample of 10 people. On the right-hand side, we have the descriptive statistics. Let’s take a look at each of them.

First, we can see that the mean weight is 72.4 kilograms. In other words, the average weight across the sample is 72.4 kilograms. Straightforward.

Next, we can see that the median is very similar to the mean (the average). This suggests that this data set has a reasonably symmetrical distribution (in other words, a relatively smooth, centred distribution of weights, clustered towards the centre).

In terms of the mode , there is no mode in this data set. This is because each number is present only once and so there cannot be a “most common number”. If there were two people who were both 65 kilograms, for example, then the mode would be 65.

Next up is the standard deviation . 10.6 indicates that there’s quite a wide spread of numbers. We can see this quite easily by looking at the numbers themselves, which range from 55 to 90, which is quite a stretch from the mean of 72.4.

And lastly, the skewness of -0.2 tells us that the data is very slightly negatively skewed. This makes sense since the mean and the median are slightly different.

As you can see, these descriptive statistics give us some useful insight into the data set. Of course, this is a very small data set (only 10 records), so we can’t read into these statistics too much. Also, keep in mind that this is not a list of all possible descriptive statistics – just the most common ones.

But why do all of these numbers matter?

While these descriptive statistics are all fairly basic, they’re important for a few reasons:

• Firstly, they help you get both a macro and micro-level view of your data. In other words, they help you understand both the big picture and the finer details.
• Secondly, they help you spot potential errors in the data – for example, if an average is way higher than you’d expect, or responses to a question are highly varied, this can act as a warning sign that you need to double-check the data.
• And lastly, these descriptive statistics help inform which inferential statistical techniques you can use, as those techniques depend on the skewness (in other words, the symmetry and normality) of the data.

Simply put, descriptive statistics are really important , even though the statistical techniques used are fairly basic. All too often at Grad Coach, we see students skimming over the descriptives in their eagerness to get to the more exciting inferential methods, and then landing up with some very flawed results.

Don’t be a sucker – give your descriptive statistics the love and attention they deserve!

Branch 2: Inferential Statistics

As I mentioned, while descriptive statistics are all about the details of your specific data set – your sample – inferential statistics aim to make inferences about the population . In other words, you’ll use inferential statistics to make predictions about what you’d expect to find in the full population.

What kind of predictions, you ask? Well, there are two common types of predictions that researchers try to make using inferential stats:

• Firstly, predictions about differences between groups – for example, height differences between children grouped by their favourite meal or gender.
• And secondly, relationships between variables – for example, the relationship between body weight and the number of hours a week a person does yoga.

In other words, inferential statistics (when done correctly), allow you to connect the dots and make predictions about what you expect to see in the real world population, based on what you observe in your sample data. For this reason, inferential statistics are used for hypothesis testing – in other words, to test hypotheses that predict changes or differences.

Of course, when you’re working with inferential statistics, the composition of your sample is really important. In other words, if your sample doesn’t accurately represent the population you’re researching, then your findings won’t necessarily be very useful.

For example, if your population of interest is a mix of 50% male and 50% female , but your sample is 80% male , you can’t make inferences about the population based on your sample, since it’s not representative. This area of statistics is called sampling, but we won’t go down that rabbit hole here (it’s a deep one!) – we’ll save that for another post .

What statistics are usually used in this branch?

There are many, many different statistical analysis methods within the inferential branch and it’d be impossible for us to discuss them all here. So we’ll just take a look at some of the most common inferential statistical methods so that you have a solid starting point.

First up are T-Tests . T-tests compare the means (the averages) of two groups of data to assess whether they’re statistically significantly different. In other words, do they have significantly different means, standard deviations and skewness.

This type of testing is very useful for understanding just how similar or different two groups of data are. For example, you might want to compare the mean blood pressure between two groups of people – one that has taken a new medication and one that hasn’t – to assess whether they are significantly different.

Kicking things up a level, we have ANOVA, which stands for “analysis of variance”. This test is similar to a T-test in that it compares the means of various groups, but ANOVA allows you to analyse multiple groups , not just two groups So it’s basically a t-test on steroids…

Next, we have correlation analysis . This type of analysis assesses the relationship between two variables. In other words, if one variable increases, does the other variable also increase, decrease or stay the same. For example, if the average temperature goes up, do average ice creams sales increase too? We’d expect some sort of relationship between these two variables intuitively , but correlation analysis allows us to measure that relationship scientifically .

Lastly, we have regression analysis – this is quite similar to correlation in that it assesses the relationship between variables, but it goes a step further to understand cause and effect between variables, not just whether they move together. In other words, does the one variable actually cause the other one to move, or do they just happen to move together naturally thanks to another force? Just because two variables correlate doesn’t necessarily mean that one causes the other.

Stats overload…

I hear you. To make this all a little more tangible, let’s take a look at an example of a correlation in action.

Here’s a scatter plot demonstrating the correlation (relationship) between weight and height. Intuitively, we’d expect there to be some relationship between these two variables, which is what we see in this scatter plot. In other words, the results tend to cluster together in a diagonal line from bottom left to top right.

As I mentioned, these are are just a handful of inferential techniques – there are many, many more. Importantly, each statistical method has its own assumptions and limitations .

For example, some methods only work with normally distributed (parametric) data, while other methods are designed specifically for non-parametric data. And that’s exactly why descriptive statistics are so important – they’re the first step to knowing which inferential techniques you can and can’t use.

How to choose the right analysis method

To choose the right statistical methods, you need to think about two important factors :

• The type of quantitative data you have (specifically, level of measurement and the shape of the data). And,
• Your research questions and hypotheses

Let’s take a closer look at each of these.

Factor 1 – Data type

The first thing you need to consider is the type of data you’ve collected (or the type of data you will collect). By data types, I’m referring to the four levels of measurement – namely, nominal, ordinal, interval and ratio. If you’re not familiar with this lingo, check out the video below.

Why does this matter?

Well, because different statistical methods and techniques require different types of data. This is one of the “assumptions” I mentioned earlier – every method has its assumptions regarding the type of data.

For example, some techniques work with categorical data (for example, yes/no type questions, or gender or ethnicity), while others work with continuous numerical data (for example, age, weight or income) – and, of course, some work with multiple data types.

If you try to use a statistical method that doesn’t support the data type you have, your results will be largely meaningless . So, make sure that you have a clear understanding of what types of data you’ve collected (or will collect). Once you have this, you can then check which statistical methods would support your data types here .

If you haven’t collected your data yet, you can work in reverse and look at which statistical method would give you the most useful insights, and then design your data collection strategy to collect the correct data types.

Another important factor to consider is the shape of your data . Specifically, does it have a normal distribution (in other words, is it a bell-shaped curve, centred in the middle) or is it very skewed to the left or the right? Again, different statistical techniques work for different shapes of data – some are designed for symmetrical data while others are designed for skewed data.

This is another reminder of why descriptive statistics are so important – they tell you all about the shape of your data.

Factor 2: Your research questions

The next thing you need to consider is your specific research questions, as well as your hypotheses (if you have some). The nature of your research questions and research hypotheses will heavily influence which statistical methods and techniques you should use.

If you’re just interested in understanding the attributes of your sample (as opposed to the entire population), then descriptive statistics are probably all you need. For example, if you just want to assess the means (averages) and medians (centre points) of variables in a group of people.

On the other hand, if you aim to understand differences between groups or relationships between variables and to infer or predict outcomes in the population, then you’ll likely need both descriptive statistics and inferential statistics.

So, it’s really important to get very clear about your research aims and research questions, as well your hypotheses – before you start looking at which statistical techniques to use.

Never shoehorn a specific statistical technique into your research just because you like it or have some experience with it. Your choice of methods must align with all the factors we’ve covered here.

Time to recap…

You’re still with me? That’s impressive. We’ve covered a lot of ground here, so let’s recap on the key points:

• Quantitative data analysis is all about  analysing number-based data  (which includes categorical and numerical data) using various statistical techniques.
• The two main  branches  of statistics are  descriptive statistics  and  inferential statistics . Descriptives describe your sample, whereas inferentials make predictions about what you’ll find in the population.
• Common  descriptive statistical methods include  mean  (average),  median , standard  deviation  and  skewness .
• Common  inferential statistical methods include  t-tests ,  ANOVA ,  correlation  and  regression  analysis.
• To choose the right statistical methods and techniques, you need to consider the  type of data you’re working with , as well as your  research questions  and hypotheses.

Psst... there’s more!

This post was based on one of our popular Research Bootcamps . If you're working on a research project, you'll definitely want to check this out ...

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75 Comments

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2.2: Quantitative Data

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• Kathryn Kozak
• Coconino Community College

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The graph for quantitative data looks similar to a bar graph, except there are some major differences. First, in a bar graph the categories can be put in any order on the horizontal axis. There is no set order for these data values. You can’t say how the data is distributed based on the shape, since the shape can change just by putting the categories in different orders. With quantitative data, the data are in specific orders, since you are dealing with numbers. With quantitative data, you can talk about a distribution, since the shape only changes a little bit depending on how many categories you set up. This is called a frequency distribution .

This leads to the second difference from bar graphs. In a bar graph, the categories that you made in the frequency table were determined by you. In quantitative data, the categories are numerical categories, and the numbers are determined by how many categories (or what are called classes) you choose. If two people have the same number of categories, then they will have the same frequency distribution. Whereas in qualitative data, there can be many different categories depending on the point of view of the author.

The third difference is that the categories touch with quantitative data, and there will be no gaps in the graph. The reason that bar graphs have gaps is to show that the categories do not continue on, like they do in quantitative data. Since the graph for quantitative data is different from qualitative data, it is given a new name. The name of the graph is a histogram . To create a histogram, you must first create the frequency distribution. The idea of a frequency distribution is to take the interval that the data spans and divide it up into equal subintervals called classes.

Summary of the Steps Involved in Making a Frequency Distribution

• Find the range = largest value – smallest value
• Pick the number of classes to use. Usually the number of classes is between five and twenty. Five classes are used if there are a small number of data points and twenty classes if there are a large number of data points (over 1000 data points). (Note: categories will now be called classes from now on.)
• Class width = \(\dfrac{\text { range }}{\# \text { classes }}\) Always round up to the next integer (even if the answer is already a whole number go to the next integer). If you don’t do this, your last class will not contain your largest data value, and you would have to add another class just for it. If you round up, then your largest data value will fall in the last class, and there are no issues.
• Create the classes. Each class has limits that determine which values fall in each class. To find the class limits, set the smallest value as the lower class limit for the first class. Then add the class width to the lower class limit to get the next lower class limit. Repeat until you get all the classes. The upper class limit for a class is one less than the lower limit for the next class.
• In order for the classes to actually touch, then one class needs to start where the previous one ends. This is known as the class boundary. To find the class boundaries, subtract 0.5 from the lower class limit and add 0.5 to the upper class limit.
• Sometimes it is useful to find the class midpoint. The process is Midpoint \(=\dfrac{\text { lower limit +upper limit }}{2}\)
• To figure out the number of data points that fall in each class, go through each data value and see which class boundaries it is between. Utilizing tally marks may be helpful in counting the data values. The frequency for a class is the number of data values that fall in the class.

The above description is for data values that are whole numbers. If you data value has decimal places, then your class width should be rounded up to the nearest value with the same number of decimal places as the original data. In addition, your class boundaries should have one more decimal place than the original data. As an example, if your data have one decimal place, then the class width would have one decimal place, and the class boundaries are formed by adding and subtracting 0.05 from each class limit.

Example \(\PageIndex{1}\) creating a frequency table

Example \(\PageIndex{1}\) contains the amount of rent paid every month for 24 students from a statistics course. Make a relative frequency distribution using 7 classes.

• Find the range: largest value - smallest value \(= 2550-350=2200\)
• Pick the number of classes: The directions to say to use 7 classes.
• Find the class width: width \(=\dfrac{\text { range }}{7}=\dfrac{2200}{7} \approx 314.286\) Round up to 315 \(\color{text}{Always round up to the next integer even if the width is already an integer.}\)
• Find the class limits: Start at the smallest value. This is the lower class limit for the first class. Add the width to get the lower limit of the next class. Keep adding the width to get all the lower limits. \(350+315=665,665+315=980,980+315=1295 \rightleftharpoons\), The upper limit is one less than the next lower limit: so for the first class the upper class limit would be \(665-1=664\). When you have all 7 classes, make sure the last number, in this case the 2550, is at least as large as the largest value in the data. If not, you made a mistake somewhere.
• Find the class boundaries: Subtract 0.5 from the lower class limit to get the class boundaries. Add 0.5 to the upper class limit for the last class's boundary. \(350-0.5=349.5, \quad 665-0.5=664.5,\quad 980-0.5=979.5, \quad 1295-0.5=1294.5 \rightleftharpoons\) Every value in the data should fall into exactly one of the classes. No data values should fall right on the boundary of two classes.
• Find the class midpoints: midpoint \(=\dfrac{\text { lower limit }+\text { upper limit }}{2}\) \(\dfrac{350+664}{2}=507, \dfrac{665+979}{2}=822, \rightleftharpoons\)
• Tally and find the frequency of the data: Go through the data and put a tally mark in the appropriate class for each piece of data by looking to see which class boundaries the data value is between. Fill in the frequency by changing each of the tallies into a number.

Make sure the total of the frequencies is the same as the number of data points.

R command for a frequency distribution:

To create a frequency distribution:

summary(variable) – so you can find out the minimum and maximum.

breaks = seq(min, number above max, by = class width)

breaks – so you can see the breaks that R made.

variable.cut=cut(variable, breaks, right=FALSE) – this will cut up the data into the classes.

variable.freq=table(variable.cut) – this will create the frequency table.

variable.freq – this will display the frequency table.

For the data in Example \(\PageIndex{1}\), the R command would be:

rent<-c(1500, 1350, 350, 1200, 850, 900, 1500, 1150, 1500, 900, 1400, 1100, 1250, 600, 610, 960, 890, 1325, 900, 800, 2550, 495, 1200, 690) summary(rent)

\(\begin{array}{cccccc}{\text{Min} }&{1\text{st Qu.}}& {\text{Median}} & {\text{Mean}} & {3\text{rd Qu.}} & {\text{Max}} \\ {350} & {837.5} & {1030 .0} & {1082.0} & {1331.0} & {2550 .0} \end{array}\)

breaks=seq(350, 3000, by = 315) breaks

Output: [1] 350 665 980 1295 1610 1925 2240 2555 2870 These are your lower limits of the frequency distribution. You can now write your own table.

rent.cut=cut(rent, breaks, right=FALSE) rent.freq=table(rent.cut)

Output: rent.cut

\(\begin{array}{cccccccc}{[350,665)} & {[665,980)} & {[980,1.3 e+03)} & {[1.3e+03, 1.61e+03)} & {[1.61e+03, 1.92e+03)} & {[1.92e+03, 2.24e+03)} & {[2.24e+03, 2.56e+03)} & {[2.56e+03, 2.87e+03)} \\ {4} & {8} & {5} & {6}& {0} & {0} & {1} & {0}\end{array}\)

It is difficult to determine the basic shape of the distribution by looking at the frequency distribution. It would be easier to look at a graph. The graph of a frequency distribution for quantitative data is called a frequency histogram or just histogram for short.

Definition \(\PageIndex{1}\): Histogram

A Histogram is a graph of the frequencies on the vertical axis and the class boundaries on the horizontal axis. Rectangles where the height is the frequency and the width is the class width are drawn for each class.

Example \(\PageIndex{2}\: Drawing a Histogram

Draw a histogram for the distribution from Example \(\PageIndex{1}\).

The class boundaries are plotted on the horizontal axis and the frequencies are plotted on the vertical axis. You can plot the midpoints of the classes instead of the class boundaries. Graph 2.2.1 was created using the midpoints because it was easier to do with the software that created the graph. On R, the command is

hist(variable, col="type in what color you want", breaks, main="type the title you want", xlab="type the label you want for the horizontal axis", ylim=c(0, number above maximum frequency) – produces histogram with specified color and using the breaks you made for the frequency distribution.

For this example, the command in R would be (assuming you created a frequency distribution in R as described previously):

hist(rent, col="blue", breaks, right=FALSE, main="Monthly Rent Paid by Students", ylim=c(0,8) xlab="Monthly Rent ($)")

If no frequency distribution was created before the histogram, then the command would be:

hist(variable, col="type in what color you want", number of classes, main="type the title you want", xlab="type the label you want for the horizontal axis") – produces histogram with specified color and number of classes (though the number of classes is an estimate and R will create the number of classes near this value).

For this example, the R command without a frequency distribution created first would be:

hist(rent, col="blue", 7, main="Monthly Rent Paid by Students", xlab="Monthly Rent ($)")

Notice the graph has the axes labeled, the tick marks are labeled on each axis, and there is a title.

Reviewing the graph you can see that most of the students pay around $750 per month for rent, with about $1500 being the other common value. You can see from the graph, that most students pay between $600 and $1600 per month for rent. Of course, these values are just estimates from the graph. There is a large gap between the $1500 class and the highest data value. This seems to say that one student is paying a great deal more than everyone else. This value could be considered an outlier. An outlier is a data value that is far from the rest of the values. It may be an unusual value or a mistake. It is a data value that should be investigated. In this case, the student lives in a very expensive part of town, thus the value is not a mistake, and is just very unusual. There are other aspects that can be discussed, but first some other concepts need to be introduced.

Frequencies are helpful, but understanding the relative size each class is to the total is also useful. To find this you can divide the frequency by the total to create a relative frequency. If you have the relative frequencies for all of the classes, then you have a relative frequency distribution.

Definition \(\PageIndex{2}\)

Relative Frequency Distribution

A variation on a frequency distribution is a relative frequency distribution. Instead of giving the frequencies for each class, the relative frequencies are calculated.

Relative frequency \(=\dfrac{\text { frequency }}{\# \text { of data points }}\)

This gives you percentages of data that fall in each class.

Example \(\PageIndex{3}\) creating a relative frequency table

Find the relative frequency for the grade data.

From Example \(\PageIndex{1}\), the frequency distribution is reproduced in Example \(\PageIndex{2}\).

Divide each frequency by the number of data points.

\(\dfrac{4}{24}=0.17, \dfrac{8}{24}=0.33, \dfrac{5}{24}=0.21, \rightleftharpoons\)

The relative frequencies should add up to 1 or 100%. (This might be off a little due to rounding errors.)

The graph of the relative frequency is known as a relative frequency histogram. It looks identical to the frequency histogram, but the vertical axis is relative frequency instead of just frequencies.

Example \(\PageIndex{4}\) drawing a relative frequency histogram

Draw a relative frequency histogram for the grade distribution from Example \(\PageIndex{1}\).

The class boundaries are plotted on the horizontal axis and the relative frequencies are plotted on the vertical axis. (This is not easy to do in R, so use another technology to graph a relative frequency histogram.)

Notice the shape is the same as the frequency distribution.

Another useful piece of information is how many data points fall below a particular class boundary. As an example, a teacher may want to know how many students received below an 80%, a doctor may want to know how many adults have cholesterol below 160, or a manager may want to know how many stores gross less than $2000 per day. This is known as a cumulative frequency . If you want to know what percent of the data falls below a certain class boundary, then this would be a cumulative relative frequency . For cumulative frequencies you are finding how many data values fall below the upper class limit.

To create a cumulative frequency distribution , count the number of data points that are below the upper class boundary, starting with the first class and working up to the top class. The last upper class boundary should have all of the data points below it. Also include the number of data points below the lowest class boundary, which is zero.

Example \(\PageIndex{5}\) creating a cumulative frequency distribution

Create a cumulative frequency distribution for the data in Example \(\PageIndex{1}\).

The frequency distribution for the data is in Example \(\PageIndex{2}\).

Now ask yourself how many data points fall below each class boundary. Below 349.5, there are 0 data points. Below 664.5 there are 4 data points, below 979.5, there are 4 + 8 = 12 data points, below 1294.5 there are 4 + 8 + 5 = 17 data points, and continue this process until you reach the upper class boundary. This is summarized in Example \(\PageIndex{4}\).

To produce cumulative frequencies in R, you need to have performed the commands for the frequency distribution. Once you have complete that, then use variable.cumfreq=cumsum(variable.freq) – creates the cumulative frequencies for the variable cumfreq0=c(0,variable.cumfreq) – creates a cumulative frequency table for the variable. cumfreq0 – displays the cumulative frequency table.

For this example the command would be: rent.cumfreq=cumsum(rent.freq) cumfreq0=c(0,rent.cumfreq) cumfreq0

\(\begin{array}{ccccccccc}{}&{[350,665)} & {[665,980)} & {[980,1.3e+03)}& {[1.3e+03, 1.61e+03)}&{[1.61e+03, 1.92e+03)}&{[1.92e+03,2.24e+03)}&{[2.24e+03, 2.56e+03)}&{[2.56e+03, 2.87e+03)} \\ {0}&{4} & {12}&{17}&{23}&{23}&{23}&{24}&{24}\end{array}\)

Now type this into a table. See Example \(\PageIndex{4}\).

Again, it is hard to look at the data the way it is. A graph would be useful. The graph for cumulative frequency is called an ogive (o-jive). To create an ogive, first create a scale on both the horizontal and vertical axes that will fit the data. Then plot the points of the class upper class boundary versus the cumulative frequency. Make sure you include the point with the lowest class boundary and the 0 cumulative frequency. Then just connect the dots.

Example \(\PageIndex{6}\) drawing an ogive

Draw an ogive for the data in Example \(\PageIndex{1}\).

In R, the commands would be: plot(breaks,cumfreq0, main="title you want to use", xlab="label you want to use", ylab="label you want to use", ylim=c(0, number above maximum cumulative frequency) – plots the ogive lines(breaks,cumfreq0) – connects the dots on the ogive

For this example, the commands would be: Plot(breaks,cumfreq0, main=”Cumulative Frequency for Monthly Rent”, xlab=”Monthly Rent ($)”, ylab=”Cumulative Frequency”, ylim=c(0,25)) lines(breaks,cumfreq0)

The usefulness of a ogive is to allow the reader to find out how many students pay less than a certain value, and also what amount of monthly rent is paid by a certain number of students. As an example, suppose you want to know how many students pay less than $1500 a month in rent, then you can go up from the $1500 until you hit the graph and then you go over to the cumulative frequency axes to see what value corresponds to this value. It appears that around 20 students pay less than $1500. (See Graph 2.2.4 .)

Also, if you want to know the amount that 15 students pay less than, then you start at 15 on the vertical axis and then go over to the graph and down to the horizontal axis where the line intersects the graph. You can see that 15 students pay less than about $1200 a month. (See Graph 2.2.5 .)

If you graph the cumulative relative frequency then you can find out what percentage is below a certain number instead of just the number of people below a certain value.

Shapes of the distribution:

When you look at a distribution, look at the basic shape. There are some basic shapes that are seen in histograms. Realize though that some distributions have no shape. The common shapes are symmetric, skewed, and uniform. Another interest is how many peaks a graph may have. This is known as modal.

Symmetric means that you can fold the graph in half down the middle and the two sides will line up. You can think of the two sides as being mirror images of each other. Skewed means one “tail” of the graph is longer than the other. The graph is skewed in the direction of the longer tail (backwards from what you would expect). A uniform graph has all the bars the same height.

Modal refers to the number of peaks. Unimodal has one peak and bimodal has two peaks. Usually if a graph has more than two peaks, the modal information is not longer of interest.

Other important features to consider are gaps between bars, a repetitive pattern, how spread out is the data, and where the center of the graph is.

Examples of Graphs :

This graph is roughly symmetric and unimodal:

This graph is symmetric and bimodal:

This graph is skewed to the right:

This graph is skewed to the left and has a gap:

This graph is uniform since all the bars are the same height:

Example \(\PageIndex{7}\) creating a frequency distribution, histogram, and ogive

The following data represents the percent change in tuition levels at public, fouryear colleges (inflation adjusted) from 2008 to 2013 (Weissmann, 2013). Create a frequency distribution, histogram, and ogive for the data.

• Find the range: largest value - smallest value = \(78.4\)% \(-2.2\)% \(=76.2\)%
• Pick the number of classes: Since there are 50 data points, then around 6 to 8 classes should be used. Let's use 8.
• Find the class width: width \(=\dfrac{\text { range }}{8}=\dfrac{76.2 \%}{8} \approx 9.525 \%\) Since the data has one decimal place, then the class width should round to one decimal place. Make sure you round up. width \(=9.6\)%
• Find the class limits: \(2.2 \%+9.6 \%=11.8 \%, 11.8 \%+9.6 \%=21.4 \%, 21.4 \%+9.6 \%=31.0 \%, \leftrightharpoons\)
• Find the class boundaries: Since the data has one decimal place, the class boundaries should have two decimal places, so subtract 0.05 from the lower class limit to get the class boundaries. Add 0.05 to the upper class limit for the last class’s boundary. \(2.2-0.05=2.15 \%, 11.8-0.05=11.75 \%, 21.4-0.05=21.35 \% \leftrightharpoons\) Every value in the data should fall into exactly one of the classes. No data values should fall right on the boundary of two classes.
• Find the class midpoints: midpoint \(=\dfrac{\text { lower limt }+\text { upper limit }}{2}\) \(\dfrac{2.2+11.7}{2}=6.95 \%, \dfrac{11.8+21.3}{2}=16.55 \%, \leftrightharpoons\)
• Tally and find the frequency of the data:

This graph is skewed right, with no gaps. This says that most percent increases in tuition were around 16.55%, with very few states having a percent increase greater than 45.35%.

Looking at the ogive, you can see that 30 states had a percent change in tuition levels of about 25% or less.

There are occasions where the class limits in the frequency distribution are predetermined. Example \(\PageIndex{8}\) demonstrates this situation.

Example \(\PageIndex{8}\) creating a frequency distribution and histogram

The following are the percentage grades of 25 students from a statistics course. Make a frequency distribution and histogram.

Since this data is percent grades, it makes more sense to make the classes in multiples of 10, since grades are usually 90 to 100%, 80 to 90%, and so forth. It is easier to not use the class boundaries, but instead use the class limits and think of the upper class limit being up to but not including the next classes lower limit. As an example the class 80 – 90 means a grade of 80% up to but not including a 90%. A student with an 89.9% would be in the 80-90 class.

It appears that most of the students had between 60 to 90%. This graph looks somewhat symmetric and also bimodal. The same number of students earned between 60 to 70% and 80 to 90%.

There are other types of graphs for quantitative data. They will be explored in the next section.

Exercise \(\PageIndex{1}\)

See solutions

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10.3: Types of Quantitative Data Analysis and Presentation Format

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If your thesis is quantitative research, you will be conducting various types of analyses (see the following table).

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7.3: Presenting Quantitative Data Graphically

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Quantitative, or numerical, data can also be summarized into frequency tables.

A teacher records scores on a 20-point quiz for the 30 students in his class. The scores are:

19 20 18 18 17 18 19 17 20 18 20 16 20 15 17 12 18 19 18 19 17 20 18 16 15 18 20 5 0 0

These scores could be summarized into a frequency table by grouping like values:

\(\begin{array}{|c|c|} \hline \textbf { Score } & \textbf { Frequency } \\ \hline 0 & 2 \\ \hline 5 & 1 \\ \hline 12 & 1 \\ \hline 15 & 2 \\ \hline 16 & 2 \\ \hline 17 & 4 \\ \hline 18 & 8 \\ \hline 19 & 4 \\ \hline 20 & 6 \\ \hline \end{array}\)

Using this table, it would be possible to create a standard bar chart from this summary, like we did for categorical data:

However, since the scores are numerical values, this chart doesn’t really make sense; the first and second bars are five values apart, while the later bars are only one value apart. It would be more correct to treat the horizontal axis as a number line. This type of graph is called a histogram .

A histogram is like a bar graph, but where the horizontal axis is a number line

For the values above, a histogram would look like:

Notice that in the histogram, a bar represents values on the horizontal axis from that on the left hand-side of the bar up to, but not including, the value on the right hand side of the bar. Some people choose to have bars start at ½ values to avoid this ambiguity.

Unfortunately, not a lot of common software packages can correctly graph a histogram. About the best you can do in Excel or Word is a bar graph with no gap between the bars and spacing added to simulate a numerical horizontal axis.

If we have a large number of widely varying data values, creating a frequency table that lists every possible value as a category would lead to an exceptionally long frequency table, and probably would not reveal any patterns. For this reason, it is common with quantitative data to group data into class intervals .

Class Intervals

Class intervals are groupings of the data. In general, we define class intervals so that:

• Each interval is equal in size. For example, if the first class contains values from 120-129, the second class should include values from 130-139.
• We have somewhere between 5 and 20 classes, typically, depending upon the number of data we’re working with.

Suppose that we have collected weights from 100 male subjects as part of a nutrition study. For our weight data, we have values ranging from a low of 121 pounds to a high of 263 pounds, giving a total span of 263-121 = 142. We could create 7 intervals with a width of around 20, 14 intervals with a width of around 10, or somewhere in between. Often time we have to experiment with a few possibilities to find something that represents the data well. Let us try using an interval width of 15. We could start at 121, or at 120 since it is a nice round number.

\(\begin{array}{|c|c|} \hline \textbf { Interval } & \textbf { Frequency } \\ \hline 120-134 & 4 \\ \hline 135-149 & 14 \\ \hline 150-164 & 16 \\ \hline 165-179 & 28 \\ \hline 180-194 & 12 \\ \hline 195-209 & 8 \\ \hline 210-224 & 7 \\ \hline 225-239 & 6 \\ \hline 240-254 & 2 \\ \hline 255-269 & 3 \\ \hline \end{array}\)

A histogram of this data would look like:

In many software packages, you can create a graph similar to a histogram by putting the class intervals as the labels on a bar chart.

Other graph types such as pie charts are possible for quantitative data. The usefulness of different graph types will vary depending upon the number of intervals and the type of data being represented. For example, a pie chart of our weight data is difficult to read because of the quantity of intervals we used.

Try it Now 3

The total cost of textbooks for the term was collected from 36 students. Create a histogram for this data.

$140 $160 $160 $165 $180 $220 $235 $240 $250 $260 $280 $285

$285 $285 $290 $300 $300 $305 $310 $310 $315 $315 $320 $320

$330 $340 $345 $350 $355 $360 $360 $380 $395 $420 $460 $460

Using a class intervals of size 55, we can group our data into six intervals:

\(\begin{array}{|l|r|} \hline \textbf { cost interval } & \textbf { Frequency } \\ \hline \$ 140-194 & 5 \\ \hline \$ 195-249 & 3 \\ \hline \$ 250-304 & 9 \\ \hline \$ 305-359 & 12 \\ \hline \$ 360-414 & 4 \\ \hline \$ 415-469 & 3 \\ \hline \end{array}\)

We can use the frequency distribution to generate the histogram.

When collecting data to compare two groups, it is desirable to create a graph that compares quantities.

The data below came from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target was a large rectangle. Time to reach the target was recorded on each trial.

\(\begin{array}{|c|c|c|} \hline \begin{array}{c} \textbf { Interval } \\ \textbf { (milliseconds) } \end{array} & \begin{array}{c} \textbf { Frequency } \\ \textbf { small target } \end{array} & \begin{array}{c} \textbf { Frequency } \\ \textbf { large target } \end{array} \\ \hline 300-399 & 0 & 0 \\ \hline 400-499 & 1 & 5 \\ \hline 500-599 & 3 & 10 \\ \hline 600-699 & 6 & 5 \\ \hline 700-799 & 5 & 0 \\ \hline 800-899 & 4 & 0 \\ \hline 900-999 & 0 & 0 \\ \hline 1000-1099 & 1 & 0 \\ \hline 1100-1199 & 0 & 0 \\ \hline \end{array}\)

One option to represent this data would be a comparative histogram or bar chart, in which bars for the small target group and large target group are placed next to each other.

Frequency polygon

An alternative representation is a frequency polygon . A frequency polygon starts out like a histogram, but instead of drawing a bar, a point is placed in the midpoint of each interval at height equal to the frequency. Typically the points are connected with straight lines to emphasize the distribution of the data.

This graph makes it easier to see that reaction times were generally shorter for the larger target, and that the reaction times for the smaller target were more spread out.

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67 Types of Quantitative Data Analysis and Presentation Format

If your thesis is quantitative research, you will be conducting various types of analyses (see the following table).

Practicing and Presenting Social Research Copyright © 2022 by Oral Robinson and Alexander Wilson is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License , except where otherwise noted.

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Module 11: Statistics: Describing Data

Presenting quantitative data graphically, learning outcomes.

• Create a frequency table, bar graph, pareto chart, pictogram, or a pie chart to represent a data set
• Identify features of ineffective representations of data
• Create a histogram, pie chart, or frequency polygon that represents numerical data
• Create a graph that compares two quantities

Visualizing Numbers

Quantitative, or numerical, data can also be summarized into frequency tables.

A teacher records scores on a 20-point quiz for the 30 students in his class. The scores are:

19 20 18 18 17 18 19 17 20 18 20 16 20 15 17 12 18 19 18 19 17 20 18 16 15 18 20 5 0 0

These scores could be summarized into a frequency table by grouping like values:

Using the table from the first example, it would be possible to create a standard bar chart from this summary, like we did for categorical data:

A histogram is like a bar graph, but where the horizontal axis is a number line.

For the values above, a histogram would look like:

Notice that in the histogram, a bar represents values on the horizontal axis from that on the left hand-side of the bar up to, but not including, the value on the right hand side of the bar. Some people choose to have bars start at ½ values to avoid this ambiguity.

This video demonstrates the creation of the histogram from this data.

Unfortunately, not a lot of common software packages can correctly graph a histogram. About the best you can do in Excel or Word is a bar graph with no gap between the bars and spacing added to simulate a numerical horizontal axis.

If we have a large number of widely varying data values, creating a frequency table that lists every possible value as a category would lead to an exceptionally long frequency table, and probably would not reveal any patterns. For this reason, it is common with quantitative data to group data into class intervals .

Class Intervals

Class intervals are groupings of the data. In general, we define class intervals so that

• each interval is equal in size. For example, if the first class contains values from 120-129, the second class should include values from 130-139.
• we have somewhere between 5 and 20 classes, typically, depending upon the number of data we’re working with.

Suppose that we have collected weights from 100 male subjects as part of a nutrition study. For our weight data, we have values ranging from a low of 121 pounds to a high of 263 pounds, giving a total span of 263-121 = 142. We could create 7 intervals with a width of around 20, 14 intervals with a width of around 10, or somewhere in between. Often time we have to experiment with a few possibilities to find something that represents the data well. Let us try using an interval width of 15. We could start at 121, or at 120 since it is a nice round number.

A histogram of this data would look like:

In many software packages, you can create a graph similar to a histogram by putting the class intervals as the labels on a bar chart.

The following video walks through this example in more detail.

Other graph types such as pie charts are possible for quantitative data. The usefulness of different graph types will vary depending upon the number of intervals and the type of data being represented. For example, a pie chart of our weight data is difficult to read because of the quantity of intervals we used.

To see more about why a pie chart isn’t useful in this case, watch the following.

The total cost of textbooks for the term was collected from 36 students. Create a histogram for this data.

$140    $160    $160    $165    $180    $220    $235    $240    $250    $260    $280    $285

$285    $285    $290    $300    $300    $305    $310    $310    $315    $315    $320    $320

$330    $340    $345    $350    $355    $360    $360    $380    $395    $420    $460    $460

When collecting data to compare two groups, it is desirable to create a graph that compares quantities.

The data below came from a task in which the goal is to move a computer mouse to a target on the screen as fast as possible. On 20 of the trials, the target was a small rectangle; on the other 20, the target was a large rectangle. Time to reach the target was recorded on each trial.

One option to represent this data would be a comparative histogram or bar chart, in which bars for the small target group and large target group are placed next to each other.

Frequency polygon

An alternative representation is a frequency polygon . A frequency polygon starts out like a histogram, but instead of drawing a bar, a point is placed in the midpoint of each interval at height equal to the frequency. Typically the points are connected with straight lines to emphasize the distribution of the data.

This graph makes it easier to see that reaction times were generally shorter for the larger target, and that the reaction times for the smaller target were more spread out.

The following video explains frequency polygon creation for this example.

• Revision and Adaptation. Provided by : Lumen Learning. License : CC BY: Attribution
• Presenting Quantitative Data Graphically. Authored by : David Lippman. Located at : http://www.opentextbookstore.com/mathinsociety/ . Project : Math in Society. License : CC BY-SA: Attribution-ShareAlike
• numbers-education-kindergarten. Authored by : karanja. Located at : https://pixabay.com/en/numbers-education-kindergarten-738068/ . License : CC0: No Rights Reserved
• Creating a histogram. Authored by : OCLPhase2's channel. Located at : https://youtu.be/180FgZ_cTrE . License : CC BY: Attribution
• Defining class intervals for a frequency table or histogram. Authored by : OCLPhase2's channel. Located at : https://youtu.be/JhshitTtdP0 . License : CC BY: Attribution
• When not use a pie chart. Authored by : OCLPhase2's channel. Located at : https://youtu.be/FQ8zmZ56-XA . License : CC BY: Attribution
• Frequency polygons. Authored by : OCLPhase2's channel. Located at : https://youtu.be/rxByzA9MFFY . License : CC BY: Attribution

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If your thesis is quantitative research, you will be conducting various types of analyses (see the following table).

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Quantitative Data – Types, Methods and Examples

Table of Contents

Quantitative Data

Definition:

Quantitative data refers to numerical data that can be measured or counted. This type of data is often used in scientific research and is typically collected through methods such as surveys, experiments, and statistical analysis.

Quantitative Data Types

There are two main types of quantitative data: discrete and continuous.

• Discrete data: Discrete data refers to numerical values that can only take on specific, distinct values. This type of data is typically represented as whole numbers and cannot be broken down into smaller units. Examples of discrete data include the number of students in a class, the number of cars in a parking lot, and the number of children in a family.
• Continuous data: Continuous data refers to numerical values that can take on any value within a certain range or interval. This type of data is typically represented as decimal or fractional values and can be broken down into smaller units. Examples of continuous data include measurements of height, weight, temperature, and time.

Quantitative Data Collection Methods

There are several common methods for collecting quantitative data. Some of these methods include:

• Surveys : Surveys involve asking a set of standardized questions to a large number of people. Surveys can be conducted in person, over the phone, via email or online, and can be used to collect data on a wide range of topics.
• Experiments : Experiments involve manipulating one or more variables and observing the effects on a specific outcome. Experiments can be conducted in a controlled laboratory setting or in the real world.
• Observational studies : Observational studies involve observing and collecting data on a specific phenomenon without intervening or manipulating any variables. Observational studies can be conducted in a natural setting or in a laboratory.
• Secondary data analysis : Secondary data analysis involves using existing data that was collected for a different purpose to answer a new research question. This method can be cost-effective and efficient, but it is important to ensure that the data is appropriate for the research question being studied.
• Physiological measures: Physiological measures involve collecting data on biological or physiological processes, such as heart rate, blood pressure, or brain activity.
• Computerized tracking: Computerized tracking involves collecting data automatically from electronic sources, such as social media, online purchases, or website analytics.

Quantitative Data Analysis Methods

There are several methods for analyzing quantitative data, including:

• Descriptive statistics: Descriptive statistics are used to summarize and describe the basic features of the data, such as the mean, median, mode, standard deviation, and range.
• Inferential statistics : Inferential statistics are used to make generalizations about a population based on a sample of data. These methods include hypothesis testing, confidence intervals, and regression analysis.
• Data visualization: Data visualization involves creating charts, graphs, and other visual representations of the data to help identify patterns and trends. Common types of data visualization include histograms, scatterplots, and bar charts.
• Time series analysis: Time series analysis involves analyzing data that is collected over time to identify patterns and trends in the data.
• Multivariate analysis : Multivariate analysis involves analyzing data with multiple variables to identify relationships between the variables.
• Factor analysis : Factor analysis involves identifying underlying factors or dimensions that explain the variation in the data.
• Cluster analysis: Cluster analysis involves identifying groups or clusters of observations that are similar to each other based on multiple variables.

Quantitative Data Formats

Quantitative data can be represented in different formats, depending on the nature of the data and the purpose of the analysis. Here are some common formats:

• Tables : Tables are a common way to present quantitative data, particularly when the data involves multiple variables. Tables can be used to show the frequency or percentage of data in different categories or to display summary statistics.
• Charts and graphs: Charts and graphs are useful for visualizing quantitative data and can be used to highlight patterns and trends in the data. Some common types of charts and graphs include line charts, bar charts, scatterplots, and pie charts.
• Databases : Quantitative data can be stored in databases, which allow for easy sorting, filtering, and analysis of large amounts of data.
• Spreadsheets : Spreadsheets can be used to organize and analyze quantitative data, particularly when the data is relatively small in size. Spreadsheets allow for calculations and data manipulation, as well as the creation of charts and graphs.
• Statistical software : Statistical software, such as SPSS, R, and SAS, can be used to analyze quantitative data. These programs allow for more advanced statistical analyses and data modeling, as well as the creation of charts and graphs.

Quantitative Data Gathering Guide

Here is a basic guide for gathering quantitative data:

• Define the research question: The first step in gathering quantitative data is to clearly define the research question. This will help determine the type of data to be collected, the sample size, and the methods of data analysis.
• Choose the data collection method: Select the appropriate method for collecting data based on the research question and available resources. This could include surveys, experiments, observational studies, or other methods.
• Determine the sample size: Determine the appropriate sample size for the research question. This will depend on the level of precision needed and the variability of the population being studied.
• Develop the data collection instrument: Develop a questionnaire or survey instrument that will be used to collect the data. The instrument should be designed to gather the specific information needed to answer the research question.
• Pilot test the data collection instrument : Before collecting data from the entire sample, pilot test the instrument on a small group to identify any potential problems or issues.
• Collect the data: Collect the data from the selected sample using the chosen data collection method.
• Clean and organize the data : Organize the data into a format that can be easily analyzed. This may involve checking for missing data, outliers, or errors.
• Analyze the data: Analyze the data using appropriate statistical methods. This may involve descriptive statistics, inferential statistics, or other types of analysis.
• Interpret the results: Interpret the results of the analysis in the context of the research question. Identify any patterns, trends, or relationships in the data and draw conclusions based on the findings.
• Communicate the findings: Communicate the findings of the analysis in a clear and concise manner, using appropriate tables, graphs, and other visual aids as necessary. The results should be presented in a way that is accessible to the intended audience.

Examples of Quantitative Data

Here are some examples of quantitative data:

• Height of a person (measured in inches or centimeters)
• Weight of a person (measured in pounds or kilograms)
• Temperature (measured in Fahrenheit or Celsius)
• Age of a person (measured in years)
• Number of cars sold in a month
• Amount of rainfall in a specific area (measured in inches or millimeters)
• Number of hours worked in a week
• GPA (grade point average) of a student
• Sales figures for a product
• Time taken to complete a task.
• Distance traveled (measured in miles or kilometers)
• Speed of an object (measured in miles per hour or kilometers per hour)
• Number of people attending an event
• Price of a product (measured in dollars or other currency)
• Blood pressure (measured in millimeters of mercury)
• Amount of sugar in a food item (measured in grams)
• Test scores (measured on a numerical scale)
• Number of website visitors per day
• Stock prices (measured in dollars)
• Crime rates (measured by the number of crimes per 100,000 people)

Applications of Quantitative Data

Quantitative data has a wide range of applications across various fields, including:

• Scientific research: Quantitative data is used extensively in scientific research to test hypotheses and draw conclusions. For example, in biology, researchers might use quantitative data to measure the growth rate of cells or the effectiveness of a drug treatment.
• Business and economics: Quantitative data is used to analyze business and economic trends, forecast future performance, and make data-driven decisions. For example, a company might use quantitative data to analyze sales figures and customer demographics to determine which products are most popular among which segments of their customer base.
• Education: Quantitative data is used in education to measure student performance, evaluate teaching methods, and identify areas where improvement is needed. For example, a teacher might use quantitative data to track the progress of their students over the course of a semester and adjust their teaching methods accordingly.
• Public policy: Quantitative data is used in public policy to evaluate the effectiveness of policies and programs, identify areas where improvement is needed, and develop evidence-based solutions. For example, a government agency might use quantitative data to evaluate the impact of a social welfare program on poverty rates.
• Healthcare : Quantitative data is used in healthcare to evaluate the effectiveness of medical treatments, track the spread of diseases, and identify risk factors for various health conditions. For example, a doctor might use quantitative data to monitor the blood pressure levels of their patients over time and adjust their treatment plan accordingly.

Purpose of Quantitative Data

The purpose of quantitative data is to provide a numerical representation of a phenomenon or observation. Quantitative data is used to measure and describe the characteristics of a population or sample, and to test hypotheses and draw conclusions based on statistical analysis. Some of the key purposes of quantitative data include:

• Measuring and describing : Quantitative data is used to measure and describe the characteristics of a population or sample, such as age, income, or education level. This allows researchers to better understand the population they are studying.
• Testing hypotheses: Quantitative data is often used to test hypotheses and theories by collecting numerical data and analyzing it using statistical methods. This can help researchers determine whether there is a statistically significant relationship between variables or whether there is support for a particular theory.
• Making predictions : Quantitative data can be used to make predictions about future events or trends based on past data. This is often done through statistical modeling or time series analysis.
• Evaluating programs and policies: Quantitative data is often used to evaluate the effectiveness of programs and policies. This can help policymakers and program managers identify areas where improvements can be made and make evidence-based decisions about future programs and policies.

When to use Quantitative Data

Quantitative data is appropriate to use when you want to collect and analyze numerical data that can be measured and analyzed using statistical methods. Here are some situations where quantitative data is typically used:

• When you want to measure a characteristic or behavior : If you want to measure something like the height or weight of a population or the number of people who smoke, you would use quantitative data to collect this information.
• When you want to compare groups: If you want to compare two or more groups, such as comparing the effectiveness of two different medical treatments, you would use quantitative data to collect and analyze the data.
• When you want to test a hypothesis : If you have a hypothesis or theory that you want to test, you would use quantitative data to collect data that can be analyzed statistically to determine whether your hypothesis is supported by the data.
• When you want to make predictions: If you want to make predictions about future trends or events, such as predicting sales for a new product, you would use quantitative data to collect and analyze data from past trends to make your prediction.
• When you want to evaluate a program or policy : If you want to evaluate the effectiveness of a program or policy, you would use quantitative data to collect data about the program or policy and analyze it statistically to determine whether it has had the intended effect.

Characteristics of Quantitative Data

Quantitative data is characterized by several key features, including:

• Numerical values : Quantitative data consists of numerical values that can be measured and counted. These values are often expressed in terms of units, such as dollars, centimeters, or kilograms.
• Continuous or discrete : Quantitative data can be either continuous or discrete. Continuous data can take on any value within a certain range, while discrete data can only take on certain values.
• Objective: Quantitative data is objective, meaning that it is not influenced by personal biases or opinions. It is based on empirical evidence that can be measured and analyzed using statistical methods.
• Large sample size: Quantitative data is often collected from a large sample size in order to ensure that the results are statistically significant and representative of the population being studied.
• Statistical analysis: Quantitative data is typically analyzed using statistical methods to determine patterns, relationships, and other characteristics of the data. This allows researchers to make more objective conclusions based on empirical evidence.
• Precision : Quantitative data is often very precise, with measurements taken to multiple decimal points or significant figures. This precision allows for more accurate analysis and interpretation of the data.

Advantages of Quantitative Data

Some advantages of quantitative data are:

• Objectivity : Quantitative data is usually objective because it is based on measurable and observable variables. This means that different people who collect the same data will generally get the same results.
• Precision : Quantitative data provides precise measurements of variables. This means that it is easier to make comparisons and draw conclusions from quantitative data.
• Replicability : Since quantitative data is based on objective measurements, it is often easier to replicate research studies using the same or similar data.
• Generalizability : Quantitative data allows researchers to generalize findings to a larger population. This is because quantitative data is often collected using random sampling methods, which help to ensure that the data is representative of the population being studied.
• Statistical analysis : Quantitative data can be analyzed using statistical methods, which allows researchers to test hypotheses and draw conclusions about the relationships between variables.
• Efficiency : Quantitative data can often be collected quickly and efficiently using surveys or other standardized instruments, which makes it a cost-effective way to gather large amounts of data.

Limitations of Quantitative Data

Some Limitations of Quantitative Data are as follows:

• Limited context: Quantitative data does not provide information about the context in which the data was collected. This can make it difficult to understand the meaning behind the numbers.
• Limited depth: Quantitative data is often limited to predetermined variables and questions, which may not capture the complexity of the phenomenon being studied.
• Difficulty in capturing qualitative aspects: Quantitative data is unable to capture the subjective experiences and qualitative aspects of human behavior, such as emotions, attitudes, and motivations.
• Possibility of bias: The collection and interpretation of quantitative data can be influenced by biases, such as sampling bias, measurement bias, or researcher bias.
• Simplification of complex phenomena: Quantitative data may oversimplify complex phenomena by reducing them to numerical measurements and statistical analyses.
• Lack of flexibility: Quantitative data collection methods may not allow for changes or adaptations in the research process, which can limit the ability to respond to unexpected findings or new insights.

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Presentation of Quantitative Data

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We often think of data as being strictly numerical values, and in business, those values are often stated in terms of dollars. Although data in the form of dollars are ubiquitous, it is quite easy to imagine other numerical units: percentages, counts in categories, units of sales, etc. This chapter, and Chap. 3 , discusses how we can best use Excel’s graphics capabilities to effectively present quantitative data ( ratio and interval ), whether it is in dollars or some other quantitative measure, to inform and influence an audience. In Chaps. 4 and 5 we will acknowledge that not all data are numerical by focusing on qualitative ( categorical/nominal or ordinal ) data. The process of data gathering often produces a combination of data types, and throughout our discussions it will be impossible to ignore this fact: quantitative and qualitative data often occur together.

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Presentation of Quantitative Data

References • Health information and basic medical statistics: Park’s Textbook of PSM, 23rd ed. 2016 • Methods in Biostatistics: B.K. Mahajan, Jaypee Brothers Medical Publishers • Informative Presentation of Tables, Graphs and Statistics: University of Reading, Statistical Services Centre. Biometrics Advisory and Support Service to DFID, March 2000 • Making Data Meaningful, A guide to presenting statistics, UNITED NATIONS, Geneva, 2009

Quantitative Data Analysis

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Quantitative Data Analysis. Edouard Manet: In the Conservatory, 1879. Quantification of Data Introduction To conduct quantitative analysis, responses to open-ended questions in survey research and the raw data collected using qualitative methods must be coded numerically.

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Presentation Transcript

Quantitative Data Analysis Edouard Manet: In the Conservatory, 1879

Quantification of Data • Introduction • To conduct quantitative analysis, responses to open-ended questions in survey research and the raw data collected using qualitative methods must be coded numerically.

Quantification of Data • Introduction (Continued) • Most responses to survey research questions already are recorded in numerical format. • In mailed and face-to-face surveys, responses are keypunched into a data file. • In telephone and internet surveys, responses are automatically recorded in numerical format.

Quantification of Data • Developing Code Categories • Coding qualitative data can use an existing scheme or one developed by examining the data. • Coding qualitative data into numerical categories sometimes can be a straightforward process. • Coding occupation, for example, can rely upon numerical categories defined by the Bureau of the Census.

Quantification of Data • Developing Code Categories (Continued) • Coding most forms of qualitative data, however, requires much effort. • This coding typically requires using an iterative procedure of trial and error. • Consider, for example, coding responses to the question, “What is the biggest problem in attending college today.” • The researcher must develop a set of codes that are: • exhaustive of the full range of responses. • mutually exclusive (mostly) of one another.

Quantification of Data • Developing Code Categories (Continued) • In coding responses to the question, “What is the biggest problem in attending college today,” the researcher might begin, for example, with a list of 5 categories, then realize that 8 would be better, then realize that it would be better to combine categories 1 and 5 into a single category and use a total of 7 categories. • Each time the researcher makes a change in the coding scheme, it is necessary to restart the coding process to code all responses using the same scheme.

Quantification of Data • Developing Code Categories (Continued) • Suppose one wanted to code more complex qualitative data (e.g., videotape of an interaction between husband and wife) into numerical categories. • How does one code the many statements, facial expressions, and body language inherent in such an interaction? • One can realize from this example that coding schemes can become highly complex.

Quantification of Data • Developing Code Categories (Continued) • Complex coding schemes can take many attempts to develop. • Once developed, they undergo continuing evaluation. • Major revisions, however, are unlikely. • Rather, new coders are required to learn the existing coding scheme and undergo continuing evaluation for their ability to correctly apply the scheme.

Quantification of Data • Codebook Construction • The end product of developing a coding scheme is the codebook. • This document describes in detail the procedures for transforming qualitative data into numerical responses. • The codebook should include notes that describe the process used to create codes, detailed descriptions of codes, and guidelines to use when uncertainty exists about how to code responses.

Quantification of Data • Data Entry • Data recorded in numerical format can be entered by keypunching or the use of sophisticated optical scanners. • Typically, responses to internet and telephone surveys are entered directly into a numerical data base. • Cleaning Data • Logical errors in responses must be reconciled. • Errors of entry must be corrected.

Quantification of Data • Collapsing Response Categories • Sometimes the researcher might want to analyze a variable by using fewer response categories than were used to measure it. • In these instances, the researcher might want to “collapse” one or more categories into a single category. • The researcher might want to collapse categories to simplify the presentation of the results or because few observations exist within some categories.

Quantification of Data • Collapsing Response Categories: Example • ResponseFrequency • Strongly disagree 2 • Disagree 22 • Neither agree nor disagree 45 • Agree 31 • Strongly Agree 1

Quantification of Data • Collapsing Response Categories: Example • One might want to collapse the extreme responses and work with just three categories: • ResponseFrequency • Disagree 24 • Neither agree nor disagree 45 • Agree 32

Quantification of Data • Handling “Don’t Knows” • When asking about knowledge of factual information (“Does your teenager drink alcohol?”) or opinions on a topic the subject might not know much about (“Do school officials do enough to discourage teenagers from drinking alcohol?”), it is wise to include a “don’t know” category as a possible response. • Analyzing “don’t know” responses, however, can be a difficult task.

Quantification of Data • Handling “Don’t Knows” (Continued) • The research-on-research literature regarding this issue is complex and without clear-cut guidelines for decision-making. • The decisions about whether to use “don’t know” response categories and how to code and analyze them tends to be idiosyncratic to the research and the researcher.

Quantitative Data Analysis • Descriptive statistics attempt to explain or predict the values of a dependent variable given certain values of one or more independent variables. • Inferential statistics attempt to generalize the results of descriptive statistics to a larger population of interest.

Quantitative Data Analysis • Data Reduction • The first step in quantitative data analysis is to calculate descriptive statistics about variables. • The researcher calculates statistics such as the mean, median, mode, range, and standard deviation. • Also, the researcher might choose to collapse response categories for variables.

Quantitative Data Analysis • Measures of Association • Next, the researcher calculates measures of association: statistics that indicate the strength of a relationship between two variables. • Measures of association rely upon the basic principle of proportionate reduction in error (PRE).

Quantitative Data Analysis • Measures of Association (Continued) • PRE represents how much better one would be at guessing the outcome of a dependent variable by knowing a value of an independent variable. • For example: How much better could I predict someone’s income if I knew how many years of formal education they have completed? If the answer to this question is “37% better,” then the PRE is 37%.

Quantitative Data Analysis • Measures of Association (Continued) • Statistics are designated by Greek letters. • Different statistics are used to indicate the strength of association between variables measured at different levels of data. • Strength of association for nominal-level variables is indicated by λ (lambda). • Strength of association for ordinal-level variables is indicated by γ (gamma). • Strength of association for interval-level variables is indicated by correlation (r).

Quantitative Data Analysis • Measures of Association (Continued) • Covariance is the extent to which two variables “change with respect to one another.” • As one variable increases, the other variable either increases (positive covariance) or decreases (negative covariance). • Correlation is a standardized measure of covariance. • Correlation ranges from -1 to +1, with figures closer to one indicating a stronger relationship.

Quantitative Data Analysis • Measures of Association (Continued) • Technically, covariance is the extent to which two variables co-vary about their means. • If a person’s years of formal education is above the mean of education for all persons and his/her income is above the mean of income for all persons, then this data point would indicate positive covariance between education and income.

Statistics • Introduction • To make inferences from descriptive statistics, one has to know the reliability of these statistics. • In the same sense that the distribution of one variable has a standard deviation, a parameter estimate has a standard error—the distribution of the estimate from its mean with respect to the normal curve.

Statistics • Introduction (Continued) • To better understand the concepts standard deviation and standard error, and why these concepts are important to our course, please review the presentation regarding standard error. • Presentation on Standard Error.

Statistics • Types of Analysis • The presentation on inferential statistics will cover univariate, bivariate and multivariate analysis. • Univariate Analysis: • Mean. • Median. • Mode. • Standard deviation.

Statistics • Types of Analysis (Continued) • Bivariate Analysis • Tests of statistical significance. • Chi-square. • Multivariate Analysis: • Ordinary least squares (OLS) regression. • Path analysis. • Time-series analysis. • Factor analysis. • Analysis of variance (ANOVA).

Univariate Analysis • Distributions • Data analysis begins by examining distributions. • One might begin, for example, by examining the distribution of responses to a question about formal education, where responses are recorded within six categories. • A frequency distribution will show the number and percent of responses in each category of a variable.

Univariate Analysis • Central Tendency • A common measure of central tendency is the average, or mean, of the responses. • The median is the value of the “middle” case when all responses are rank-ordered. • The mode is the most common response. • When data are highly skewed, meaning heavily balanced toward one end of the distribution, the median or mode might better represent the “most common” or “centered” response.

Univariate Analysis • Central Tendency (Continued) • Consider this distribution of respondent ages: • 18, 19, 19, 19, 20, 20, 21, 22, 85 • The mean equals 27. But this number does not adequately represent the “common” respondent because the one person who is 85 skews the distribution toward the high end. • The median equals 20. • This measure of central tendency gives a more accurate portrayal of the “middle of the distribution.”

Univariate Analysis • Dispersion • Dispersion refers to the way the values are distributed around some central value, typically the mean. • The range is the distance separating the lowest and highest values (e.g., the range of the ages listed previously equals 18-85). • The standard deviation is an index of the amount of variability in a set of data.

Univariate Analysis • Dispersion (Continued) • The standard deviation represents dispersion with respect to the normal (bell-shaped) curve. • Assuming a set of numbers is normally distributed, then each standard deviation equals a certain distance from the mean. • Each standard deviation (+1, +2, etc.) is the same distance from each other on the bell-shaped curve, but represents a declining percentage of responses because of the shape of the curve (see: Chapter 7).

Univariate Analysis • Dispersion (Continued) • For example, the first standard deviation accounts for 34.1% of the values below and above the mean. • The figure 34.1% is derived from probability theory and the shape of the curve. • Thus, approximately 68% of all responses fall within one standard deviation of the mean. • The second standard deviation accounts for the next 13.6% of the responses from the mean (27.2% of all responses), and so on.

Univariate Analysis • Dispersion (Continued) • If the responses are distributed approximately normal and the range of responses is low—meaning that most responses fall close to the mean—then the standard deviation will be small. • The standard deviation of professional golfer’s scores on a golf course will be low. • The standard deviation of amateur golfer’s scores on a golf course will be high.

Univariate Analysis • Continuous and Discrete Variables • Continuous variables have responses that form a steady progression (e.g., age, income). • Discrete (i.e., categorical) variables have responses that are considered to be separate from one another (i.e., sex of respondent, religious affiliation).

Univariate Analysis • Continuous and Discrete Variables • Sometimes, it is a matter of debate within the community of scholars about whether a measured variable is continuous or discrete. • This issue is important because the statistical procedures appropriate for continuous-level data are more powerful, easier to use, and easier to interpret than those for discrete-level data, especially as related to the measurement of the dependent variable.

Univariate Analysis • Continuous and Discrete Variables (Continued) • Example: Suppose one measures amount of formal education within five categories: less than hs, hs, 2-years vocational/college, college, post-college). • Is this measure continuous (i.e., 1-5) or discrete? • In practice, five categories seems to be a cutoff point for considering a variable as continuous. • Using a seven-point response scale will give the researcher a greater chance of deeming a variable to be continuous.

Bivariate Analysis • Introduction • Bivariate analysis refers to an examination of the relationship between two variables. • We might ask these questions about the relationship between two variables: • Do they seem to vary in relation to one another? That is, as one variable increases in size does the other variable increase or decrease in size? • What is the strength of the relationship between the variables?

Bivariate Analysis • Introduction (Continued) • Divide the cases into groups according to the attributes of the independent variable (e.g., men and women). • Describe each subgroup in terms of attributes of the dependent variable (e.g., what percent of men approve of sexual equality and what percent of women approve of sexual equality).

Bivariate Analysis • Introduction (Continued) • Read the table by comparing the independent variable subgroups with one another in terms of a given attribute of the dependent variable (e.g., compare the percentages of men and women who approve of sexual equality). • Bivariate analysis gives an indication of how the dependent variable differs across levels or categories of an independent variable. • This relationship does not necessarily indicate causality.

Bivariate Analysis • Introduction (Continued) • Tables that compare responses to a dependent variable across levels/categories of an independent variable are called contingency tables (or sometimes, “crosstabs”). • When writing a research report, it is common practice, even when conducting highly sophisticated statistical analysis, to present contingency tables also to give readers a sense of the distributions and bivariate relationships among variables.

Bivariate Analysis • Tests of Statistical Significance • If one assumes a normal distribution, then one can examine parameters and their standard errors with respect to the normal curve to evaluate whether an observed parameter differs from zero by some set margin of error. • Assume that the researcher sets the probability of a Type-1 error (i.e., the probability of assuming causality when there is none) at 5%. • That is, we set our margin of error very low, just 5%.

Bivariate Analysis • Tests of Statistical Significance (Continued) • To evaluate statistical significance, the researcher compares a parameter estimate to a “zero point” on a normal curve (its center). • The question becomes: Is this parameter estimate sufficiently large, given its standard error, that, within a 5% probability of error, we can state that it is not equal to zero?

Bivariate Analysis • Tests of Statistical Significance (Continued) • To achieve a probability of error of 5%, the parameter estimate must be almost two (i.e., 1.96) standard deviations from zero, given its standard error. • Sometimes in sociological research, scholars say “two standard deviations” in referring to a 5% error rate. Most of the time, they are more precise and state 1.96.

Bivariate Analysis • Tests of Statistical Significance (Continued) • Consider this example: • Suppose the unstandardized estimate of the effect of self-esteem on marital satisfaction equals 3.50 (i.e., each additional amount of self-esteem on its scale results in 3.50 additional amount of marital satisfaction on its scale). • Suppose the standard error of this estimate equals 1.20.

Bivariate Analysis • Tests of Statistical Significance (Continued) • If we divide 3.50 by 1.20 we obtain the ratio of 2.92. This figure is called a t-ratio (or, t-value). • The figure 2.92 means that the estimate 3.50 is 2.92 standard deviations from zero. • Based upon our set margin of error of 5% (which is equivalent to 1.96 standard deviations), we can state that at prob. < .05, the effect of self-esteem on marital satisfaction is statistically significant.

Bivariate Analysis • Tests of Statistical Significance (Continued) • The t-ratio is the ratio of a parameter estimate to its standard error. • The t-ratio equals the number of standard deviations that an estimate lies from the “zero point” (i.e., center) of the normal curve.

Bivariate Analysis • Tests of Statistical Significance (Continued) • Why do we state that we need to have 1.96 standard deviations from the zero point of the normal curve? • Recall the area beneath the normal curve: • The first standard deviation covers 34.1% of the observations on one side of the zero point. • The second standard deviation covers the next 13.6% of the observations.

Bivariate Analysis • Tests of Statistical Significance (Continued) • Let’s assume for a moment that our estimate is greater than the “real” effect of self-esteem on marital satisfaction. • Then, at 1.96 standard deviations, we have covered the 50% probability below the “real” effect, and we have covered 34.1% + 13.4% probability above this effect. • In total, we have accounted for 97.5% of the probability that our estimate does not equal zero.

Bivariate Analysis • Tests of Statistical Significance (Continued) • That leaves 2.5% of the probability above the “real” estimate. • But we have to recognize that our estimate might have fallen below the “real” estimate. • So, we have the probability of error on both sides of “reality.” • 2.5% + 2.5% equals 5% • This is our set margin of error!

Bivariate Analysis • Tests of Statistical Significance (Continued) • Thus, inferential statistics are calculated with respect to the properties of the normal curve. • There are other types of distributions besides the normal curve, but the normal distribution is the one most often used in sociological analysis.

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