empirical research data analysis

What is Empirical Research? Definition, Methods, Examples

Appinio Research · 09.02.2024 · 35min read

Ever wondered how we gather the facts, unveil hidden truths, and make informed decisions in a world filled with questions? Empirical research holds the key.

In this guide, we'll delve deep into the art and science of empirical research, unraveling its methods, mysteries, and manifold applications. From defining the core principles to mastering data analysis and reporting findings, we're here to equip you with the knowledge and tools to navigate the empirical landscape.

What is Empirical Research?

Empirical research is the cornerstone of scientific inquiry, providing a systematic and structured approach to investigating the world around us. It is the process of gathering and analyzing empirical or observable data to test hypotheses, answer research questions, or gain insights into various phenomena. This form of research relies on evidence derived from direct observation or experimentation, allowing researchers to draw conclusions based on real-world data rather than purely theoretical or speculative reasoning.

Characteristics of Empirical Research

Empirical research is characterized by several key features:

Observation and Measurement : It involves the systematic observation or measurement of variables, events, or behaviors.
Data Collection : Researchers collect data through various methods, such as surveys, experiments, observations, or interviews.
Testable Hypotheses : Empirical research often starts with testable hypotheses that are evaluated using collected data.
Quantitative or Qualitative Data : Data can be quantitative (numerical) or qualitative (non-numerical), depending on the research design.
Statistical Analysis : Quantitative data often undergo statistical analysis to determine patterns , relationships, or significance.
Objectivity and Replicability : Empirical research strives for objectivity, minimizing researcher bias . It should be replicable, allowing other researchers to conduct the same study to verify results.
Conclusions and Generalizations : Empirical research generates findings based on data and aims to make generalizations about larger populations or phenomena.

Importance of Empirical Research

Empirical research plays a pivotal role in advancing knowledge across various disciplines. Its importance extends to academia, industry, and society as a whole. Here are several reasons why empirical research is essential:

Evidence-Based Knowledge : Empirical research provides a solid foundation of evidence-based knowledge. It enables us to test hypotheses, confirm or refute theories, and build a robust understanding of the world.
Scientific Progress : In the scientific community, empirical research fuels progress by expanding the boundaries of existing knowledge. It contributes to the development of theories and the formulation of new research questions.
Problem Solving : Empirical research is instrumental in addressing real-world problems and challenges. It offers insights and data-driven solutions to complex issues in fields like healthcare, economics, and environmental science.
Informed Decision-Making : In policymaking, business, and healthcare, empirical research informs decision-makers by providing data-driven insights. It guides strategies, investments, and policies for optimal outcomes.
Quality Assurance : Empirical research is essential for quality assurance and validation in various industries, including pharmaceuticals, manufacturing, and technology. It ensures that products and processes meet established standards.
Continuous Improvement : Businesses and organizations use empirical research to evaluate performance, customer satisfaction, and product effectiveness. This data-driven approach fosters continuous improvement and innovation.
Human Advancement : Empirical research in fields like medicine and psychology contributes to the betterment of human health and well-being. It leads to medical breakthroughs, improved therapies, and enhanced psychological interventions.
Critical Thinking and Problem Solving : Engaging in empirical research fosters critical thinking skills, problem-solving abilities, and a deep appreciation for evidence-based decision-making.

Empirical research empowers us to explore, understand, and improve the world around us. It forms the bedrock of scientific inquiry and drives progress in countless domains, shaping our understanding of both the natural and social sciences.

How to Conduct Empirical Research?

So, you've decided to dive into the world of empirical research. Let's begin by exploring the crucial steps involved in getting started with your research project.

1. Select a Research Topic

Selecting the right research topic is the cornerstone of a successful empirical study. It's essential to choose a topic that not only piques your interest but also aligns with your research goals and objectives. Here's how to go about it:

Identify Your Interests : Start by reflecting on your passions and interests. What topics fascinate you the most? Your enthusiasm will be your driving force throughout the research process.
Brainstorm Ideas : Engage in brainstorming sessions to generate potential research topics. Consider the questions you've always wanted to answer or the issues that intrigue you.
Relevance and Significance : Assess the relevance and significance of your chosen topic. Does it contribute to existing knowledge? Is it a pressing issue in your field of study or the broader community?
Feasibility : Evaluate the feasibility of your research topic. Do you have access to the necessary resources, data, and participants (if applicable)?

2. Formulate Research Questions

Once you've narrowed down your research topic, the next step is to formulate clear and precise research questions . These questions will guide your entire research process and shape your study's direction. To create effective research questions:

Specificity : Ensure that your research questions are specific and focused. Vague or overly broad questions can lead to inconclusive results.
Relevance : Your research questions should directly relate to your chosen topic. They should address gaps in knowledge or contribute to solving a particular problem.
Testability : Ensure that your questions are testable through empirical methods. You should be able to gather data and analyze it to answer these questions.
Avoid Bias : Craft your questions in a way that avoids leading or biased language. Maintain neutrality to uphold the integrity of your research.

3. Review Existing Literature

Before you embark on your empirical research journey, it's essential to immerse yourself in the existing body of literature related to your chosen topic. This step, often referred to as a literature review, serves several purposes:

Contextualization : Understand the historical context and current state of research in your field. What have previous studies found, and what questions remain unanswered?
Identifying Gaps : Identify gaps or areas where existing research falls short. These gaps will help you formulate meaningful research questions and hypotheses.
Theory Development : If your study is theoretical, consider how existing theories apply to your topic. If it's empirical, understand how previous studies have approached data collection and analysis.
Methodological Insights : Learn from the methodologies employed in previous research. What methods were successful, and what challenges did researchers face?

4. Define Variables

Variables are fundamental components of empirical research. They are the factors or characteristics that can change or be manipulated during your study. Properly defining and categorizing variables is crucial for the clarity and validity of your research. Here's what you need to know:

Independent Variables : These are the variables that you, as the researcher, manipulate or control. They are the "cause" in cause-and-effect relationships.
Dependent Variables : Dependent variables are the outcomes or responses that you measure or observe. They are the "effect" influenced by changes in independent variables.
Operational Definitions : To ensure consistency and clarity, provide operational definitions for your variables. Specify how you will measure or manipulate each variable.
Control Variables : In some studies, controlling for other variables that may influence your dependent variable is essential. These are known as control variables.

Understanding these foundational aspects of empirical research will set a solid foundation for the rest of your journey. Now that you've grasped the essentials of getting started, let's delve deeper into the intricacies of research design.

Empirical Research Design

Now that you've selected your research topic, formulated research questions, and defined your variables, it's time to delve into the heart of your empirical research journey – research design . This pivotal step determines how you will collect data and what methods you'll employ to answer your research questions. Let's explore the various facets of research design in detail.

Types of Empirical Research

Empirical research can take on several forms, each with its own unique approach and methodologies. Understanding the different types of empirical research will help you choose the most suitable design for your study. Here are some common types:

Experimental Research : In this type, researchers manipulate one or more independent variables to observe their impact on dependent variables. It's highly controlled and often conducted in a laboratory setting.
Observational Research : Observational research involves the systematic observation of subjects or phenomena without intervention. Researchers are passive observers, documenting behaviors, events, or patterns.
Survey Research : Surveys are used to collect data through structured questionnaires or interviews. This method is efficient for gathering information from a large number of participants.
Case Study Research : Case studies focus on in-depth exploration of one or a few cases. Researchers gather detailed information through various sources such as interviews, documents, and observations.
Qualitative Research : Qualitative research aims to understand behaviors, experiences, and opinions in depth. It often involves open-ended questions, interviews, and thematic analysis.
Quantitative Research : Quantitative research collects numerical data and relies on statistical analysis to draw conclusions. It involves structured questionnaires, experiments, and surveys.

Your choice of research type should align with your research questions and objectives. Experimental research, for example, is ideal for testing cause-and-effect relationships, while qualitative research is more suitable for exploring complex phenomena.

Experimental Design

Experimental research is a systematic approach to studying causal relationships. It's characterized by the manipulation of one or more independent variables while controlling for other factors. Here are some key aspects of experimental design:

Control and Experimental Groups : Participants are randomly assigned to either a control group or an experimental group. The independent variable is manipulated for the experimental group but not for the control group.
Randomization : Randomization is crucial to eliminate bias in group assignment. It ensures that each participant has an equal chance of being in either group.
Hypothesis Testing : Experimental research often involves hypothesis testing. Researchers formulate hypotheses about the expected effects of the independent variable and use statistical analysis to test these hypotheses.

Observational Design

Observational research entails careful and systematic observation of subjects or phenomena. It's advantageous when you want to understand natural behaviors or events. Key aspects of observational design include:

Participant Observation : Researchers immerse themselves in the environment they are studying. They become part of the group being observed, allowing for a deep understanding of behaviors.
Non-Participant Observation : In non-participant observation, researchers remain separate from the subjects. They observe and document behaviors without direct involvement.
Data Collection Methods : Observational research can involve various data collection methods, such as field notes, video recordings, photographs, or coding of observed behaviors.

Survey Design

Surveys are a popular choice for collecting data from a large number of participants. Effective survey design is essential to ensure the validity and reliability of your data. Consider the following:

Questionnaire Design : Create clear and concise questions that are easy for participants to understand. Avoid leading or biased questions.
Sampling Methods : Decide on the appropriate sampling method for your study, whether it's random, stratified, or convenience sampling.
Data Collection Tools : Choose the right tools for data collection, whether it's paper surveys, online questionnaires, or face-to-face interviews.

Case Study Design

Case studies are an in-depth exploration of one or a few cases to gain a deep understanding of a particular phenomenon. Key aspects of case study design include:

Single Case vs. Multiple Case Studies : Decide whether you'll focus on a single case or multiple cases. Single case studies are intensive and allow for detailed examination, while multiple case studies provide comparative insights.
Data Collection Methods : Gather data through interviews, observations, document analysis, or a combination of these methods.

Qualitative vs. Quantitative Research

In empirical research, you'll often encounter the distinction between qualitative and quantitative research . Here's a closer look at these two approaches:

Qualitative Research : Qualitative research seeks an in-depth understanding of human behavior, experiences, and perspectives. It involves open-ended questions, interviews, and the analysis of textual or narrative data. Qualitative research is exploratory and often used when the research question is complex and requires a nuanced understanding.
Quantitative Research : Quantitative research collects numerical data and employs statistical analysis to draw conclusions. It involves structured questionnaires, experiments, and surveys. Quantitative research is ideal for testing hypotheses and establishing cause-and-effect relationships.

Understanding the various research design options is crucial in determining the most appropriate approach for your study. Your choice should align with your research questions, objectives, and the nature of the phenomenon you're investigating.

Data Collection for Empirical Research

Now that you've established your research design, it's time to roll up your sleeves and collect the data that will fuel your empirical research. Effective data collection is essential for obtaining accurate and reliable results.

Sampling Methods

Sampling methods are critical in empirical research, as they determine the subset of individuals or elements from your target population that you will study. Here are some standard sampling methods:

Random Sampling : Random sampling ensures that every member of the population has an equal chance of being selected. It minimizes bias and is often used in quantitative research.
Stratified Sampling : Stratified sampling involves dividing the population into subgroups or strata based on specific characteristics (e.g., age, gender, location). Samples are then randomly selected from each stratum, ensuring representation of all subgroups.
Convenience Sampling : Convenience sampling involves selecting participants who are readily available or easily accessible. While it's convenient, it may introduce bias and limit the generalizability of results.
Snowball Sampling : Snowball sampling is instrumental when studying hard-to-reach or hidden populations. One participant leads you to another, creating a "snowball" effect. This method is common in qualitative research.
Purposive Sampling : In purposive sampling, researchers deliberately select participants who meet specific criteria relevant to their research questions. It's often used in qualitative studies to gather in-depth information.

The choice of sampling method depends on the nature of your research, available resources, and the degree of precision required. It's crucial to carefully consider your sampling strategy to ensure that your sample accurately represents your target population.

Data Collection Instruments

Data collection instruments are the tools you use to gather information from your participants or sources. These instruments should be designed to capture the data you need accurately. Here are some popular data collection instruments:

Questionnaires : Questionnaires consist of structured questions with predefined response options. When designing questionnaires, consider the clarity of questions, the order of questions, and the response format (e.g., Likert scale , multiple-choice).
Interviews : Interviews involve direct communication between the researcher and participants. They can be structured (with predetermined questions) or unstructured (open-ended). Effective interviews require active listening and probing for deeper insights.
Observations : Observations entail systematically and objectively recording behaviors, events, or phenomena. Researchers must establish clear criteria for what to observe, how to record observations, and when to observe.
Surveys : Surveys are a common data collection instrument for quantitative research. They can be administered through various means, including online surveys, paper surveys, and telephone surveys.
Documents and Archives : In some cases, data may be collected from existing documents, records, or archives. Ensure that the sources are reliable, relevant, and properly documented.

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Data Collection Procedures

Data collection procedures outline the step-by-step process for gathering data. These procedures should be meticulously planned and executed to maintain the integrity of your research.

Training : If you have a research team, ensure that they are trained in data collection methods and protocols. Consistency in data collection is crucial.
Pilot Testing : Before launching your data collection, conduct a pilot test with a small group to identify any potential problems with your instruments or procedures. Make necessary adjustments based on feedback.
Data Recording : Establish a systematic method for recording data. This may include timestamps, codes, or identifiers for each data point.
Data Security : Safeguard the confidentiality and security of collected data. Ensure that only authorized individuals have access to the data.
Data Storage : Properly organize and store your data in a secure location, whether in physical or digital form. Back up data to prevent loss.

Ethical Considerations

Ethical considerations are paramount in empirical research, as they ensure the well-being and rights of participants are protected.

Informed Consent : Obtain informed consent from participants, providing clear information about the research purpose, procedures, risks, and their right to withdraw at any time.
Privacy and Confidentiality : Protect the privacy and confidentiality of participants. Ensure that data is anonymized and sensitive information is kept confidential.
Beneficence : Ensure that your research benefits participants and society while minimizing harm. Consider the potential risks and benefits of your study.
Honesty and Integrity : Conduct research with honesty and integrity. Report findings accurately and transparently, even if they are not what you expected.
Respect for Participants : Treat participants with respect, dignity, and sensitivity to cultural differences. Avoid any form of coercion or manipulation.
Institutional Review Board (IRB) : If required, seek approval from an IRB or ethics committee before conducting your research, particularly when working with human participants.

Adhering to ethical guidelines is not only essential for the ethical conduct of research but also crucial for the credibility and validity of your study. Ethical research practices build trust between researchers and participants and contribute to the advancement of knowledge with integrity.

With a solid understanding of data collection, including sampling methods, instruments, procedures, and ethical considerations, you are now well-equipped to gather the data needed to answer your research questions.

Empirical Research Data Analysis

Now comes the exciting phase of data analysis, where the raw data you've diligently collected starts to yield insights and answers to your research questions. We will explore the various aspects of data analysis, from preparing your data to drawing meaningful conclusions through statistics and visualization.

Data Preparation

Data preparation is the crucial first step in data analysis. It involves cleaning, organizing, and transforming your raw data into a format that is ready for analysis. Effective data preparation ensures the accuracy and reliability of your results.

Data Cleaning : Identify and rectify errors, missing values, and inconsistencies in your dataset. This may involve correcting typos, removing outliers, and imputing missing data.
Data Coding : Assign numerical values or codes to categorical variables to make them suitable for statistical analysis. For example, converting "Yes" and "No" to 1 and 0.
Data Transformation : Transform variables as needed to meet the assumptions of the statistical tests you plan to use. Common transformations include logarithmic or square root transformations.
Data Integration : If your data comes from multiple sources, integrate it into a unified dataset, ensuring that variables match and align.
Data Documentation : Maintain clear documentation of all data preparation steps, as well as the rationale behind each decision. This transparency is essential for replicability.

Effective data preparation lays the foundation for accurate and meaningful analysis. It allows you to trust the results that will follow in the subsequent stages.

Descriptive Statistics

Descriptive statistics help you summarize and make sense of your data by providing a clear overview of its key characteristics. These statistics are essential for understanding the central tendencies, variability, and distribution of your variables. Descriptive statistics include:

Measures of Central Tendency : These include the mean (average), median (middle value), and mode (most frequent value). They help you understand the typical or central value of your data.
Measures of Dispersion : Measures like the range, variance, and standard deviation provide insights into the spread or variability of your data points.
Frequency Distributions : Creating frequency distributions or histograms allows you to visualize the distribution of your data across different values or categories.

Descriptive statistics provide the initial insights needed to understand your data's basic characteristics, which can inform further analysis.

Inferential Statistics

Inferential statistics take your analysis to the next level by allowing you to make inferences or predictions about a larger population based on your sample data. These methods help you test hypotheses and draw meaningful conclusions. Key concepts in inferential statistics include:

Hypothesis Testing : Hypothesis tests (e.g., t-tests, chi-squared tests) help you determine whether observed differences or associations in your data are statistically significant or occurred by chance.
Confidence Intervals : Confidence intervals provide a range within which population parameters (e.g., population mean) are likely to fall based on your sample data.
Regression Analysis : Regression models (linear, logistic, etc.) help you explore relationships between variables and make predictions.
Analysis of Variance (ANOVA) : ANOVA tests are used to compare means between multiple groups, allowing you to assess whether differences are statistically significant.

Inferential statistics are powerful tools for drawing conclusions from your data and assessing the generalizability of your findings to the broader population.

Qualitative Data Analysis

Qualitative data analysis is employed when working with non-numerical data, such as text, interviews, or open-ended survey responses. It focuses on understanding the underlying themes, patterns, and meanings within qualitative data. Qualitative analysis techniques include:

Thematic Analysis : Identifying and analyzing recurring themes or patterns within textual data.
Content Analysis : Categorizing and coding qualitative data to extract meaningful insights.
Grounded Theory : Developing theories or frameworks based on emergent themes from the data.
Narrative Analysis : Examining the structure and content of narratives to uncover meaning.

Qualitative data analysis provides a rich and nuanced understanding of complex phenomena and human experiences.

Data Visualization

Data visualization is the art of representing data graphically to make complex information more understandable and accessible. Effective data visualization can reveal patterns, trends, and outliers in your data. Common types of data visualization include:

Bar Charts and Histograms : Used to display the distribution of categorical or discrete data.
Line Charts : Ideal for showing trends and changes in data over time.
Scatter Plots : Visualize relationships and correlations between two variables.
Pie Charts : Display the composition of a whole in terms of its parts.
Heatmaps : Depict patterns and relationships in multidimensional data through color-coding.
Box Plots : Provide a summary of the data distribution, including outliers.
Interactive Dashboards : Create dynamic visualizations that allow users to explore data interactively.

Data visualization not only enhances your understanding of the data but also serves as a powerful communication tool to convey your findings to others.

As you embark on the data analysis phase of your empirical research, remember that the specific methods and techniques you choose will depend on your research questions, data type, and objectives. Effective data analysis transforms raw data into valuable insights, bringing you closer to the answers you seek.

How to Report Empirical Research Results?

At this stage, you get to share your empirical research findings with the world. Effective reporting and presentation of your results are crucial for communicating your research's impact and insights.

1. Write the Research Paper

Writing a research paper is the culmination of your empirical research journey. It's where you synthesize your findings, provide context, and contribute to the body of knowledge in your field.

Title and Abstract : Craft a clear and concise title that reflects your research's essence. The abstract should provide a brief summary of your research objectives, methods, findings, and implications.
Introduction : In the introduction, introduce your research topic, state your research questions or hypotheses, and explain the significance of your study. Provide context by discussing relevant literature.
Methods : Describe your research design, data collection methods, and sampling procedures. Be precise and transparent, allowing readers to understand how you conducted your study.
Results : Present your findings in a clear and organized manner. Use tables, graphs, and statistical analyses to support your results. Avoid interpreting your findings in this section; focus on the presentation of raw data.
Discussion : Interpret your findings and discuss their implications. Relate your results to your research questions and the existing literature. Address any limitations of your study and suggest avenues for future research.
Conclusion : Summarize the key points of your research and its significance. Restate your main findings and their implications.
References : Cite all sources used in your research following a specific citation style (e.g., APA, MLA, Chicago). Ensure accuracy and consistency in your citations.
Appendices : Include any supplementary material, such as questionnaires, data coding sheets, or additional analyses, in the appendices.

Writing a research paper is a skill that improves with practice. Ensure clarity, coherence, and conciseness in your writing to make your research accessible to a broader audience.

2. Create Visuals and Tables

Visuals and tables are powerful tools for presenting complex data in an accessible and understandable manner.

Clarity : Ensure that your visuals and tables are clear and easy to interpret. Use descriptive titles and labels.
Consistency : Maintain consistency in formatting, such as font size and style, across all visuals and tables.
Appropriateness : Choose the most suitable visual representation for your data. Bar charts, line graphs, and scatter plots work well for different types of data.
Simplicity : Avoid clutter and unnecessary details. Focus on conveying the main points.
Accessibility : Make sure your visuals and tables are accessible to a broad audience, including those with visual impairments.
Captions : Include informative captions that explain the significance of each visual or table.

Compelling visuals and tables enhance the reader's understanding of your research and can be the key to conveying complex information efficiently.

3. Interpret Findings

Interpreting your findings is where you bridge the gap between data and meaning. It's your opportunity to provide context, discuss implications, and offer insights. When interpreting your findings:

Relate to Research Questions : Discuss how your findings directly address your research questions or hypotheses.
Compare with Literature : Analyze how your results align with or deviate from previous research in your field. What insights can you draw from these comparisons?
Discuss Limitations : Be transparent about the limitations of your study. Address any constraints, biases, or potential sources of error.
Practical Implications : Explore the real-world implications of your findings. How can they be applied or inform decision-making?
Future Research Directions : Suggest areas for future research based on the gaps or unanswered questions that emerged from your study.

Interpreting findings goes beyond simply presenting data; it's about weaving a narrative that helps readers grasp the significance of your research in the broader context.

With your research paper written, structured, and enriched with visuals, and your findings expertly interpreted, you are now prepared to communicate your research effectively. Sharing your insights and contributing to the body of knowledge in your field is a significant accomplishment in empirical research.

Examples of Empirical Research

To solidify your understanding of empirical research, let's delve into some real-world examples across different fields. These examples will illustrate how empirical research is applied to gather data, analyze findings, and draw conclusions.

Social Sciences

In the realm of social sciences, consider a sociological study exploring the impact of socioeconomic status on educational attainment. Researchers gather data from a diverse group of individuals, including their family backgrounds, income levels, and academic achievements.

Through statistical analysis, they can identify correlations and trends, revealing whether individuals from lower socioeconomic backgrounds are less likely to attain higher levels of education. This empirical research helps shed light on societal inequalities and informs policymakers on potential interventions to address disparities in educational access.

Environmental Science

Environmental scientists often employ empirical research to assess the effects of environmental changes. For instance, researchers studying the impact of climate change on wildlife might collect data on animal populations, weather patterns, and habitat conditions over an extended period.

By analyzing this empirical data, they can identify correlations between climate fluctuations and changes in wildlife behavior, migration patterns, or population sizes. This empirical research is crucial for understanding the ecological consequences of climate change and informing conservation efforts.

Business and Economics

In the business world, empirical research is essential for making data-driven decisions. Consider a market research study conducted by a business seeking to launch a new product. They collect data through surveys, focus groups, and consumer behavior analysis.

By examining this empirical data, the company can gauge consumer preferences, demand, and potential market size. Empirical research in business helps guide product development, pricing strategies, and marketing campaigns, increasing the likelihood of a successful product launch.

Psychological studies frequently rely on empirical research to understand human behavior and cognition. For instance, a psychologist interested in examining the impact of stress on memory might design an experiment. Participants are exposed to stress-inducing situations, and their memory performance is assessed through various tasks.

By analyzing the data collected, the psychologist can determine whether stress has a significant effect on memory recall. This empirical research contributes to our understanding of the complex interplay between psychological factors and cognitive processes.

These examples highlight the versatility and applicability of empirical research across diverse fields. Whether in medicine, social sciences, environmental science, business, or psychology, empirical research serves as a fundamental tool for gaining insights, testing hypotheses, and driving advancements in knowledge and practice.

Conclusion for Empirical Research

Empirical research is a powerful tool for gaining insights, testing hypotheses, and making informed decisions. By following the steps outlined in this guide, you've learned how to select research topics, collect data, analyze findings, and effectively communicate your research to the world. Remember, empirical research is a journey of discovery, and each step you take brings you closer to a deeper understanding of the world around you. Whether you're a scientist, a student, or someone curious about the process, the principles of empirical research empower you to explore, learn, and contribute to the ever-expanding realm of knowledge.

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University of Memphis Libraries
Research Guides

Empirical Research: Defining, Identifying, & Finding

Defining empirical research, what is empirical research, quantitative or qualitative.

Introduction
Database Tools
Search Terms
Image Descriptions

Calfee & Chambliss (2005) (UofM login required) describe empirical research as a "systematic approach for answering certain types of questions." Those questions are answered "[t]hrough the collection of evidence under carefully defined and replicable conditions" (p. 43).

The evidence collected during empirical research is often referred to as "data."

Characteristics of Empirical Research

Emerald Publishing's guide to conducting empirical research identifies a number of common elements to empirical research:

A research question , which will determine research objectives.
A particular and planned design for the research, which will depend on the question and which will find ways of answering it with appropriate use of resources.
The gathering of primary data , which is then analysed.
A particular methodology for collecting and analysing the data, such as an experiment or survey.
The limitation of the data to a particular group, area or time scale, known as a sample [emphasis added]: for example, a specific number of employees of a particular company type, or all users of a library over a given time scale. The sample should be somehow representative of a wider population.
The ability to recreate the study and test the results. This is known as reliability .
The ability to generalize from the findings to a larger sample and to other situations.

If you see these elements in a research article, you can feel confident that you have found empirical research. Emerald's guide goes into more detail on each element.

Empirical research methodologies can be described as quantitative, qualitative, or a mix of both (usually called mixed-methods).

Ruane (2016) (UofM login required) gets at the basic differences in approach between quantitative and qualitative research:

Quantitative research -- an approach to documenting reality that relies heavily on numbers both for the measurement of variables and for data analysis (p. 33).
Qualitative research -- an approach to documenting reality that relies on words and images as the primary data source (p. 33).

Both quantitative and qualitative methods are empirical . If you can recognize that a research study is quantitative or qualitative study, then you have also recognized that it is empirical study.

Below are information on the characteristics of quantitative and qualitative research. This video from Scribbr also offers a good overall introduction to the two approaches to research methodology:

Characteristics of Quantitative Research

Researchers test hypotheses, or theories, based in assumptions about causality, i.e. we expect variable X to cause variable Y. Variables have to be controlled as much as possible to ensure validity. The results explain the relationship between the variables. Measures are based in pre-defined instruments.

Examples: experimental or quasi-experimental design, pretest & post-test, survey or questionnaire with closed-ended questions. Studies that identify factors that influence an outcomes, the utility of an intervention, or understanding predictors of outcomes.

Characteristics of Qualitative Research

Researchers explore “meaning individuals or groups ascribe to social or human problems (Creswell & Creswell, 2018, p3).” Questions and procedures emerge rather than being prescribed. Complexity, nuance, and individual meaning are valued. Research is both inductive and deductive. Data sources are multiple and varied, i.e. interviews, observations, documents, photographs, etc. The researcher is a key instrument and must be reflective of their background, culture, and experiences as influential of the research.

Examples: open question interviews and surveys, focus groups, case studies, grounded theory, ethnography, discourse analysis, narrative, phenomenology, participatory action research.

Calfee, R. C. & Chambliss, M. (2005). The design of empirical research. In J. Flood, D. Lapp, J. R. Squire, & J. Jensen (Eds.), Methods of research on teaching the English language arts: The methodology chapters from the handbook of research on teaching the English language arts (pp. 43-78). Routledge. http://ezproxy.memphis.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=125955&site=eds-live&scope=site .

Creswell, J. W., & Creswell, J. D. (2018). Research design: Qualitative, quantitative, and mixed methods approaches (5th ed.). Thousand Oaks: Sage.

How to... conduct empirical research . (n.d.). Emerald Publishing. https://www.emeraldgrouppublishing.com/how-to/research-methods/conduct-empirical-research .

Scribbr. (2019). Quantitative vs. qualitative: The differences explained [video]. YouTube. https://www.youtube.com/watch?v=a-XtVF7Bofg .

Ruane, J. M. (2016). Introducing social research methods : Essentials for getting the edge . Wiley-Blackwell. http://ezproxy.memphis.edu/login?url=http://search.ebscohost.com/login.aspx?direct=true&db=nlebk&AN=1107215&site=eds-live&scope=site .

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Empirical Research: A Comprehensive Guide for Academics

Empirical research relies on gathering and studying real, observable data. The term ’empirical’ comes from the Greek word ’empeirikos,’ meaning ‘experienced’ or ‘based on experience.’ So, what is empirical research? Instead of using theories or opinions, empirical research depends on real data obtained through direct observation or experimentation.

Why Empirical Research?

Empirical research plays a key role in checking or improving current theories, providing a systematic way to grow knowledge across different areas. By focusing on objectivity, it makes research findings more trustworthy, which is critical in research fields like medicine, psychology, economics, and public policy. In the end, the strengths of empirical research lie in deepening our awareness of the world and improving our capacity to tackle problems wisely. 1,2

Qualitative and Quantitative Methods

There are two main types of empirical research methods – qualitative and quantitative. 3,4 Qualitative research delves into intricate phenomena using non-numerical data, such as interviews or observations, to offer in-depth insights into human experiences. In contrast, quantitative research analyzes numerical data to spot patterns and relationships, aiming for objectivity and the ability to apply findings to a wider context.

Steps for Conducting Empirical Research

When it comes to conducting research, there are some simple steps that researchers can follow. 5,6

Create Research Hypothesis: Clearly state the specific question you want to answer or the hypothesis you want to explore in your study.
Examine Existing Research: Read and study existing research on your topic. Understand what’s already known, identify existing gaps in knowledge, and create a framework for your own study based on what you learn.
Plan Your Study: Decide how you’ll conduct your research—whether through qualitative methods, quantitative methods, or a mix of both. Choose suitable techniques like surveys, experiments, interviews, or observations based on your research question.
Develop Research Instruments: Create reliable research collection tools, such as surveys or questionnaires, to help you collate data. Ensure these tools are well-designed and effective.
Collect Data: Systematically gather the information you need for your research according to your study design and protocols using the chosen research methods.
Data Analysis: Analyze the collected data using suitable statistical or qualitative methods that align with your research question and objectives.
Interpret Results: Understand and explain the significance of your analysis results in the context of your research question or hypothesis.
Draw Conclusions: Summarize your findings and draw conclusions based on the evidence. Acknowledge any study limitations and propose areas for future research.

Advantages of Empirical Research

Empirical research is valuable because it stays objective by relying on observable data, lessening the impact of personal biases. This objectivity boosts the trustworthiness of research findings. Also, using precise quantitative methods helps in accurate measurement and statistical analysis. This precision ensures researchers can draw reliable conclusions from numerical data, strengthening our understanding of the studied phenomena. 4

Disadvantages of Empirical Research

While empirical research has notable strengths, researchers must also be aware of its limitations when deciding on the right research method for their study.4 One significant drawback of empirical research is the risk of oversimplifying complex phenomena, especially when relying solely on quantitative methods. These methods may struggle to capture the richness and nuances present in certain social, cultural, or psychological contexts. Another challenge is the potential for confounding variables or biases during data collection, impacting result accuracy.

Tips for Empirical Writing

In empirical research, the writing is usually done in research papers, articles, or reports. The empirical writing follows a set structure, and each section has a specific role. Here are some tips for your empirical writing. 7

Define Your Objectives: When you write about your research, start by making your goals clear. Explain what you want to find out or prove in a simple and direct way. This helps guide your research and lets others know what you have set out to achieve.
Be Specific in Your Literature Review: In the part where you talk about what others have studied before you, focus on research that directly relates to your research question. Keep it short and pick studies that help explain why your research is important. This part sets the stage for your work.
Explain Your Methods Clearly : When you talk about how you did your research (Methods), explain it in detail. Be clear about your research plan, who took part, and what you did; this helps others understand and trust your study. Also, be honest about any rules you follow to make sure your study is ethical and reproducible.
Share Your Results Clearly : After doing your empirical research, share what you found in a simple way. Use tables or graphs to make it easier for your audience to understand your research. Also, talk about any numbers you found and clearly state if they are important or not. Ensure that others can see why your research findings matter.
Talk About What Your Findings Mean: In the part where you discuss your research results, explain what they mean. Discuss why your findings are important and if they connect to what others have found before. Be honest about any problems with your study and suggest ideas for more research in the future.
Wrap It Up Clearly: Finally, end your empirical research paper by summarizing what you found and why it’s important. Remind everyone why your study matters. Keep your writing clear and fix any mistakes before you share it. Ask someone you trust to read it and give you feedback before you finish.

References:

Empirical Research in the Social Sciences and Education, Penn State University Libraries. Available online at https://guides.libraries.psu.edu/emp
How to conduct empirical research, Emerald Publishing. Available online at https://www.emeraldgrouppublishing.com/how-to/research-methods/conduct-empirical-research
Empirical Research: Quantitative & Qualitative, Arrendale Library, Piedmont University. Available online at https://library.piedmont.edu/empirical-research
Bouchrika, I. What Is Empirical Research? Definition, Types & Samples in 2024. Research.com, January 2024. Available online at https://research.com/research/what-is-empirical-research
Quantitative and Empirical Research vs. Other Types of Research. California State University, April 2023. Available online at https://libguides.csusb.edu/quantitative
Empirical Research, Definitions, Methods, Types and Examples, Studocu.com website. Available online at https://www.studocu.com/row/document/uganda-christian-university/it-research-methods/emperical-research-definitions-methods-types-and-examples/55333816
Writing an Empirical Paper in APA Style. Psychology Writing Center, University of Washington. Available online at https://psych.uw.edu/storage/writing_center/APApaper.pdf

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Empirical Research: Definition, Methods, Types and Examples

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Empirical research: Definition

Empirical research: origin, quantitative research methods, qualitative research methods, steps for conducting empirical research, empirical research methodology cycle, advantages of empirical research, disadvantages of empirical research, why is there a need for empirical research.

Empirical research is defined as any research where conclusions of the study is strictly drawn from concretely empirical evidence, and therefore “verifiable” evidence.

This empirical evidence can be gathered using quantitative market research and qualitative market research methods.

For example: A research is being conducted to find out if listening to happy music in the workplace while working may promote creativity? An experiment is conducted by using a music website survey on a set of audience who are exposed to happy music and another set who are not listening to music at all, and the subjects are then observed. The results derived from such a research will give empirical evidence if it does promote creativity or not.

LEARN ABOUT: Behavioral Research

You must have heard the quote” I will not believe it unless I see it”. This came from the ancient empiricists, a fundamental understanding that powered the emergence of medieval science during the renaissance period and laid the foundation of modern science, as we know it today. The word itself has its roots in greek. It is derived from the greek word empeirikos which means “experienced”.

In today’s world, the word empirical refers to collection of data using evidence that is collected through observation or experience or by using calibrated scientific instruments. All of the above origins have one thing in common which is dependence of observation and experiments to collect data and test them to come up with conclusions.

LEARN ABOUT: Causal Research

Types and methodologies of empirical research

Empirical research can be conducted and analysed using qualitative or quantitative methods.

Quantitative research : Quantitative research methods are used to gather information through numerical data. It is used to quantify opinions, behaviors or other defined variables . These are predetermined and are in a more structured format. Some of the commonly used methods are survey, longitudinal studies, polls, etc
Qualitative research: Qualitative research methods are used to gather non numerical data. It is used to find meanings, opinions, or the underlying reasons from its subjects. These methods are unstructured or semi structured. The sample size for such a research is usually small and it is a conversational type of method to provide more insight or in-depth information about the problem Some of the most popular forms of methods are focus groups, experiments, interviews, etc.

Data collected from these will need to be analysed. Empirical evidence can also be analysed either quantitatively and qualitatively. Using this, the researcher can answer empirical questions which have to be clearly defined and answerable with the findings he has got. The type of research design used will vary depending on the field in which it is going to be used. Many of them might choose to do a collective research involving quantitative and qualitative method to better answer questions which cannot be studied in a laboratory setting.

LEARN ABOUT: Qualitative Research Questions and Questionnaires

Quantitative research methods aid in analyzing the empirical evidence gathered. By using these a researcher can find out if his hypothesis is supported or not.

Survey research: Survey research generally involves a large audience to collect a large amount of data. This is a quantitative method having a predetermined set of closed questions which are pretty easy to answer. Because of the simplicity of such a method, high responses are achieved. It is one of the most commonly used methods for all kinds of research in today’s world.

Previously, surveys were taken face to face only with maybe a recorder. However, with advancement in technology and for ease, new mediums such as emails , or social media have emerged.

For example: Depletion of energy resources is a growing concern and hence there is a need for awareness about renewable energy. According to recent studies, fossil fuels still account for around 80% of energy consumption in the United States. Even though there is a rise in the use of green energy every year, there are certain parameters because of which the general population is still not opting for green energy. In order to understand why, a survey can be conducted to gather opinions of the general population about green energy and the factors that influence their choice of switching to renewable energy. Such a survey can help institutions or governing bodies to promote appropriate awareness and incentive schemes to push the use of greener energy.

Learn more: Renewable Energy Survey Template Descriptive Research vs Correlational Research

Experimental research: In experimental research , an experiment is set up and a hypothesis is tested by creating a situation in which one of the variable is manipulated. This is also used to check cause and effect. It is tested to see what happens to the independent variable if the other one is removed or altered. The process for such a method is usually proposing a hypothesis, experimenting on it, analyzing the findings and reporting the findings to understand if it supports the theory or not.

For example: A particular product company is trying to find what is the reason for them to not be able to capture the market. So the organisation makes changes in each one of the processes like manufacturing, marketing, sales and operations. Through the experiment they understand that sales training directly impacts the market coverage for their product. If the person is trained well, then the product will have better coverage.

Correlational research: Correlational research is used to find relation between two set of variables . Regression analysis is generally used to predict outcomes of such a method. It can be positive, negative or neutral correlation.

LEARN ABOUT: Level of Analysis

For example: Higher educated individuals will get higher paying jobs. This means higher education enables the individual to high paying job and less education will lead to lower paying jobs.

Longitudinal study: Longitudinal study is used to understand the traits or behavior of a subject under observation after repeatedly testing the subject over a period of time. Data collected from such a method can be qualitative or quantitative in nature.

For example: A research to find out benefits of exercise. The target is asked to exercise everyday for a particular period of time and the results show higher endurance, stamina, and muscle growth. This supports the fact that exercise benefits an individual body.

Cross sectional: Cross sectional study is an observational type of method, in which a set of audience is observed at a given point in time. In this type, the set of people are chosen in a fashion which depicts similarity in all the variables except the one which is being researched. This type does not enable the researcher to establish a cause and effect relationship as it is not observed for a continuous time period. It is majorly used by healthcare sector or the retail industry.

For example: A medical study to find the prevalence of under-nutrition disorders in kids of a given population. This will involve looking at a wide range of parameters like age, ethnicity, location, incomes and social backgrounds. If a significant number of kids coming from poor families show under-nutrition disorders, the researcher can further investigate into it. Usually a cross sectional study is followed by a longitudinal study to find out the exact reason.

Causal-Comparative research : This method is based on comparison. It is mainly used to find out cause-effect relationship between two variables or even multiple variables.

For example: A researcher measured the productivity of employees in a company which gave breaks to the employees during work and compared that to the employees of the company which did not give breaks at all.

LEARN ABOUT: Action Research

Some research questions need to be analysed qualitatively, as quantitative methods are not applicable there. In many cases, in-depth information is needed or a researcher may need to observe a target audience behavior, hence the results needed are in a descriptive analysis form. Qualitative research results will be descriptive rather than predictive. It enables the researcher to build or support theories for future potential quantitative research. In such a situation qualitative research methods are used to derive a conclusion to support the theory or hypothesis being studied.

LEARN ABOUT: Qualitative Interview

Case study: Case study method is used to find more information through carefully analyzing existing cases. It is very often used for business research or to gather empirical evidence for investigation purpose. It is a method to investigate a problem within its real life context through existing cases. The researcher has to carefully analyse making sure the parameter and variables in the existing case are the same as to the case that is being investigated. Using the findings from the case study, conclusions can be drawn regarding the topic that is being studied.

For example: A report mentioning the solution provided by a company to its client. The challenges they faced during initiation and deployment, the findings of the case and solutions they offered for the problems. Such case studies are used by most companies as it forms an empirical evidence for the company to promote in order to get more business.

Observational method: Observational method is a process to observe and gather data from its target. Since it is a qualitative method it is time consuming and very personal. It can be said that observational research method is a part of ethnographic research which is also used to gather empirical evidence. This is usually a qualitative form of research, however in some cases it can be quantitative as well depending on what is being studied.

For example: setting up a research to observe a particular animal in the rain-forests of amazon. Such a research usually take a lot of time as observation has to be done for a set amount of time to study patterns or behavior of the subject. Another example used widely nowadays is to observe people shopping in a mall to figure out buying behavior of consumers.

One-on-one interview: Such a method is purely qualitative and one of the most widely used. The reason being it enables a researcher get precise meaningful data if the right questions are asked. It is a conversational method where in-depth data can be gathered depending on where the conversation leads.

For example: A one-on-one interview with the finance minister to gather data on financial policies of the country and its implications on the public.

Focus groups: Focus groups are used when a researcher wants to find answers to why, what and how questions. A small group is generally chosen for such a method and it is not necessary to interact with the group in person. A moderator is generally needed in case the group is being addressed in person. This is widely used by product companies to collect data about their brands and the product.

For example: A mobile phone manufacturer wanting to have a feedback on the dimensions of one of their models which is yet to be launched. Such studies help the company meet the demand of the customer and position their model appropriately in the market.

Text analysis: Text analysis method is a little new compared to the other types. Such a method is used to analyse social life by going through images or words used by the individual. In today’s world, with social media playing a major part of everyone’s life, such a method enables the research to follow the pattern that relates to his study.

For example: A lot of companies ask for feedback from the customer in detail mentioning how satisfied are they with their customer support team. Such data enables the researcher to take appropriate decisions to make their support team better.

Sometimes a combination of the methods is also needed for some questions that cannot be answered using only one type of method especially when a researcher needs to gain a complete understanding of complex subject matter.

We recently published a blog that talks about examples of qualitative data in education ; why don’t you check it out for more ideas?

Since empirical research is based on observation and capturing experiences, it is important to plan the steps to conduct the experiment and how to analyse it. This will enable the researcher to resolve problems or obstacles which can occur during the experiment.

Step #1: Define the purpose of the research

This is the step where the researcher has to answer questions like what exactly do I want to find out? What is the problem statement? Are there any issues in terms of the availability of knowledge, data, time or resources. Will this research be more beneficial than what it will cost.

Before going ahead, a researcher has to clearly define his purpose for the research and set up a plan to carry out further tasks.

Step #2 : Supporting theories and relevant literature

The researcher needs to find out if there are theories which can be linked to his research problem . He has to figure out if any theory can help him support his findings. All kind of relevant literature will help the researcher to find if there are others who have researched this before, or what are the problems faced during this research. The researcher will also have to set up assumptions and also find out if there is any history regarding his research problem

Step #3: Creation of Hypothesis and measurement

Before beginning the actual research he needs to provide himself a working hypothesis or guess what will be the probable result. Researcher has to set up variables, decide the environment for the research and find out how can he relate between the variables.

Researcher will also need to define the units of measurements, tolerable degree for errors, and find out if the measurement chosen will be acceptable by others.

Step #4: Methodology, research design and data collection

In this step, the researcher has to define a strategy for conducting his research. He has to set up experiments to collect data which will enable him to propose the hypothesis. The researcher will decide whether he will need experimental or non experimental method for conducting the research. The type of research design will vary depending on the field in which the research is being conducted. Last but not the least, the researcher will have to find out parameters that will affect the validity of the research design. Data collection will need to be done by choosing appropriate samples depending on the research question. To carry out the research, he can use one of the many sampling techniques. Once data collection is complete, researcher will have empirical data which needs to be analysed.

LEARN ABOUT: Best Data Collection Tools

Step #5: Data Analysis and result

Data analysis can be done in two ways, qualitatively and quantitatively. Researcher will need to find out what qualitative method or quantitative method will be needed or will he need a combination of both. Depending on the unit of analysis of his data, he will know if his hypothesis is supported or rejected. Analyzing this data is the most important part to support his hypothesis.

Step #6: Conclusion

A report will need to be made with the findings of the research. The researcher can give the theories and literature that support his research. He can make suggestions or recommendations for further research on his topic.

A.D. de Groot, a famous dutch psychologist and a chess expert conducted some of the most notable experiments using chess in the 1940’s. During his study, he came up with a cycle which is consistent and now widely used to conduct empirical research. It consists of 5 phases with each phase being as important as the next one. The empirical cycle captures the process of coming up with hypothesis about how certain subjects work or behave and then testing these hypothesis against empirical data in a systematic and rigorous approach. It can be said that it characterizes the deductive approach to science. Following is the empirical cycle.

Observation: At this phase an idea is sparked for proposing a hypothesis. During this phase empirical data is gathered using observation. For example: a particular species of flower bloom in a different color only during a specific season.
Induction: Inductive reasoning is then carried out to form a general conclusion from the data gathered through observation. For example: As stated above it is observed that the species of flower blooms in a different color during a specific season. A researcher may ask a question “does the temperature in the season cause the color change in the flower?” He can assume that is the case, however it is a mere conjecture and hence an experiment needs to be set up to support this hypothesis. So he tags a few set of flowers kept at a different temperature and observes if they still change the color?
Deduction: This phase helps the researcher to deduce a conclusion out of his experiment. This has to be based on logic and rationality to come up with specific unbiased results.For example: In the experiment, if the tagged flowers in a different temperature environment do not change the color then it can be concluded that temperature plays a role in changing the color of the bloom.
Testing: This phase involves the researcher to return to empirical methods to put his hypothesis to the test. The researcher now needs to make sense of his data and hence needs to use statistical analysis plans to determine the temperature and bloom color relationship. If the researcher finds out that most flowers bloom a different color when exposed to the certain temperature and the others do not when the temperature is different, he has found support to his hypothesis. Please note this not proof but just a support to his hypothesis.
Evaluation: This phase is generally forgotten by most but is an important one to keep gaining knowledge. During this phase the researcher puts forth the data he has collected, the support argument and his conclusion. The researcher also states the limitations for the experiment and his hypothesis and suggests tips for others to pick it up and continue a more in-depth research for others in the future. LEARN MORE: Population vs Sample

LEARN MORE: Population vs Sample

There is a reason why empirical research is one of the most widely used method. There are a few advantages associated with it. Following are a few of them.

It is used to authenticate traditional research through various experiments and observations.
This research methodology makes the research being conducted more competent and authentic.
It enables a researcher understand the dynamic changes that can happen and change his strategy accordingly.
The level of control in such a research is high so the researcher can control multiple variables.
It plays a vital role in increasing internal validity .

Even though empirical research makes the research more competent and authentic, it does have a few disadvantages. Following are a few of them.

Such a research needs patience as it can be very time consuming. The researcher has to collect data from multiple sources and the parameters involved are quite a few, which will lead to a time consuming research.
Most of the time, a researcher will need to conduct research at different locations or in different environments, this can lead to an expensive affair.
There are a few rules in which experiments can be performed and hence permissions are needed. Many a times, it is very difficult to get certain permissions to carry out different methods of this research.
Collection of data can be a problem sometimes, as it has to be collected from a variety of sources through different methods.

LEARN ABOUT: Social Communication Questionnaire

Empirical research is important in today’s world because most people believe in something only that they can see, hear or experience. It is used to validate multiple hypothesis and increase human knowledge and continue doing it to keep advancing in various fields.

For example: Pharmaceutical companies use empirical research to try out a specific drug on controlled groups or random groups to study the effect and cause. This way, they prove certain theories they had proposed for the specific drug. Such research is very important as sometimes it can lead to finding a cure for a disease that has existed for many years. It is useful in science and many other fields like history, social sciences, business, etc.

LEARN ABOUT: 12 Best Tools for Researchers

With the advancement in today’s world, empirical research has become critical and a norm in many fields to support their hypothesis and gain more knowledge. The methods mentioned above are very useful for carrying out such research. However, a number of new methods will keep coming up as the nature of new investigative questions keeps getting unique or changing.

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Open Access

Raising awareness of uncertain choices in empirical data analysis: A teaching concept toward replicable research practices

Roles Conceptualization, Formal analysis, Investigation, Software, Visualization, Writing – original draft, Writing – review & editing

* E-mail: [email protected]

Current address: Institute for Medical Information Processing, Biometry and Epidemiology, Medical Faculty, Ludwig-Maximilians-Universität München, München, Germany

Affiliations Institute for Medical Information Processing, Biometry and Epidemiology, Medical Faculty, Ludwig-Maximilians-Universität München, München, Germany, Munich Center for Machine Learning (MCML), München, Germany, LMU Open Science Center, München, Germany

Roles Conceptualization, Writing – original draft, Writing – review & editing

Affiliations Institute for Medical Information Processing, Biometry and Epidemiology, Medical Faculty, Ludwig-Maximilians-Universität München, München, Germany, LMU Open Science Center, München, Germany, Department of Statistics, Ludwig-Maximilians-Universität München, München, Germany

Roles Writing – review & editing

Affiliation Department of Statistics, Ludwig-Maximilians-Universität München, München, Germany

Affiliation Institute for Medical Information Processing, Biometry and Epidemiology, Medical Faculty, Ludwig-Maximilians-Universität München, München, Germany

Roles Conceptualization, Funding acquisition, Project administration, Supervision, Writing – original draft, Writing – review & editing

Maximilian M. Mandl,
Sabine Hoffmann,
Sebastian Bieringer,
Anna E. Jacob,
Marie Kraft,
Simon Lemster,
Anne-Laure Boulesteix

Published: March 28, 2024

https://doi.org/10.1371/journal.pcbi.1011936
Reader Comments

Author summary

Throughout their education and when reading the scientific literature, students may get the impression that there is a unique and correct analysis strategy for every data analysis task and that this analysis strategy will always yield a significant and noteworthy result. This expectation conflicts with a growing realization that there is a multiplicity of possible analysis strategies in empirical research, which will lead to overoptimism and nonreplicable research findings if it is combined with result-dependent selective reporting. Here, we argue that students are often ill-equipped for real-world data analysis tasks and unprepared for the dangers of selectively reporting the most promising results. We present a seminar course intended for advanced undergraduates and beginning graduate students of data analysis fields such as statistics, data science, or bioinformatics that aims to increase the awareness of uncertain choices in the analysis of empirical data and present ways to deal with these choices through theoretical modules and practical hands-on sessions.

Citation: Mandl MM, Hoffmann S, Bieringer S, Jacob AE, Kraft M, Lemster S, et al. (2024) Raising awareness of uncertain choices in empirical data analysis: A teaching concept toward replicable research practices. PLoS Comput Biol 20(3): e1011936. https://doi.org/10.1371/journal.pcbi.1011936

Editor: B.F. Francis Ouellette, bioinformatics.ca, CANADA

Copyright: © 2024 Mandl et al. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: The authors gratefully acknowledge the funding by DFG grants BO3139/7-1 and BO3139/9-1 to A-LB. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.

Competing interests: The authors have declared that no competing interests exist.

Introduction

Statistics and data analysis education frequently focuses on acquiring skills and techniques concerning specific topics that are covered successively and in isolation. Students may, for instance, first take a course on general techniques for regression modeling without considering the challenges associated with missing data, outliers, or nonrepresentative sampling mechanisms. They may then acquire skills to specifically address these additional challenges in a later course. In the classroom, students are often presented with clear examples and with clean data sets to practice these skills and techniques on. These exercises typically have unique, correct solutions to the analysis task and often yield significant results, possibly conditioning students to expect the same from real-world data. In this vein, problems arising during the analysis are considered in isolation, even though they occur simultaneously and may be interrelated. While the simplified and sequential treatment of specific topics certainly makes sense from a pedagogical standpoint, it may convey the unrealistic expectation that for any data analysis task, there is a unique and correct analysis approach that will always yield a significant or interesting finding. This expectation is further strengthened when reading published research articles in which the authors commonly describe a single analysis strategy and report a significant finding without a detailed discussion of alternative analysis options.

This impression conflicts with a growing realization that there is a multiplicity of possible analysis strategies when analyzing empirical data [ 1 – 3 ] and that data analysts require the ability to make subjective decisions and acknowledge the multiplicity of possible perspectives [ 4 ]. In particular, so-called multianalyst projects [ 5 – 7 ] show that different teams of researchers make very different choices when they are asked to answer the same research question on the same data set. These uncertain choices, which are also referred to as researcher degrees of freedom [ 8 , 9 ], can be combined with result-dependent selective reporting to obtain the “most noteworthy” or impressive results. This is a practice known as “p-hacking” or “fishing for significance” in the context of hypothesis testing and, more generally, “fishing expeditions” or “cherry-picking.” These practices lead to overconfident and nonreplicable research findings in the literature and, ultimately, to situations where some may argue that “most published research findings are false,” especially in combination with a low prior probability of the hypothesis being true [ 10 , 11 ]. Computational biology as a field is, unfortunately, not immune to these types of problems [ 3 , 12 ].

For example, Ullmann et al. [ 3 ] show how the combination of researchers’ expectations and selective reporting may lead to overoptimistic results in the context of unsupervised microbiome analysis. Their paper highlights the relevance of open science practices in the field of computational biology.

Here, we argue that if students always encounter clean data sets with a correct unique analysis strategy yielding a significant and/or noteworthy finding during their training, they are ill-equipped for real-world data analysis tasks and unprepared for the dangers of selectively reporting the most promising results. In particular, data analysis courses commonly teach students to understand and apply statistical models, but in order to equip them against the cherry-picking, we need to strengthen awareness and understanding of uncertainties in the analysis of empirical research data. To address this point, we present a seminar course intended for advanced undergraduates and beginning graduate students of data analysis fields such as statistics, data science, or bioinformatics that aims to increase awareness of the multiplicity of analysis strategies and of ways to deal with this multiplicity through the introduction of theoretical concepts and practical hands-on sessions.

The remainder of the article is organized as follows: Section “Teaching concept” presents the general teaching concept of the proposed seminar course. Section “Implementation and student feedback” provides evidence on the instructional value of the proposed course. Section “Potential adaptations” discusses potential adaptations of the course, and in Section “Conclusion,” we highlight key skills and takeaways that we hope students will gain.

Teaching concept

The course consists of theoretical modules and practical hands-on sessions. It starts with two short lectures, providing a brief introduction to the concepts of reproducibility and replicability. Subsequently, it focuses on reproducibility by introducing the students to version control software and R-Markdown to make their analyses reproducible, i.e., they learn to prepare their code in a way that all results can be reproduced “by mouse click.” In this paper, we follow the definition by Nosek et al. [ 13 ], i.e., reproducibility involves verifying the reliability of a previous discovery by employing the identical data and analysis strategy.

The second part of the course is devoted to replicability in a broad sense, where a result is said to be replicable if one obtains a similar result when repeating the same study including the collection of independent data. More specifically, the students participate in a hands-on session, in which each student is asked to perform a regression analysis on the same data set. After this first hands-on session, they are presented with a second theoretical module that focuses on uncertain choices in the analysis of empirical data, the consequences of result-dependent selective reporting, and ways to address these issues. While the hands-on session can be seen as an evaluation of the extent of selective reporting in the classroom, this second theoretical module can be seen as an intervention. It aims to prevent the students from selectively reporting the most promosing results arising through the multiplicity of possible analysis strategies. The effect of this intervention can, to some extent, be measured by comparing the results of the first phase of the hands-on session with a second phase, which follows the theoretical module on researcher degrees of freedom, in which the students are again asked to analyze a data set that has been generated according to the same model and parameter values as the data set in phase 1. The students’ experience with the two hands-on sessions, the results concerning this intervention effect, and their takeaways are discussed in the last two sessions of the course. A sample weekly schedule for a 10-week academic term is shown in Table 1 . Note that the course might alternatively be conducted as an intensive course in one or few days as discussed in the section on potential adaptations.

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https://doi.org/10.1371/journal.pcbi.1011936.t001

Practical hands-on sessions

In the two hands-on sessions, which should ideally take around 3 hours and be onsite to guarantee that there is no exchange between the students, each student receives the same simulated data set and is asked to estimate the effect of a predictor of interest in a linear regression model and to provide a point estimate and a 95% confidence interval. See Section C “Instructions for the students” in S1 Appendix for more details on the exact instructions received by the students.

The analysis task is designed in such a way that several uncertain choices related to model selection, treatment of missing values, and handling of outliers are required. Although we realize that such questions should ideally be tackled at the design stage of a study, in practice many researchers unfortunately address these difficulties post hoc.

To help the students with these choices, they are provided with literature that gives an overview of methods and guidance on these choices (see, for instance, [ 14 , 15 ]) and they are able to ask the lecturer for advice during the entire session. Additionally, the students are given information on the “likely range” of the effect of interest, while the true effect is somewhat below this range. The goal is to mimic a realistic data analysis situation in which the life scientist may hope for a large effect and exert gentle pressure on the data analyst toward observing it in the data. For each of the hands-on sessions, students are asked to analyze the data in the best possible way (which is not necessarily the same for both phases) and to hand in their results and reproducible analysis code.

Theoretical module on uncertain choices in the analysis of empirical data and ways to address them

The theoretical module consists of lectures that address the ubiquity of uncertain choices in the analysis of empirical data, their consequences on the validity of statistical inference if they are combined with selective reporting, and solutions to address this issue. In particular, the lectures detail how result-dependent selective reporting (cherry-picking, HARKing [ 16 ], and selective publication of significant findings) can lead to overoptimism. Further, they outline that there is increasing evidence that this practice is both common and detrimental for the replicability and credibility of the scientific literature.

Finally, as an outlook, the theoretical module also presents general strategies to deal with the multiplicity of possible analysis strategies while preserving the validity of statistical inference. This can include preregistration, blind analysis, and multiverse-style analyses. A list of articles that can be used to design this theoretical module can be found in Section A “Details on the implementation” in S1 Appendix .

The last two sessions leave space for the discussion of the results of the two hands-on sessions, of the students’ experience with the course, and of student takeaways. In the first session, the students are presented with the results of the first hands-on session in which they analyzed the same data set. Due to the uncertain choices in the analysis of this data set, it is likely that the students chose a variety of analysis strategies and obtained different results, providing them with first-hand experience that there is not a single correct analysis strategy for every data analysis task. These results are then compared with the true parameter value that was used to generate the data, providing insight to the extent of selective reporting that was performed during the analysis. Instructors may stress that true parameter values are not known in real data analysis and point out the principles of statistical simulations and their importance for data analysis methods by mimicking real-world scenarios with known truth.

In the second debriefing session, the results of the two hands-on sessions are compared to assess the intervention effect of the theoretical module on uncertain choices in the analysis of empirical data. As seminar courses tend to be small (with less than 30 students) and some students might lack motivation or skills to either perform multiple analyses (and selective reporting) in the first hands-on session or to change their analysis strategy in the second hands-on session, it is unlikely that a statistically significant intervention effect would be observed. Such a nonsignificant finding opens the discussion to reasons for this “failed experiment,” including lack of power, imperfect adherence and, more generally, that this nonsignificant finding cannot be interpreted as evidence that the intervention is useless since “absence of evidence is not evidence of absence” [ 17 ] and that practical importance and significance are distinct concepts [ 18 ]. After discussing the realities of experimental design, the lecturer can present the students with alternative possible results on this intervention effect resulting, for instance, from more or less plausible inclusion and exclusion criteria or outcome switching that would lead to a statistically significant intervention effect. This could raise student awareness of their own preconceived expectations that it is only a matter of finding the right analysis strategy to produce an intended result. This is a common fallacy that can arise, especially in the analysis of underpowered studies.

Implementation and student feedback

We implemented a version of the course concept described in Section “Teaching concept” as a seminar course for advanced undergraduate students in statistics at Ludwig-Maximilians-Universität München (Germany) in 2021/2022.

The overall feedback from the students was very positive and indicated that the course had the intended effect of raising awareness of uncertain choices in the analysis of empirical data and of the dangers of result-dependent selective reporting.

The following 2 student statements, which we received after asking the students for more detailed feedback, further support this conclusion:

“I think that the learning effect of the seminar was greater than in a classical seminar, which consists exclusively of frontal teaching and presentations. […] This also made me aware of how difficult it is to make statistical decisions on the basis of the available information.”

“The seminar was very practical compared to other seminars, which made itself and the experience unique. This seminar and the experiment have had a sustainable effect on the way I do statistics. For example, it is okay to get an inconclusive result when analysing data, not everything has to be significant.”

Fig 1 shows the difference between the estimated and true effects (represented as relative under- or overestimation) in phases 1 and 2 for the full sample ( n = 26) and 3 further selected subsamples. In phase 1, the students reported a parameter estimate that was on average 17.55% larger than the true parameter value (one-sided t test: p = 0.03; Wilcoxon: p = 0.04), indicating that our instructions may indeed have incited the students to selectively report promising results.

(a) Full sample ( n = 26); (b) students with higher grades ( n = 15); (c) students who overestimated the true effect in phase 1 ( n = 18); (d) female students ( n = 11). Connected points represent the values for phases 1 and 2 for each student. Red lines indicate an increased estimated effect size in phase 2 compared to phase 1, and blue lines indicate the reverse.

https://doi.org/10.1371/journal.pcbi.1011936.g001

In phase 2, the reported effect was on average 11.67% larger than the true effect (one-sided t test: p = 0.18; Wilcoxon: p = 0.05), providing less evidence for result-dependent selective reporting after the theoretical module on uncertain choices and their consequences for the validity of statistical inference. Even if there was a significant overestimation of the effect in phase 1 (17.55%) but not in phase 2 (11.67%), the 2 phases did not significantly differ with respect to this difference (paired one-sided t test: p = 0.35; Wilcoxon: p = 0.40), a result that may appear counterintuitive to students and is certainly worth pointing out.

An aspect worth being discussed with the students is shown in Fig 1 . The intervention effect becomes significant (or very close to the 5% level) if we (slightly) change our analysis strategy, for instance, by performing the analysis only on students who overestimated the effect in phase 1 ( Fig 1(c) : n = 18, paired one-sided t test: p = 0.04; Wilcoxon: p = 0.06) or only on female students ( Fig 1(d) : n = 11, paired one-sided t test: p = 0.06; Wilcoxon: p = 0.09), leaving room for the selective reporting of promising intervention effects in this highly underpowered experiment. Conversely, the p -value of the intervention effect can also increase if we include only the students who performed well in terms of grades in the course ( Fig 1(b) : n = 15, paired one-sided t test: p = 0.57; Wilcoxon: p = 0.68).

For more details, see Sections A “Details on the implementation,” B “Data simulation,” and C “Instructions for the students” in S1 Appendix . The code and data can be found on GitHub ( https://github.com/mmax-code/teaching_concept ).

Potential adaptations

Since the multiplicity of possible analysis strategies and result-dependent selective reporting are complex issues with many different aspects, there are several potential adaptations that can be made to tailor the course to varying preferences and needs.

In our implementation of the course, we chose to have the students work on simulated data sets, but it is of course possible to choose real data sets for the hands-on-sessions. To decide between these two options, it is important to decide whether one merely intends to raise awareness for the multiplicity of possible analysis strategies or to caution students against the dangers of result-dependent selective reporting. More generally, questionable research practices that may result from this multiplicity of possible analysis strategies include HARKing, fishing for significance, and data dredging. In the case where the aim is to caution against result-dependent selective reporting, it is indispensable to use simulated data sets in the hands-on session to be able to show how these practices lead to an overestimation of the true parameter value (which would be impossible on a real data set since the true parameter value is unknown). If, on the other hand, the course only focuses on raising awareness of uncertain choices and the multiplicity of possible analysis strategies, it seems more advisable to use real data sets with all their “ugly” features including, for instance, complex patterns of missing data and outliers since they offer a more realistic framework to achieve this teaching purpose, in the vein of the multiverse analysis in the classroom suggested by Heyman and Vanpaemel [ 19 ].

A second important decision in the teaching concept concerns the question of whether to focus on long-term strategies to address the multiplicity of possible analysis strategies or to present students with short-term solutions whose effects will be more observable when comparing the results from the first and the second phase of the hands-on session. The course concept that we presented here was designed to be instructive in the long term (such an effect being impossible to demonstrate in the course setting) rather than to show a large intervention effect. In this sense, the strategies that we presented to prevent result-dependent selective reporting included preregistration, blind analysis, and multiverse analyses. While these strategies are indubitably very helpful for students to address the multiplicity of possible analysis strategies in future projects, they may be of rather limited value in the second hands-on session of the course.

Related to this latter point, we chose the timing of the course to be rather early in the students’ curriculum to inoculate them against result-dependent selective reporting among a multiplicity of possible analysis strategies. This is hopefully before they were even aware of the wealth of methods and modeling strategies that they could choose from. While we believe that this may very well increase the long-term effectiveness of the teaching intervention, it will inevitably reduce the size of the intervention effect that we can observe when comparing the first and the second phase of the hands-on session because this lack of awareness reduces the number of analysis strategies that the students can choose from. In contrast, one could choose a later timing of the course in the students’ curriculum or provide the students with abundant literature on various methods and include additional lectures on methods (for instance, on model selection or missing values) in the course. In our implementation of the course of limited volume, we deliberately decided not to handle methodological issues beyond a brief introduction, in order to focus on reproducibility and replicability. The fact that students used (mostly the same) rather simple methods (for instance, AIC-based model selection) in the implementation suggests that they were probably not aware of the many possibilities they had—which may de facto prevent them from fishing for significance. Presenting the students with a multiplicity of methods before or during the hands-on sessions, on the other hand, might increase their fishing behavior, at least in the first hands-on session. Finally, we did not explicitly ask the students to change their analysis strategies, which may have led students with limited motivation to keep the same analysis strategy for both phases.

This focus on the long-term effectiveness of the course rather than on short-term strategies that may be perceivable in the comparison of the first and the second hands-on session might very well explain why we did not observe a significant reduction in result-dependent selective reporting between the two phases. However, as pointed out in Section “Debriefing,” we would consider this nonsignificant result less of a bug and more of a feature since it opens the discussion to topics including lack of power, imperfect adherence and, more generally, reminds the students that a nonsignificant finding cannot be interpreted as evidence that an intervention did not work.

On a completely different level, the course could be adapted to other types of data analyses in a broad sense beyond the generic example of effect estimation with regression models considered here. Selective reporting is relevant and may be considered in various contexts such as supervised learning [ 20 ], cluster and network analysis [ 3 ], or gene set analysis [ 21 ] rather than statistical testing in regression models. Examples inspired from these studies may be appropriate for students majoring in fields related to computational biology. Note that even though a prerequisite for our course is the use of an interpreted programming language such as R or Python and at least basic knowledge of regression models, the general concept of the course can, in principle, also be applied to students with a weaker computational background. For example, one could implement the course with a simple hypothesis test setting using a statistical software framework including a user interface (for instance, SPSS).

Finally, depending on the complexity of the considered analyses and the amount of effort required from students to understand and execute the analyses, the course concept could also be adapted to a one or multiple day intensive course. With such a shorter format, the complexity of the hands-on task and the width of the covered theoretical topics (see section A in S1 Appendix ) should probably be reduced compared to our original version of the course. For example, one could address primarily the multiplicity of analysis strategies and put less focus on specific software aspects (such as the use of R-Markdown).

There has been growing evidence in recent years that the current use (and misuse) of data analysis methods has contributed to what has been referred to as a “replication crisis” or “statistical crisis” in science. We argue that we need to address these problems in the way we teach statistics and data analysis [ 22 ]. In particular, we need to raise awareness regarding the potential dangers of selective reporting in the education of computational scientists. With the concept of the presented course, we address this issue through practical hands-on sessions and theoretical modules. Going beyond selective reporting, the course also provides the opportunity to teach students reproducible research practices [ 23 ] and to discuss important issues in the design and analysis of experimental studies, including lack of statistical power, nonadherence, and the common misinterpretation of absence of evidence as evidence of absence.

While the combination of a multiplicity of possible analysis strategies with selective reporting is an important issue today, it is likely to pose even more challenges in the future with the increasing availability of large complex data sets. In the analysis of these data sets, researchers are faced with even more uncertain choices than in data that are collected within simple focused experiments, as there is far less knowledge of the data generating mechanisms and control over measurement procedures. To avoid what Meng [ 24 ] calls “Big data paradoxes” in the analysis of these data sets (“the more the data, the surer we fool ourselves”), we urgently need to prepare our students for the realities of empirical data analysis by fostering their awareness and understanding of uncertain choices and ways to address these choices that preserve the validity of statistical inference.

Supporting information

S1 appendix. details on the implementation, data simulation, and instructions for the students..

https://doi.org/10.1371/journal.pcbi.1011936.s001

Acknowledgments

We thank Roman Hornung, Christina Sauer, and Theresa Ullmann for their comments and helpful discussions and Savanna Ratky for valuable language corrections.

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Empirical Research: Quantitative & Qualitative

Empirical Research

Introduction: What is Empirical Research?

Quantitative methods, qualitative methods.

Quantitative vs. Qualitative
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Empirical research is based on phenomena that can be observed and measured. Empirical research derives knowledge from actual experience rather than from theory or belief.

Key characteristics of empirical research include:

Specific research questions to be answered;
Definitions of the population, behavior, or phenomena being studied;
Description of the methodology or research design used to study this population or phenomena, including selection criteria, controls, and testing instruments (such as surveys);
Two basic research processes or methods in empirical research: quantitative methods and qualitative methods (see the rest of the guide for more about these methods).

(based on the original from the Connelly LIbrary of LaSalle University)

Empirical Research: Qualitative vs. Quantitative

Learn about common types of journal articles that use APA Style, including empirical studies; meta-analyses; literature reviews; and replication, theoretical, and methodological articles.

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Quantitative Research

A quantitative research project is characterized by having a population about which the researcher wants to draw conclusions, but it is not possible to collect data on the entire population.

For an observational study, it is necessary to select a proper, statistical random sample and to use methods of statistical inference to draw conclusions about the population.
For an experimental study, it is necessary to have a random assignment of subjects to experimental and control groups in order to use methods of statistical inference.

Statistical methods are used in all three stages of a quantitative research project.

For observational studies, the data are collected using statistical sampling theory. Then, the sample data are analyzed using descriptive statistical analysis. Finally, generalizations are made from the sample data to the entire population using statistical inference.

For experimental studies, the subjects are allocated to experimental and control group using randomizing methods. Then, the experimental data are analyzed using descriptive statistical analysis. Finally, just as for observational data, generalizations are made to a larger population.

Iversen, G. (2004). Quantitative research . In M. Lewis-Beck, A. Bryman, & T. Liao (Eds.), Encyclopedia of social science research methods . (pp. 897-898). Thousand Oaks, CA: SAGE Publications, Inc.

Qualitative Research

What makes a work deserving of the label qualitative research is the demonstrable effort to produce richly and relevantly detailed descriptions and particularized interpretations of people and the social, linguistic, material, and other practices and events that shape and are shaped by them.

Qualitative research typically includes, but is not limited to, discerning the perspectives of these people, or what is often referred to as the actor’s point of view. Although both philosophically and methodologically a highly diverse entity, qualitative research is marked by certain defining imperatives that include its case (as opposed to its variable) orientation, sensitivity to cultural and historical context, and reflexivity.

In its many guises, qualitative research is a form of empirical inquiry that typically entails some form of purposive sampling for information-rich cases; in-depth interviews and open-ended interviews, lengthy participant/field observations, and/or document or artifact study; and techniques for analysis and interpretation of data that move beyond the data generated and their surface appearances.

Sandelowski, M. (2004). Qualitative research . In M. Lewis-Beck, A. Bryman, & T. Liao (Eds.), Encyclopedia of social science research methods . (pp. 893-894). Thousand Oaks, CA: SAGE Publications, Inc.

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Research Guide

Chapter 6 the empirical analysis.

Any quantitative research in economics is centered on the analysis we perform on the data we collected. This is the most crucial part of the paper and will define if our work is a success or not (this is, of course linked to having a good research question and a plausible hypothesis).

In this section, I provide a set of guidelines of some of the elements to keep in mind when conducting quantitative research. This material, of course, is not exhaustive as there are many elements we need to take into account, but it may provide you with some structure as to what are the issues we need to keep in mind.

6.1 The Data

There are two different types of data that exist. Experimental data is collected when an experiment or study is conducted to examine the effects of a given policy or intervention. One example may be when looking if there is an increase in vaccination when providing incentives. One group may not receive any sort of incentive, whereas another group may receive a monetary incentive and another one an in-kind incentive. Data is collected to ensure that all the arms in the study have a similar configuration, so when the study is conducted, we can verify that the true effects come from the treatment (the incentives) and not from a different factor affecting the configuration of the sample.

The most popular sort of data, however, is observational data. This information is collected by either administrative sources (think of the U.S. Census data or the World Bank). This data is collected using surveys or accessing historical records. Sometimes, it is hard to use this data for econometric analysis as there is no random assignment of a treatment, so it is harder to elicit the true effect . However, there are multiple tools that we can use to deal with these issues and estimate causal effects.

6.1.1 Data configuration

6.1.1.1 cross-sectional data.

Cross-sectional data includes data on different subjects (individuals, households, government units, countries) for a single time period . This means that we only have one level of analysis and one observation per subject (the i ). This type of data allows us to learn more about the relationship among different variables.

One example of this type of data is the survey on smallholder farmers collected in the Ivory Coast in 2015 by the World Bank, where about 2,500 smallholder farmers were surveyed to ask questions about farming practices, investment and access to financial services.

6.1.1.2 Time-series Data

In this case, data for a single subject is collected during multiple time periods. In this case, the main unit of analysis will be based on time (the t ).

The most common type of data used for this type of analysis is macroeconomic data (GDP, unemployment, etc.) and is highly used to do forecasting.

6.1.1.3 Panel Data

Panel, or longitudinal, data includes multiple observations for each subject Mostly, we are going to see that data is collected for the same object during multiple time periods, so we will see that for the same i , we will have data for multiple t ’s.

This data is highly used in econometrics. One example is, for instance, the number of violent crimes per county (the i ) for the period between 2000 and 2020 (the t ).

It is extremely important to understand the configuration of your data, as this will define the type of econometric analysis that you can conduct.

6.1.2 Describing your Variables

After we have identified the configuration of our data, it is necessary that we think deeper about the configuration of the variables that we will use in our analysis. It is crucial that you identify their characteristics, as well as their distribution. This will then help you evaluate if you need to conduct any sort of transformation to your variables, and understand how to interpret the coefficients of your regressions. Here, I am just including the most relevant aspects of this steps, but you can read Nick Hunington-Kelin’s book for more details.

6.1.2.1 Types of Variables

Continuous variables : In theory, this variables can include any value, but sometimes they may be censored in some way (for instance, some variables cannot be negative). Some examples of this type of variable are income, for example.
Count variables : Most times, we treat this variables in the same way as we treat continuous variables, but in this case, these variables represent how many or how much there is of a certain variable (they count). When we plot them, it is clear that these variables are not continuous.
Categorical variables : Multiple times, surveys include questions that have a pre-set number of values or where the respondent needs to provide an answer that can then be grouped in a given category. For instance, ethnicity, religion, age group, etc. Many times, these variables are or can be transformed into binary (or indicator) variables. A clear example of the former is sex, but a new set of variables for different religions can be created to identify Christians, Jewish, Muslims, and so forth. Depending on the original category, a new set of dichotomous variables can be created to identify if a person identifies with one of these religions.
Qualitative Variables : Sometimes, responses require a more detailed explanation and therefore cannot be grouped into categories (at least not on first sight). For instance, the ACLED data, a source on conflict data, includes a variable that explains the details of a given conflict event.

6.1.3 Visualizing your Data

After you identify the type of variables you are using in your analysis, it is key that you understand their distribution. What are the different values that a variable can take? How often these values occur?

This can be done in multiple ways. The easiest one is to generate a table for the variable. In Stata, this is done with:

To tabulate a variable in R, you can use:

You can also plot your variables to obtain a clear visualization of their distribution. You can use histograms for non-continuous variables, and density plots for continuous variables.

6.1.4 Distribution

Many times, it is important to know more about the different moments of the distribution of your variables: mean, variance (or standard deviation), skewness, and sometimes, the kurtosis.

Although a visual representation of your data is very useful in these cases, obtaining a table with this information may also be necessary, to also obtain the range of your data, as well as other important characteristics.

In Stata, you can obtain a set of descriptive statistics using:

In R, you can get a range of descriptive statistics using

Why is this important? Because remember, we are trying to draw some inferences from the sample we have and apply it to the real world (to the whole population we are analyzing). Many times, we have some idea of theoretical distribution of the variables we are interested in In most cases, it is plausible to assume a normal distribution (remember the Central Limit Theorem ). This is one of the reasons we prefer larger samples than smaller ones. In some cases, we may get a distribution that is skewed to the right and has a very fat right-tail, but once we obtain the natural logarithm, it becomes normal. This refers to a log-normal distribution. As we proceed with analysis and do hypothesis testing, remember that you are using a limited sample to learn more about a bigger population.

6.2 Initial Description of a Relationship

Once we know how our specific variables are distributed, we may be interested in learning more about how they are linked. We want to see how our independent variable(s) is(are) linked to the dependent variable.

The most straightforward way to do this is by using a scatterplot, where we plot the independent and dependent variable and see how they correlate.

We may also look at some conditional distributions and plot histograms and scatterplots, looking at a subsample of the data or plotting it for different groups.

In addition, we can obtain an initial image on the relationship between X and Y doing a simple OLS regression (with no control variables). We may even plot this fitted OLS line.

For more examples and a more detailed description, please check Nick Hunington-Kelin’s book .

6.3 Handouts

How to Interpret Coefficients?

Empirical Research

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Njoku, E.T. (2020). Empirical Research. In: Leeming, D.A. (eds) Encyclopedia of Psychology and Religion. Springer, Cham. https://doi.org/10.1007/978-3-030-24348-7_200051

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What is empirical research: Methods, types & examples

What is empirical research: Methods, types & examples

Defne Çobanoğlu

Having opinions on matters based on observation is okay sometimes. Same as having theories on the subject you want to solve. However, some theories need to be tested. Just like Robert Oppenheimer says, “Theory will take you only so far .”

In that case, when you have your research question ready and you want to make sure it is correct, the next step would be experimentation. Because only then you can test your ideas and collect tangible information. Now, let us start with the empirical research definition:

What is empirical research?

Empirical research is a research type where the aim of the study is based on finding concrete and provable evidence . The researcher using this method to draw conclusions can use both quantitative and qualitative methods. Different than theoretical research, empirical research uses scientific experimentation and investigation.

Using experimentation makes sense when you need to have tangible evidence to act on whatever you are planning to do. As the researcher, you can be a marketer who is planning on creating a new ad for the target audience, or you can be an educator who wants the best for the students. No matter how big or small, data gathered from the real world using this research helps break down the question at hand.

When to use empirical research?

Empirical research methods are used when the researcher needs to gather data analysis on direct, observable, and measurable data. Research findings are a great way to make grounded ideas. Here are some situations when one may need to do empirical research:

1. When quantitative or qualitative data is needed

There are times when a researcher, marketer, or producer needs to gather data on specific research questions to make an informed decision. And the concrete data gathered in the research process gives a good starting point.

2. When you need to test a hypothesis

When you have a hypothesis on a subject, you can test the hypothesis through observation or experiment. Making a planned study is a great way to collect information and test whether or not your hypothesis is correct.

3. When you want to establish causality

Experimental research is a good way to explore whether or not there is any correlation between two variables. Researchers usually establish causality by changing a variable and observing if the independent variable changes accordingly.

Types of empirical research

The aim of empirical research is to collect information about a subject from the people by doing experimentation and other data collection methods. However, the methods and data collected are divided into two groups: one collects numerical data, and the other one collects opinion-like data. Let us see the difference between these two types:

Quantitative research

Quantitative research methods are used to collect data in a numerical way. Therefore, the results gathered by these methods will be numbers, statistics, charts, etc. The results can be used to quantify behaviors, opinions, and other variables. Quantitative research methods are surveys, questionnaires, and experimental research.

Qualitiative research

Qualitative research methods are not used to collect numerical answers, instead, they are used to collect the participants’ reasons, opinions, and other meaningful aspects. Qualitative research methods include case studies, observations, interviews, focus groups, and text analysis.

5 steps to conduct empirical research

Necessary steps for empirical research

When you want to collect direct and concrete data on a subject, empirical research is a great way to go. And, just like every other project and research, it is best to have a clear structure in mind. This is even more important in studies that may take a long time, such as experiments that take years. Let us look at a clear plan on how to do empirical research:

1. Define the research question

The very first step of every study is to have the question you will explore ready. Because you do not want to change your mind in the middle of the study after investing and spending time on the experimentation.

2. Go through relevant literature

This is the step where you sit down and do a desk research where you gather relevant data and see if other researchers have tried to explore similar research questions. If so, you can see how well they were able to answer the question or what kind of difficulties they faced during the research process.

3. Decide on the methodology

Once you are done going through the relevant literature, you can decide on which method or methods you can use. The appropriate methods are observation, experimentation, surveys, interviews, focus groups, etc.

4. Do data analysis

When you get to this step, it means you have successfully gathered enough data to make a data analysis. Now, all you need to do is look at the data you collected and make an informed analysis.

5. Conclusion

This is the last step, where you are finished with the experimentation and data analysis process. Now, it is time to decide what to do with this information. You can publish a paper and make informed decisions about whatever your goal is.

Empirical research methodologies

Some essential methodologies to conduct empirical research

The aim of this type of research is to explore brand-new evidence and facts. Therefore, the methods should be primary and gathered in real life, directly from the people. There is more than one method for this goal, and it is up to the researcher to use which one(s). Let us see the methods of empirical research:

Observation

The method of observation is a great way to collect information on people without the effect of interference. The researcher can choose the appropriate area, time, or situation and observe the people and their interactions with one another. The researcher can be just an outside observer or can be a participant as an observer or a full participant.

Experimentation

The experimentation process can be done in the real world by intervening in some elements to unify the environment for all participants. This method can also be done in a laboratory environment. The experimentation process is good for being able to change the variables according to the aim of the study.

The case study method is done by making an in-depth analysis of already existing cases. When the parameters and variables are similar to the research question at hand, it is wise to go through what was researched before.

Focus groups

The case study method is done by using a group of individuals or multiple groups and using their opinions, characteristics, and responses. The scientists gather the data from this group and generalize it to the whole population.

Surveys are an effective way to gather data directly from people. It is a systematic approach to collecting information. If it is done in an online setting as an online survey , it would be even easier to reach out to people and ask their opinions in open-ended or close-ended questions.

Interviews are similar to surveys as you are using questions to collect information and opinions of the people. Unlike a survey, this process is done face-to-face, as a phone call, or as a video call.

Advantages of empirical research

Empirical research is effective for many reasons, and helps researchers from numerous fields. Here are some advantages of empirical research to have in mind for your next research:

Empirical research improves the internal validity of the study.
Empirical evidence gathered from the study is used to authenticate the research question.
Collecting provable evidence is important for the success of the study.
The researcher is able to make informed decisions based on the data collected using empirical research.
Disadvantages of empirical research

After learning about the positive aspects of empirical research, it is time to mention the negative aspects. Because this type may not be suitable for everyone and the researcher should be mindful of the disadvantages of empirical research. Here are the disadvantages of empirical research:

As it is similar to other research types, a case study where experimentation is included will be time-consuming no matter what. It has more steps and variables than concluding a secondary research.
There are a lot of variables that need to be controlled and considered. Therefore, it may be a challenging task to be mindful of all the details.
Doing evidence-based research can be expensive if you need to complete it on a large scale.
When you are conducting an experiment, you may need some waivers and permissions.
Frequently asked questions about empirical research

Empirical research is one of the many research types, and there may be some questions in mind about its similarities and differences to other research types.

Is empirical research qualitative or quantitative?

The data collected by empirical research can be qualitative, quantitative, or a mix of both. It is up to the aim of researcher to what kind of data is needed and searched for.

Is empirical research the same as quantitative research?

As quantitative research heavily relies on data collection methods of observation and experimentation, it is, in nature, an empirical study. Some professors may even use the terms interchangeably. However, that does not mean that empirical research is only a quantitative one.

What is the difference between theoretical and empirical research?

Empirical studies are based on data collection to prove theories or answer questions, and it is done by using methods such as observation and experimentation. Therefore, empirical research relies on finding evidence that backs up theories. On the other hand, theoretical research relies on theorizing on empirical research data and trying to make connections and correlations.

What is the difference between conceptual and empirical research?

Conceptual research is about thoughts and ideas and does not involve any kind of experimentation. Empirical research, on the other hand, works with provable data and hard evidence.

What is the difference between empirical vs applied research?

Some scientists may use these two terms interchangeably however, there is a difference between them. Applied research involves applying theories to solve real-life problems. On the other hand, empirical research involves the obtaining and analysis of data to test hypotheses and theories.

Final words

Empirical research is a good means when the goal of your study is to find concrete data to go with. You may need to do empirical research when you need to test a theory, establish causality, or need qualitative/quantitative data. For example, you are a scientist and want to know if certain colors have an effect on people’s moods, or you are a marketer and want to test your theory on ad places on websites.

In both scenarios, you can collect information by using empirical research methods and make informed decisions afterward. These are just the two of empirical research examples. This research type can be applied to many areas of work life and social sciences. Lastly, for all your research needs, you can visit forms.app to use its many useful features and over 1000 form and survey templates!

Defne is a content writer at forms.app. She is also a translator specializing in literary translation. Defne loves reading, writing, and translating professionally and as a hobby. Her expertise lies in survey research, research methodologies, content writing, and translation.

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Indian J Anaesth
v.60(9); 2016 Sep

Basic statistical tools in research and data analysis

Zulfiqar ali.

Department of Anaesthesiology, Division of Neuroanaesthesiology, Sheri Kashmir Institute of Medical Sciences, Soura, Srinagar, Jammu and Kashmir, India

S Bala Bhaskar

1 Department of Anaesthesiology and Critical Care, Vijayanagar Institute of Medical Sciences, Bellary, Karnataka, India

Statistical methods involved in carrying out a study include planning, designing, collecting data, analysing, drawing meaningful interpretation and reporting of the research findings. The statistical analysis gives meaning to the meaningless numbers, thereby breathing life into a lifeless data. The results and inferences are precise only if proper statistical tests are used. This article will try to acquaint the reader with the basic research tools that are utilised while conducting various studies. The article covers a brief outline of the variables, an understanding of quantitative and qualitative variables and the measures of central tendency. An idea of the sample size estimation, power analysis and the statistical errors is given. Finally, there is a summary of parametric and non-parametric tests used for data analysis.

INTRODUCTION

Statistics is a branch of science that deals with the collection, organisation, analysis of data and drawing of inferences from the samples to the whole population.[ 1 ] This requires a proper design of the study, an appropriate selection of the study sample and choice of a suitable statistical test. An adequate knowledge of statistics is necessary for proper designing of an epidemiological study or a clinical trial. Improper statistical methods may result in erroneous conclusions which may lead to unethical practice.[ 2 ]

Variable is a characteristic that varies from one individual member of population to another individual.[ 3 ] Variables such as height and weight are measured by some type of scale, convey quantitative information and are called as quantitative variables. Sex and eye colour give qualitative information and are called as qualitative variables[ 3 ] [ Figure 1 ].

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Classification of variables

Quantitative variables

Quantitative or numerical data are subdivided into discrete and continuous measurements. Discrete numerical data are recorded as a whole number such as 0, 1, 2, 3,… (integer), whereas continuous data can assume any value. Observations that can be counted constitute the discrete data and observations that can be measured constitute the continuous data. Examples of discrete data are number of episodes of respiratory arrests or the number of re-intubations in an intensive care unit. Similarly, examples of continuous data are the serial serum glucose levels, partial pressure of oxygen in arterial blood and the oesophageal temperature.

A hierarchical scale of increasing precision can be used for observing and recording the data which is based on categorical, ordinal, interval and ratio scales [ Figure 1 ].

Categorical or nominal variables are unordered. The data are merely classified into categories and cannot be arranged in any particular order. If only two categories exist (as in gender male and female), it is called as a dichotomous (or binary) data. The various causes of re-intubation in an intensive care unit due to upper airway obstruction, impaired clearance of secretions, hypoxemia, hypercapnia, pulmonary oedema and neurological impairment are examples of categorical variables.

Ordinal variables have a clear ordering between the variables. However, the ordered data may not have equal intervals. Examples are the American Society of Anesthesiologists status or Richmond agitation-sedation scale.

Interval variables are similar to an ordinal variable, except that the intervals between the values of the interval variable are equally spaced. A good example of an interval scale is the Fahrenheit degree scale used to measure temperature. With the Fahrenheit scale, the difference between 70° and 75° is equal to the difference between 80° and 85°: The units of measurement are equal throughout the full range of the scale.

Ratio scales are similar to interval scales, in that equal differences between scale values have equal quantitative meaning. However, ratio scales also have a true zero point, which gives them an additional property. For example, the system of centimetres is an example of a ratio scale. There is a true zero point and the value of 0 cm means a complete absence of length. The thyromental distance of 6 cm in an adult may be twice that of a child in whom it may be 3 cm.

STATISTICS: DESCRIPTIVE AND INFERENTIAL STATISTICS

Descriptive statistics[ 4 ] try to describe the relationship between variables in a sample or population. Descriptive statistics provide a summary of data in the form of mean, median and mode. Inferential statistics[ 4 ] use a random sample of data taken from a population to describe and make inferences about the whole population. It is valuable when it is not possible to examine each member of an entire population. The examples if descriptive and inferential statistics are illustrated in Table 1 .

Example of descriptive and inferential statistics

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Descriptive statistics

The extent to which the observations cluster around a central location is described by the central tendency and the spread towards the extremes is described by the degree of dispersion.

Measures of central tendency

The measures of central tendency are mean, median and mode.[ 6 ] Mean (or the arithmetic average) is the sum of all the scores divided by the number of scores. Mean may be influenced profoundly by the extreme variables. For example, the average stay of organophosphorus poisoning patients in ICU may be influenced by a single patient who stays in ICU for around 5 months because of septicaemia. The extreme values are called outliers. The formula for the mean is

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where x = each observation and n = number of observations. Median[ 6 ] is defined as the middle of a distribution in a ranked data (with half of the variables in the sample above and half below the median value) while mode is the most frequently occurring variable in a distribution. Range defines the spread, or variability, of a sample.[ 7 ] It is described by the minimum and maximum values of the variables. If we rank the data and after ranking, group the observations into percentiles, we can get better information of the pattern of spread of the variables. In percentiles, we rank the observations into 100 equal parts. We can then describe 25%, 50%, 75% or any other percentile amount. The median is the 50 th percentile. The interquartile range will be the observations in the middle 50% of the observations about the median (25 th -75 th percentile). Variance[ 7 ] is a measure of how spread out is the distribution. It gives an indication of how close an individual observation clusters about the mean value. The variance of a population is defined by the following formula:

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where σ 2 is the population variance, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The variance of a sample is defined by slightly different formula:

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where s 2 is the sample variance, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. The formula for the variance of a population has the value ‘ n ’ as the denominator. The expression ‘ n −1’ is known as the degrees of freedom and is one less than the number of parameters. Each observation is free to vary, except the last one which must be a defined value. The variance is measured in squared units. To make the interpretation of the data simple and to retain the basic unit of observation, the square root of variance is used. The square root of the variance is the standard deviation (SD).[ 8 ] The SD of a population is defined by the following formula:

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where σ is the population SD, X is the population mean, X i is the i th element from the population and N is the number of elements in the population. The SD of a sample is defined by slightly different formula:

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where s is the sample SD, x is the sample mean, x i is the i th element from the sample and n is the number of elements in the sample. An example for calculation of variation and SD is illustrated in Table 2 .

Example of mean, variance, standard deviation

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Normal distribution or Gaussian distribution

Most of the biological variables usually cluster around a central value, with symmetrical positive and negative deviations about this point.[ 1 ] The standard normal distribution curve is a symmetrical bell-shaped. In a normal distribution curve, about 68% of the scores are within 1 SD of the mean. Around 95% of the scores are within 2 SDs of the mean and 99% within 3 SDs of the mean [ Figure 2 ].

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Normal distribution curve

Skewed distribution

It is a distribution with an asymmetry of the variables about its mean. In a negatively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the right of Figure 1 . In a positively skewed distribution [ Figure 3 ], the mass of the distribution is concentrated on the left of the figure leading to a longer right tail.

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Curves showing negatively skewed and positively skewed distribution

Inferential statistics

In inferential statistics, data are analysed from a sample to make inferences in the larger collection of the population. The purpose is to answer or test the hypotheses. A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. Hypothesis tests are thus procedures for making rational decisions about the reality of observed effects.

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty).

In inferential statistics, the term ‘null hypothesis’ ( H 0 ‘ H-naught ,’ ‘ H-null ’) denotes that there is no relationship (difference) between the population variables in question.[ 9 ]

Alternative hypothesis ( H 1 and H a ) denotes that a statement between the variables is expected to be true.[ 9 ]

The P value (or the calculated probability) is the probability of the event occurring by chance if the null hypothesis is true. The P value is a numerical between 0 and 1 and is interpreted by researchers in deciding whether to reject or retain the null hypothesis [ Table 3 ].

P values with interpretation

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If P value is less than the arbitrarily chosen value (known as α or the significance level), the null hypothesis (H0) is rejected [ Table 4 ]. However, if null hypotheses (H0) is incorrectly rejected, this is known as a Type I error.[ 11 ] Further details regarding alpha error, beta error and sample size calculation and factors influencing them are dealt with in another section of this issue by Das S et al .[ 12 ]

Illustration for null hypothesis

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PARAMETRIC AND NON-PARAMETRIC TESTS

Numerical data (quantitative variables) that are normally distributed are analysed with parametric tests.[ 13 ]

Two most basic prerequisites for parametric statistical analysis are:

The assumption of normality which specifies that the means of the sample group are normally distributed
The assumption of equal variance which specifies that the variances of the samples and of their corresponding population are equal.

However, if the distribution of the sample is skewed towards one side or the distribution is unknown due to the small sample size, non-parametric[ 14 ] statistical techniques are used. Non-parametric tests are used to analyse ordinal and categorical data.

Parametric tests

The parametric tests assume that the data are on a quantitative (numerical) scale, with a normal distribution of the underlying population. The samples have the same variance (homogeneity of variances). The samples are randomly drawn from the population, and the observations within a group are independent of each other. The commonly used parametric tests are the Student's t -test, analysis of variance (ANOVA) and repeated measures ANOVA.

Student's t -test

Student's t -test is used to test the null hypothesis that there is no difference between the means of the two groups. It is used in three circumstances:

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where X = sample mean, u = population mean and SE = standard error of mean

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where X 1 − X 2 is the difference between the means of the two groups and SE denotes the standard error of the difference.

To test if the population means estimated by two dependent samples differ significantly (the paired t -test). A usual setting for paired t -test is when measurements are made on the same subjects before and after a treatment.

The formula for paired t -test is:

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where d is the mean difference and SE denotes the standard error of this difference.

The group variances can be compared using the F -test. The F -test is the ratio of variances (var l/var 2). If F differs significantly from 1.0, then it is concluded that the group variances differ significantly.

Analysis of variance

The Student's t -test cannot be used for comparison of three or more groups. The purpose of ANOVA is to test if there is any significant difference between the means of two or more groups.

In ANOVA, we study two variances – (a) between-group variability and (b) within-group variability. The within-group variability (error variance) is the variation that cannot be accounted for in the study design. It is based on random differences present in our samples.

However, the between-group (or effect variance) is the result of our treatment. These two estimates of variances are compared using the F-test.

A simplified formula for the F statistic is:

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where MS b is the mean squares between the groups and MS w is the mean squares within groups.

Repeated measures analysis of variance

As with ANOVA, repeated measures ANOVA analyses the equality of means of three or more groups. However, a repeated measure ANOVA is used when all variables of a sample are measured under different conditions or at different points in time.

As the variables are measured from a sample at different points of time, the measurement of the dependent variable is repeated. Using a standard ANOVA in this case is not appropriate because it fails to model the correlation between the repeated measures: The data violate the ANOVA assumption of independence. Hence, in the measurement of repeated dependent variables, repeated measures ANOVA should be used.

Non-parametric tests

When the assumptions of normality are not met, and the sample means are not normally, distributed parametric tests can lead to erroneous results. Non-parametric tests (distribution-free test) are used in such situation as they do not require the normality assumption.[ 15 ] Non-parametric tests may fail to detect a significant difference when compared with a parametric test. That is, they usually have less power.

As is done for the parametric tests, the test statistic is compared with known values for the sampling distribution of that statistic and the null hypothesis is accepted or rejected. The types of non-parametric analysis techniques and the corresponding parametric analysis techniques are delineated in Table 5 .

Analogue of parametric and non-parametric tests

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Median test for one sample: The sign test and Wilcoxon's signed rank test

The sign test and Wilcoxon's signed rank test are used for median tests of one sample. These tests examine whether one instance of sample data is greater or smaller than the median reference value.

This test examines the hypothesis about the median θ0 of a population. It tests the null hypothesis H0 = θ0. When the observed value (Xi) is greater than the reference value (θ0), it is marked as+. If the observed value is smaller than the reference value, it is marked as − sign. If the observed value is equal to the reference value (θ0), it is eliminated from the sample.

If the null hypothesis is true, there will be an equal number of + signs and − signs.

The sign test ignores the actual values of the data and only uses + or − signs. Therefore, it is useful when it is difficult to measure the values.

Wilcoxon's signed rank test

There is a major limitation of sign test as we lose the quantitative information of the given data and merely use the + or – signs. Wilcoxon's signed rank test not only examines the observed values in comparison with θ0 but also takes into consideration the relative sizes, adding more statistical power to the test. As in the sign test, if there is an observed value that is equal to the reference value θ0, this observed value is eliminated from the sample.

Wilcoxon's rank sum test ranks all data points in order, calculates the rank sum of each sample and compares the difference in the rank sums.

Mann-Whitney test

It is used to test the null hypothesis that two samples have the same median or, alternatively, whether observations in one sample tend to be larger than observations in the other.

Mann–Whitney test compares all data (xi) belonging to the X group and all data (yi) belonging to the Y group and calculates the probability of xi being greater than yi: P (xi > yi). The null hypothesis states that P (xi > yi) = P (xi < yi) =1/2 while the alternative hypothesis states that P (xi > yi) ≠1/2.

Kolmogorov-Smirnov test

The two-sample Kolmogorov-Smirnov (KS) test was designed as a generic method to test whether two random samples are drawn from the same distribution. The null hypothesis of the KS test is that both distributions are identical. The statistic of the KS test is a distance between the two empirical distributions, computed as the maximum absolute difference between their cumulative curves.

Kruskal-Wallis test

The Kruskal–Wallis test is a non-parametric test to analyse the variance.[ 14 ] It analyses if there is any difference in the median values of three or more independent samples. The data values are ranked in an increasing order, and the rank sums calculated followed by calculation of the test statistic.

Jonckheere test

In contrast to Kruskal–Wallis test, in Jonckheere test, there is an a priori ordering that gives it a more statistical power than the Kruskal–Wallis test.[ 14 ]

Friedman test

The Friedman test is a non-parametric test for testing the difference between several related samples. The Friedman test is an alternative for repeated measures ANOVAs which is used when the same parameter has been measured under different conditions on the same subjects.[ 13 ]

Tests to analyse the categorical data

Chi-square test, Fischer's exact test and McNemar's test are used to analyse the categorical or nominal variables. The Chi-square test compares the frequencies and tests whether the observed data differ significantly from that of the expected data if there were no differences between groups (i.e., the null hypothesis). It is calculated by the sum of the squared difference between observed ( O ) and the expected ( E ) data (or the deviation, d ) divided by the expected data by the following formula:

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A Yates correction factor is used when the sample size is small. Fischer's exact test is used to determine if there are non-random associations between two categorical variables. It does not assume random sampling, and instead of referring a calculated statistic to a sampling distribution, it calculates an exact probability. McNemar's test is used for paired nominal data. It is applied to 2 × 2 table with paired-dependent samples. It is used to determine whether the row and column frequencies are equal (that is, whether there is ‘marginal homogeneity’). The null hypothesis is that the paired proportions are equal. The Mantel-Haenszel Chi-square test is a multivariate test as it analyses multiple grouping variables. It stratifies according to the nominated confounding variables and identifies any that affects the primary outcome variable. If the outcome variable is dichotomous, then logistic regression is used.

SOFTWARES AVAILABLE FOR STATISTICS, SAMPLE SIZE CALCULATION AND POWER ANALYSIS

Numerous statistical software systems are available currently. The commonly used software systems are Statistical Package for the Social Sciences (SPSS – manufactured by IBM corporation), Statistical Analysis System ((SAS – developed by SAS Institute North Carolina, United States of America), R (designed by Ross Ihaka and Robert Gentleman from R core team), Minitab (developed by Minitab Inc), Stata (developed by StataCorp) and the MS Excel (developed by Microsoft).

There are a number of web resources which are related to statistical power analyses. A few are:

StatPages.net – provides links to a number of online power calculators
G-Power – provides a downloadable power analysis program that runs under DOS
Power analysis for ANOVA designs an interactive site that calculates power or sample size needed to attain a given power for one effect in a factorial ANOVA design
SPSS makes a program called SamplePower. It gives an output of a complete report on the computer screen which can be cut and paste into another document.

It is important that a researcher knows the concepts of the basic statistical methods used for conduct of a research study. This will help to conduct an appropriately well-designed study leading to valid and reliable results. Inappropriate use of statistical techniques may lead to faulty conclusions, inducing errors and undermining the significance of the article. Bad statistics may lead to bad research, and bad research may lead to unethical practice. Hence, an adequate knowledge of statistics and the appropriate use of statistical tests are important. An appropriate knowledge about the basic statistical methods will go a long way in improving the research designs and producing quality medical research which can be utilised for formulating the evidence-based guidelines.

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Published: 17 April 2024

The economic commitment of climate change

Maximilian Kotz ORCID: orcid.org/0000-0003-2564-5043 1 , 2 ,
Anders Levermann ORCID: orcid.org/0000-0003-4432-4704 1 , 2 &
Leonie Wenz ORCID: orcid.org/0000-0002-8500-1568 1 , 3

Nature volume 628 , pages 551–557 ( 2024 ) Cite this article

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Environmental economics
Environmental health
Interdisciplinary studies
Projection and prediction

Global projections of macroeconomic climate-change damages typically consider impacts from average annual and national temperatures over long time horizons 1 , 2 , 3 , 4 , 5 , 6 . Here we use recent empirical findings from more than 1,600 regions worldwide over the past 40 years to project sub-national damages from temperature and precipitation, including daily variability and extremes 7 , 8 . Using an empirical approach that provides a robust lower bound on the persistence of impacts on economic growth, we find that the world economy is committed to an income reduction of 19% within the next 26 years independent of future emission choices (relative to a baseline without climate impacts, likely range of 11–29% accounting for physical climate and empirical uncertainty). These damages already outweigh the mitigation costs required to limit global warming to 2 °C by sixfold over this near-term time frame and thereafter diverge strongly dependent on emission choices. Committed damages arise predominantly through changes in average temperature, but accounting for further climatic components raises estimates by approximately 50% and leads to stronger regional heterogeneity. Committed losses are projected for all regions except those at very high latitudes, at which reductions in temperature variability bring benefits. The largest losses are committed at lower latitudes in regions with lower cumulative historical emissions and lower present-day income.

Climate damage projections beyond annual temperature

Paul Waidelich, Fulden Batibeniz, … Sonia I. Seneviratne

Investment incentive reduced by climate damages can be restored by optimal policy

Sven N. Willner, Nicole Glanemann & Anders Levermann

Climate economics support for the UN climate targets

Martin C. Hänsel, Moritz A. Drupp, … Thomas Sterner

Projections of the macroeconomic damage caused by future climate change are crucial to informing public and policy debates about adaptation, mitigation and climate justice. On the one hand, adaptation against climate impacts must be justified and planned on the basis of an understanding of their future magnitude and spatial distribution 9 . This is also of importance in the context of climate justice 10 , as well as to key societal actors, including governments, central banks and private businesses, which increasingly require the inclusion of climate risks in their macroeconomic forecasts to aid adaptive decision-making 11 , 12 . On the other hand, climate mitigation policy such as the Paris Climate Agreement is often evaluated by balancing the costs of its implementation against the benefits of avoiding projected physical damages. This evaluation occurs both formally through cost–benefit analyses 1 , 4 , 5 , 6 , as well as informally through public perception of mitigation and damage costs 13 .

Projections of future damages meet challenges when informing these debates, in particular the human biases relating to uncertainty and remoteness that are raised by long-term perspectives 14 . Here we aim to overcome such challenges by assessing the extent of economic damages from climate change to which the world is already committed by historical emissions and socio-economic inertia (the range of future emission scenarios that are considered socio-economically plausible 15 ). Such a focus on the near term limits the large uncertainties about diverging future emission trajectories, the resulting long-term climate response and the validity of applying historically observed climate–economic relations over long timescales during which socio-technical conditions may change considerably. As such, this focus aims to simplify the communication and maximize the credibility of projected economic damages from future climate change.

In projecting the future economic damages from climate change, we make use of recent advances in climate econometrics that provide evidence for impacts on sub-national economic growth from numerous components of the distribution of daily temperature and precipitation 3 , 7 , 8 . Using fixed-effects panel regression models to control for potential confounders, these studies exploit within-region variation in local temperature and precipitation in a panel of more than 1,600 regions worldwide, comprising climate and income data over the past 40 years, to identify the plausibly causal effects of changes in several climate variables on economic productivity 16 , 17 . Specifically, macroeconomic impacts have been identified from changing daily temperature variability, total annual precipitation, the annual number of wet days and extreme daily rainfall that occur in addition to those already identified from changing average temperature 2 , 3 , 18 . Moreover, regional heterogeneity in these effects based on the prevailing local climatic conditions has been found using interactions terms. The selection of these climate variables follows micro-level evidence for mechanisms related to the impacts of average temperatures on labour and agricultural productivity 2 , of temperature variability on agricultural productivity and health 7 , as well as of precipitation on agricultural productivity, labour outcomes and flood damages 8 (see Extended Data Table 1 for an overview, including more detailed references). References 7 , 8 contain a more detailed motivation for the use of these particular climate variables and provide extensive empirical tests about the robustness and nature of their effects on economic output, which are summarized in Methods . By accounting for these extra climatic variables at the sub-national level, we aim for a more comprehensive description of climate impacts with greater detail across both time and space.

Constraining the persistence of impacts

A key determinant and source of discrepancy in estimates of the magnitude of future climate damages is the extent to which the impact of a climate variable on economic growth rates persists. The two extreme cases in which these impacts persist indefinitely or only instantaneously are commonly referred to as growth or level effects 19 , 20 (see Methods section ‘Empirical model specification: fixed-effects distributed lag models’ for mathematical definitions). Recent work shows that future damages from climate change depend strongly on whether growth or level effects are assumed 20 . Following refs. 2 , 18 , we provide constraints on this persistence by using distributed lag models to test the significance of delayed effects separately for each climate variable. Notably, and in contrast to refs. 2 , 18 , we use climate variables in their first-differenced form following ref. 3 , implying a dependence of the growth rate on a change in climate variables. This choice means that a baseline specification without any lags constitutes a model prior of purely level effects, in which a permanent change in the climate has only an instantaneous effect on the growth rate 3 , 19 , 21 . By including lags, one can then test whether any effects may persist further. This is in contrast to the specification used by refs. 2 , 18 , in which climate variables are used without taking the first difference, implying a dependence of the growth rate on the level of climate variables. In this alternative case, the baseline specification without any lags constitutes a model prior of pure growth effects, in which a change in climate has an infinitely persistent effect on the growth rate. Consequently, including further lags in this alternative case tests whether the initial growth impact is recovered 18 , 19 , 21 . Both of these specifications suffer from the limiting possibility that, if too few lags are included, one might falsely accept the model prior. The limitations of including a very large number of lags, including loss of data and increasing statistical uncertainty with an increasing number of parameters, mean that such a possibility is likely. By choosing a specification in which the model prior is one of level effects, our approach is therefore conservative by design, avoiding assumptions of infinite persistence of climate impacts on growth and instead providing a lower bound on this persistence based on what is observable empirically (see Methods section ‘Empirical model specification: fixed-effects distributed lag models’ for further exposition of this framework). The conservative nature of such a choice is probably the reason that ref. 19 finds much greater consistency between the impacts projected by models that use the first difference of climate variables, as opposed to their levels.

We begin our empirical analysis of the persistence of climate impacts on growth using ten lags of the first-differenced climate variables in fixed-effects distributed lag models. We detect substantial effects on economic growth at time lags of up to approximately 8–10 years for the temperature terms and up to approximately 4 years for the precipitation terms (Extended Data Fig. 1 and Extended Data Table 2 ). Furthermore, evaluation by means of information criteria indicates that the inclusion of all five climate variables and the use of these numbers of lags provide a preferable trade-off between best-fitting the data and including further terms that could cause overfitting, in comparison with model specifications excluding climate variables or including more or fewer lags (Extended Data Fig. 3 , Supplementary Methods Section 1 and Supplementary Table 1 ). We therefore remove statistically insignificant terms at later lags (Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ). Further tests using Monte Carlo simulations demonstrate that the empirical models are robust to autocorrelation in the lagged climate variables (Supplementary Methods Section 2 and Supplementary Figs. 4 and 5 ), that information criteria provide an effective indicator for lag selection (Supplementary Methods Section 2 and Supplementary Fig. 6 ), that the results are robust to concerns of imperfect multicollinearity between climate variables and that including several climate variables is actually necessary to isolate their separate effects (Supplementary Methods Section 3 and Supplementary Fig. 7 ). We provide a further robustness check using a restricted distributed lag model to limit oscillations in the lagged parameter estimates that may result from autocorrelation, finding that it provides similar estimates of cumulative marginal effects to the unrestricted model (Supplementary Methods Section 4 and Supplementary Figs. 8 and 9 ). Finally, to explicitly account for any outstanding uncertainty arising from the precise choice of the number of lags, we include empirical models with marginally different numbers of lags in the error-sampling procedure of our projection of future damages. On the basis of the lag-selection procedure (the significance of lagged terms in Extended Data Fig. 1 and Extended Data Table 2 , as well as information criteria in Extended Data Fig. 3 ), we sample from models with eight to ten lags for temperature and four for precipitation (models shown in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ). In summary, this empirical approach to constrain the persistence of climate impacts on economic growth rates is conservative by design in avoiding assumptions of infinite persistence, but nevertheless provides a lower bound on the extent of impact persistence that is robust to the numerous tests outlined above.

Committed damages until mid-century

We combine these empirical economic response functions (Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) with an ensemble of 21 climate models (see Supplementary Table 5 ) from the Coupled Model Intercomparison Project Phase 6 (CMIP-6) 22 to project the macroeconomic damages from these components of physical climate change (see Methods for further details). Bias-adjusted climate models that provide a highly accurate reproduction of observed climatological patterns with limited uncertainty (Supplementary Table 6 ) are used to avoid introducing biases in the projections. Following a well-developed literature 2 , 3 , 19 , these projections do not aim to provide a prediction of future economic growth. Instead, they are a projection of the exogenous impact of future climate conditions on the economy relative to the baselines specified by socio-economic projections, based on the plausibly causal relationships inferred by the empirical models and assuming ceteris paribus. Other exogenous factors relevant for the prediction of economic output are purposefully assumed constant.

A Monte Carlo procedure that samples from climate model projections, empirical models with different numbers of lags and model parameter estimates (obtained by 1,000 block-bootstrap resamples of each of the regressions in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) is used to estimate the combined uncertainty from these sources. Given these uncertainty distributions, we find that projected global damages are statistically indistinguishable across the two most extreme emission scenarios until 2049 (at the 5% significance level; Fig. 1 ). As such, the climate damages occurring before this time constitute those to which the world is already committed owing to the combination of past emissions and the range of future emission scenarios that are considered socio-economically plausible 15 . These committed damages comprise a permanent income reduction of 19% on average globally (population-weighted average) in comparison with a baseline without climate-change impacts (with a likely range of 11–29%, following the likelihood classification adopted by the Intergovernmental Panel on Climate Change (IPCC); see caption of Fig. 1 ). Even though levels of income per capita generally still increase relative to those of today, this constitutes a permanent income reduction for most regions, including North America and Europe (each with median income reductions of approximately 11%) and with South Asia and Africa being the most strongly affected (each with median income reductions of approximately 22%; Fig. 1 ). Under a middle-of-the road scenario of future income development (SSP2, in which SSP stands for Shared Socio-economic Pathway), this corresponds to global annual damages in 2049 of 38 trillion in 2005 international dollars (likely range of 19–59 trillion 2005 international dollars). Compared with empirical specifications that assume pure growth or pure level effects, our preferred specification that provides a robust lower bound on the extent of climate impact persistence produces damages between these two extreme assumptions (Extended Data Fig. 3 ).

Estimates of the projected reduction in income per capita from changes in all climate variables based on empirical models of climate impacts on economic output with a robust lower bound on their persistence (Extended Data Fig. 1 ) under a low-emission scenario compatible with the 2 °C warming target and a high-emission scenario (SSP2-RCP2.6 and SSP5-RCP8.5, respectively) are shown in purple and orange, respectively. Shading represents the 34% and 10% confidence intervals reflecting the likely and very likely ranges, respectively (following the likelihood classification adopted by the IPCC), having estimated uncertainty from a Monte Carlo procedure, which samples the uncertainty from the choice of physical climate models, empirical models with different numbers of lags and bootstrapped estimates of the regression parameters shown in Supplementary Figs. 1 – 3 . Vertical dashed lines show the time at which the climate damages of the two emission scenarios diverge at the 5% and 1% significance levels based on the distribution of differences between emission scenarios arising from the uncertainty sampling discussed above. Note that uncertainty in the difference of the two scenarios is smaller than the combined uncertainty of the two respective scenarios because samples of the uncertainty (climate model and empirical model choice, as well as model parameter bootstrap) are consistent across the two emission scenarios, hence the divergence of damages occurs while the uncertainty bounds of the two separate damage scenarios still overlap. Estimates of global mitigation costs from the three IAMs that provide results for the SSP2 baseline and SSP2-RCP2.6 scenario are shown in light green in the top panel, with the median of these estimates shown in bold.

Damages already outweigh mitigation costs

We compare the damages to which the world is committed over the next 25 years to estimates of the mitigation costs required to achieve the Paris Climate Agreement. Taking estimates of mitigation costs from the three integrated assessment models (IAMs) in the IPCC AR6 database 23 that provide results under comparable scenarios (SSP2 baseline and SSP2-RCP2.6, in which RCP stands for Representative Concentration Pathway), we find that the median committed climate damages are larger than the median mitigation costs in 2050 (six trillion in 2005 international dollars) by a factor of approximately six (note that estimates of mitigation costs are only provided every 10 years by the IAMs and so a comparison in 2049 is not possible). This comparison simply aims to compare the magnitude of future damages against mitigation costs, rather than to conduct a formal cost–benefit analysis of transitioning from one emission path to another. Formal cost–benefit analyses typically find that the net benefits of mitigation only emerge after 2050 (ref. 5 ), which may lead some to conclude that physical damages from climate change are simply not large enough to outweigh mitigation costs until the second half of the century. Our simple comparison of their magnitudes makes clear that damages are actually already considerably larger than mitigation costs and the delayed emergence of net mitigation benefits results primarily from the fact that damages across different emission paths are indistinguishable until mid-century (Fig. 1 ).

Although these near-term damages constitute those to which the world is already committed, we note that damage estimates diverge strongly across emission scenarios after 2049, conveying the clear benefits of mitigation from a purely economic point of view that have been emphasized in previous studies 4 , 24 . As well as the uncertainties assessed in Fig. 1 , these conclusions are robust to structural choices, such as the timescale with which changes in the moderating variables of the empirical models are estimated (Supplementary Figs. 10 and 11 ), as well as the order in which one accounts for the intertemporal and international components of currency comparison (Supplementary Fig. 12 ; see Methods for further details).

Damages from variability and extremes

Committed damages primarily arise through changes in average temperature (Fig. 2 ). This reflects the fact that projected changes in average temperature are larger than those in other climate variables when expressed as a function of their historical interannual variability (Extended Data Fig. 4 ). Because the historical variability is that on which the empirical models are estimated, larger projected changes in comparison with this variability probably lead to larger future impacts in a purely statistical sense. From a mechanistic perspective, one may plausibly interpret this result as implying that future changes in average temperature are the most unprecedented from the perspective of the historical fluctuations to which the economy is accustomed and therefore will cause the most damage. This insight may prove useful in terms of guiding adaptation measures to the sources of greatest damage.

Estimates of the median projected reduction in sub-national income per capita across emission scenarios (SSP2-RCP2.6 and SSP2-RCP8.5) as well as climate model, empirical model and model parameter uncertainty in the year in which climate damages diverge at the 5% level (2049, as identified in Fig. 1 ). a , Impacts arising from all climate variables. b – f , Impacts arising separately from changes in annual mean temperature ( b ), daily temperature variability ( c ), total annual precipitation ( d ), the annual number of wet days (>1 mm) ( e ) and extreme daily rainfall ( f ) (see Methods for further definitions). Data on national administrative boundaries are obtained from the GADM database version 3.6 and are freely available for academic use ( https://gadm.org/ ).

Nevertheless, future damages based on empirical models that consider changes in annual average temperature only and exclude the other climate variables constitute income reductions of only 13% in 2049 (Extended Data Fig. 5a , likely range 5–21%). This suggests that accounting for the other components of the distribution of temperature and precipitation raises net damages by nearly 50%. This increase arises through the further damages that these climatic components cause, but also because their inclusion reveals a stronger negative economic response to average temperatures (Extended Data Fig. 5b ). The latter finding is consistent with our Monte Carlo simulations, which suggest that the magnitude of the effect of average temperature on economic growth is underestimated unless accounting for the impacts of other correlated climate variables (Supplementary Fig. 7 ).

In terms of the relative contributions of the different climatic components to overall damages, we find that accounting for daily temperature variability causes the largest increase in overall damages relative to empirical frameworks that only consider changes in annual average temperature (4.9 percentage points, likely range 2.4–8.7 percentage points, equivalent to approximately 10 trillion international dollars). Accounting for precipitation causes smaller increases in overall damages, which are—nevertheless—equivalent to approximately 1.2 trillion international dollars: 0.01 percentage points (−0.37–0.33 percentage points), 0.34 percentage points (0.07–0.90 percentage points) and 0.36 percentage points (0.13–0.65 percentage points) from total annual precipitation, the number of wet days and extreme daily precipitation, respectively. Moreover, climate models seem to underestimate future changes in temperature variability 25 and extreme precipitation 26 , 27 in response to anthropogenic forcing as compared with that observed historically, suggesting that the true impacts from these variables may be larger.

The distribution of committed damages

The spatial distribution of committed damages (Fig. 2a ) reflects a complex interplay between the patterns of future change in several climatic components and those of historical economic vulnerability to changes in those variables. Damages resulting from increasing annual mean temperature (Fig. 2b ) are negative almost everywhere globally, and larger at lower latitudes in regions in which temperatures are already higher and economic vulnerability to temperature increases is greatest (see the response heterogeneity to mean temperature embodied in Extended Data Fig. 1a ). This occurs despite the amplified warming projected at higher latitudes 28 , suggesting that regional heterogeneity in economic vulnerability to temperature changes outweighs heterogeneity in the magnitude of future warming (Supplementary Fig. 13a ). Economic damages owing to daily temperature variability (Fig. 2c ) exhibit a strong latitudinal polarisation, primarily reflecting the physical response of daily variability to greenhouse forcing in which increases in variability across lower latitudes (and Europe) contrast decreases at high latitudes 25 (Supplementary Fig. 13b ). These two temperature terms are the dominant determinants of the pattern of overall damages (Fig. 2a ), which exhibits a strong polarity with damages across most of the globe except at the highest northern latitudes. Future changes in total annual precipitation mainly bring economic benefits except in regions of drying, such as the Mediterranean and central South America (Fig. 2d and Supplementary Fig. 13c ), but these benefits are opposed by changes in the number of wet days, which produce damages with a similar pattern of opposite sign (Fig. 2e and Supplementary Fig. 13d ). By contrast, changes in extreme daily rainfall produce damages in all regions, reflecting the intensification of daily rainfall extremes over global land areas 29 , 30 (Fig. 2f and Supplementary Fig. 13e ).

The spatial distribution of committed damages implies considerable injustice along two dimensions: culpability for the historical emissions that have caused climate change and pre-existing levels of socio-economic welfare. Spearman’s rank correlations indicate that committed damages are significantly larger in countries with smaller historical cumulative emissions, as well as in regions with lower current income per capita (Fig. 3 ). This implies that those countries that will suffer the most from the damages already committed are those that are least responsible for climate change and which also have the least resources to adapt to it.

Estimates of the median projected change in national income per capita across emission scenarios (RCP2.6 and RCP8.5) as well as climate model, empirical model and model parameter uncertainty in the year in which climate damages diverge at the 5% level (2049, as identified in Fig. 1 ) are plotted against cumulative national emissions per capita in 2020 (from the Global Carbon Project) and coloured by national income per capita in 2020 (from the World Bank) in a and vice versa in b . In each panel, the size of each scatter point is weighted by the national population in 2020 (from the World Bank). Inset numbers indicate the Spearman’s rank correlation ρ and P -values for a hypothesis test whose null hypothesis is of no correlation, as well as the Spearman’s rank correlation weighted by national population.

To further quantify this heterogeneity, we assess the difference in committed damages between the upper and lower quartiles of regions when ranked by present income levels and historical cumulative emissions (using a population weighting to both define the quartiles and estimate the group averages). On average, the quartile of countries with lower income are committed to an income loss that is 8.9 percentage points (or 61%) greater than the upper quartile (Extended Data Fig. 6 ), with a likely range of 3.8–14.7 percentage points across the uncertainty sampling of our damage projections (following the likelihood classification adopted by the IPCC). Similarly, the quartile of countries with lower historical cumulative emissions are committed to an income loss that is 6.9 percentage points (or 40%) greater than the upper quartile, with a likely range of 0.27–12 percentage points. These patterns reemphasize the prevalence of injustice in climate impacts 31 , 32 , 33 in the context of the damages to which the world is already committed by historical emissions and socio-economic inertia.

Contextualizing the magnitude of damages

The magnitude of projected economic damages exceeds previous literature estimates 2 , 3 , arising from several developments made on previous approaches. Our estimates are larger than those of ref. 2 (see first row of Extended Data Table 3 ), primarily because of the facts that sub-national estimates typically show a steeper temperature response (see also refs. 3 , 34 ) and that accounting for other climatic components raises damage estimates (Extended Data Fig. 5 ). However, we note that our empirical approach using first-differenced climate variables is conservative compared with that of ref. 2 in regard to the persistence of climate impacts on growth (see introduction and Methods section ‘Empirical model specification: fixed-effects distributed lag models’), an important determinant of the magnitude of long-term damages 19 , 21 . Using a similar empirical specification to ref. 2 , which assumes infinite persistence while maintaining the rest of our approach (sub-national data and further climate variables), produces considerably larger damages (purple curve of Extended Data Fig. 3 ). Compared with studies that do take the first difference of climate variables 3 , 35 , our estimates are also larger (see second and third rows of Extended Data Table 3 ). The inclusion of further climate variables (Extended Data Fig. 5 ) and a sufficient number of lags to more adequately capture the extent of impact persistence (Extended Data Figs. 1 and 2 ) are the main sources of this difference, as is the use of specifications that capture nonlinearities in the temperature response when compared with ref. 35 . In summary, our estimates develop on previous studies by incorporating the latest data and empirical insights 7 , 8 , as well as in providing a robust empirical lower bound on the persistence of impacts on economic growth, which constitutes a middle ground between the extremes of the growth-versus-levels debate 19 , 21 (Extended Data Fig. 3 ).

Compared with the fraction of variance explained by the empirical models historically (<5%), the projection of reductions in income of 19% may seem large. This arises owing to the fact that projected changes in climatic conditions are much larger than those that were experienced historically, particularly for changes in average temperature (Extended Data Fig. 4 ). As such, any assessment of future climate-change impacts necessarily requires an extrapolation outside the range of the historical data on which the empirical impact models were evaluated. Nevertheless, these models constitute the most state-of-the-art methods for inference of plausibly causal climate impacts based on observed data. Moreover, we take explicit steps to limit out-of-sample extrapolation by capping the moderating variables of the interaction terms at the 95th percentile of the historical distribution (see Methods ). This avoids extrapolating the marginal effects outside what was observed historically. Given the nonlinear response of economic output to annual mean temperature (Extended Data Fig. 1 and Extended Data Table 2 ), this is a conservative choice that limits the magnitude of damages that we project. Furthermore, back-of-the-envelope calculations indicate that the projected damages are consistent with the magnitude and patterns of historical economic development (see Supplementary Discussion Section 5 ).

Missing impacts and spatial spillovers

Despite assessing several climatic components from which economic impacts have recently been identified 3 , 7 , 8 , this assessment of aggregate climate damages should not be considered comprehensive. Important channels such as impacts from heatwaves 31 , sea-level rise 36 , tropical cyclones 37 and tipping points 38 , 39 , as well as non-market damages such as those to ecosystems 40 and human health 41 , are not considered in these estimates. Sea-level rise is unlikely to be feasibly incorporated into empirical assessments such as this because historical sea-level variability is mostly small. Non-market damages are inherently intractable within our estimates of impacts on aggregate monetary output and estimates of these impacts could arguably be considered as extra to those identified here. Recent empirical work suggests that accounting for these channels would probably raise estimates of these committed damages, with larger damages continuing to arise in the global south 31 , 36 , 37 , 38 , 39 , 40 , 41 , 42 .

Moreover, our main empirical analysis does not explicitly evaluate the potential for impacts in local regions to produce effects that ‘spill over’ into other regions. Such effects may further mitigate or amplify the impacts we estimate, for example, if companies relocate production from one affected region to another or if impacts propagate along supply chains. The current literature indicates that trade plays a substantial role in propagating spillover effects 43 , 44 , making their assessment at the sub-national level challenging without available data on sub-national trade dependencies. Studies accounting for only spatially adjacent neighbours indicate that negative impacts in one region induce further negative impacts in neighbouring regions 45 , 46 , 47 , 48 , suggesting that our projected damages are probably conservative by excluding these effects. In Supplementary Fig. 14 , we assess spillovers from neighbouring regions using a spatial-lag model. For simplicity, this analysis excludes temporal lags, focusing only on contemporaneous effects. The results show that accounting for spatial spillovers can amplify the overall magnitude, and also the heterogeneity, of impacts. Consistent with previous literature, this indicates that the overall magnitude (Fig. 1 ) and heterogeneity (Fig. 3 ) of damages that we project in our main specification may be conservative without explicitly accounting for spillovers. We note that further analysis that addresses both spatially and trade-connected spillovers, while also accounting for delayed impacts using temporal lags, would be necessary to adequately address this question fully. These approaches offer fruitful avenues for further research but are beyond the scope of this manuscript, which primarily aims to explore the impacts of different climate conditions and their persistence.

Policy implications

We find that the economic damages resulting from climate change until 2049 are those to which the world economy is already committed and that these greatly outweigh the costs required to mitigate emissions in line with the 2 °C target of the Paris Climate Agreement (Fig. 1 ). This assessment is complementary to formal analyses of the net costs and benefits associated with moving from one emission path to another, which typically find that net benefits of mitigation only emerge in the second half of the century 5 . Our simple comparison of the magnitude of damages and mitigation costs makes clear that this is primarily because damages are indistinguishable across emissions scenarios—that is, committed—until mid-century (Fig. 1 ) and that they are actually already much larger than mitigation costs. For simplicity, and owing to the availability of data, we compare damages to mitigation costs at the global level. Regional estimates of mitigation costs may shed further light on the national incentives for mitigation to which our results already hint, of relevance for international climate policy. Although these damages are committed from a mitigation perspective, adaptation may provide an opportunity to reduce them. Moreover, the strong divergence of damages after mid-century reemphasizes the clear benefits of mitigation from a purely economic perspective, as highlighted in previous studies 1 , 4 , 6 , 24 .

Historical climate data

Historical daily 2-m temperature and precipitation totals (in mm) are obtained for the period 1979–2019 from the W5E5 database. The W5E5 dataset comes from ERA-5, a state-of-the-art reanalysis of historical observations, but has been bias-adjusted by applying version 2.0 of the WATCH Forcing Data to ERA-5 reanalysis data and precipitation data from version 2.3 of the Global Precipitation Climatology Project to better reflect ground-based measurements 49 , 50 , 51 . We obtain these data on a 0.5° × 0.5° grid from the Inter-Sectoral Impact Model Intercomparison Project (ISIMIP) database. Notably, these historical data have been used to bias-adjust future climate projections from CMIP-6 (see the following section), ensuring consistency between the distribution of historical daily weather on which our empirical models were estimated and the climate projections used to estimate future damages. These data are publicly available from the ISIMIP database. See refs. 7 , 8 for robustness tests of the empirical models to the choice of climate data reanalysis products.

Future climate data

Daily 2-m temperature and precipitation totals (in mm) are taken from 21 climate models participating in CMIP-6 under a high (RCP8.5) and a low (RCP2.6) greenhouse gas emission scenario from 2015 to 2100. The data have been bias-adjusted and statistically downscaled to a common half-degree grid to reflect the historical distribution of daily temperature and precipitation of the W5E5 dataset using the trend-preserving method developed by the ISIMIP 50 , 52 . As such, the climate model data reproduce observed climatological patterns exceptionally well (Supplementary Table 5 ). Gridded data are publicly available from the ISIMIP database.

Historical economic data

Historical economic data come from the DOSE database of sub-national economic output 53 . We use a recent revision to the DOSE dataset that provides data across 83 countries, 1,660 sub-national regions with varying temporal coverage from 1960 to 2019. Sub-national units constitute the first administrative division below national, for example, states for the USA and provinces for China. Data come from measures of gross regional product per capita (GRPpc) or income per capita in local currencies, reflecting the values reported in national statistical agencies, yearbooks and, in some cases, academic literature. We follow previous literature 3 , 7 , 8 , 54 and assess real sub-national output per capita by first converting values from local currencies to US dollars to account for diverging national inflationary tendencies and then account for US inflation using a US deflator. Alternatively, one might first account for national inflation and then convert between currencies. Supplementary Fig. 12 demonstrates that our conclusions are consistent when accounting for price changes in the reversed order, although the magnitude of estimated damages varies. See the documentation of the DOSE dataset for further discussion of these choices. Conversions between currencies are conducted using exchange rates from the FRED database of the Federal Reserve Bank of St. Louis 55 and the national deflators from the World Bank 56 .

Future socio-economic data

Baseline gridded gross domestic product (GDP) and population data for the period 2015–2100 are taken from the middle-of-the-road scenario SSP2 (ref. 15 ). Population data have been downscaled to a half-degree grid by the ISIMIP following the methodologies of refs. 57 , 58 , which we then aggregate to the sub-national level of our economic data using the spatial aggregation procedure described below. Because current methodologies for downscaling the GDP of the SSPs use downscaled population to do so, per-capita estimates of GDP with a realistic distribution at the sub-national level are not readily available for the SSPs. We therefore use national-level GDP per capita (GDPpc) projections for all sub-national regions of a given country, assuming homogeneity within countries in terms of baseline GDPpc. Here we use projections that have been updated to account for the impact of the COVID-19 pandemic on the trajectory of future income, while remaining consistent with the long-term development of the SSPs 59 . The choice of baseline SSP alters the magnitude of projected climate damages in monetary terms, but when assessed in terms of percentage change from the baseline, the choice of socio-economic scenario is inconsequential. Gridded SSP population data and national-level GDPpc data are publicly available from the ISIMIP database. Sub-national estimates as used in this study are available in the code and data replication files.

Climate variables

Following recent literature 3 , 7 , 8 , we calculate an array of climate variables for which substantial impacts on macroeconomic output have been identified empirically, supported by further evidence at the micro level for plausible underlying mechanisms. See refs. 7 , 8 for an extensive motivation for the use of these particular climate variables and for detailed empirical tests on the nature and robustness of their effects on economic output. To summarize, these studies have found evidence for independent impacts on economic growth rates from annual average temperature, daily temperature variability, total annual precipitation, the annual number of wet days and extreme daily rainfall. Assessments of daily temperature variability were motivated by evidence of impacts on agricultural output and human health, as well as macroeconomic literature on the impacts of volatility on growth when manifest in different dimensions, such as government spending, exchange rates and even output itself 7 . Assessments of precipitation impacts were motivated by evidence of impacts on agricultural productivity, metropolitan labour outcomes and conflict, as well as damages caused by flash flooding 8 . See Extended Data Table 1 for detailed references to empirical studies of these physical mechanisms. Marked impacts of daily temperature variability, total annual precipitation, the number of wet days and extreme daily rainfall on macroeconomic output were identified robustly across different climate datasets, spatial aggregation schemes, specifications of regional time trends and error-clustering approaches. They were also found to be robust to the consideration of temperature extremes 7 , 8 . Furthermore, these climate variables were identified as having independent effects on economic output 7 , 8 , which we further explain here using Monte Carlo simulations to demonstrate the robustness of the results to concerns of imperfect multicollinearity between climate variables (Supplementary Methods Section 2 ), as well as by using information criteria (Supplementary Table 1 ) to demonstrate that including several lagged climate variables provides a preferable trade-off between optimally describing the data and limiting the possibility of overfitting.

We calculate these variables from the distribution of daily, d , temperature, T x , d , and precipitation, P x , d , at the grid-cell, x , level for both the historical and future climate data. As well as annual mean temperature, ${\bar{T}}_{x,y}$ , and annual total precipitation, P x , y , we calculate annual, y , measures of daily temperature variability, ${\widetilde{T}}_{x,y}$ :

the number of wet days, Pwd x , y :

and extreme daily rainfall:

in which T x , d , m , y is the grid-cell-specific daily temperature in month m and year y , ${\bar{T}}_{x,m,{y}}$ is the year and grid-cell-specific monthly, m , mean temperature, D m and D y the number of days in a given month m or year y , respectively, H the Heaviside step function, 1 mm the threshold used to define wet days and P 99.9 x is the 99.9th percentile of historical (1979–2019) daily precipitation at the grid-cell level. Units of the climate measures are degrees Celsius for annual mean temperature and daily temperature variability, millimetres for total annual precipitation and extreme daily precipitation, and simply the number of days for the annual number of wet days.

We also calculated weighted standard deviations of monthly rainfall totals as also used in ref. 8 but do not include them in our projections as we find that, when accounting for delayed effects, their effect becomes statistically indistinct and is better captured by changes in total annual rainfall.

Spatial aggregation

We aggregate grid-cell-level historical and future climate measures, as well as grid-cell-level future GDPpc and population, to the level of the first administrative unit below national level of the GADM database, using an area-weighting algorithm that estimates the portion of each grid cell falling within an administrative boundary. We use this as our baseline specification following previous findings that the effect of area or population weighting at the sub-national level is negligible 7 , 8 .

Empirical model specification: fixed-effects distributed lag models

Following a wide range of climate econometric literature 16 , 60 , we use panel regression models with a selection of fixed effects and time trends to isolate plausibly exogenous variation with which to maximize confidence in a causal interpretation of the effects of climate on economic growth rates. The use of region fixed effects, μ r , accounts for unobserved time-invariant differences between regions, such as prevailing climatic norms and growth rates owing to historical and geopolitical factors. The use of yearly fixed effects, η y , accounts for regionally invariant annual shocks to the global climate or economy such as the El Niño–Southern Oscillation or global recessions. In our baseline specification, we also include region-specific linear time trends, k r y , to exclude the possibility of spurious correlations resulting from common slow-moving trends in climate and growth.

The persistence of climate impacts on economic growth rates is a key determinant of the long-term magnitude of damages. Methods for inferring the extent of persistence in impacts on growth rates have typically used lagged climate variables to evaluate the presence of delayed effects or catch-up dynamics 2 , 18 . For example, consider starting from a model in which a climate condition, C r , y , (for example, annual mean temperature) affects the growth rate, Δlgrp r , y (the first difference of the logarithm of gross regional product) of region r in year y :

which we refer to as a ‘pure growth effects’ model in the main text. Typically, further lags are included,

and the cumulative effect of all lagged terms is evaluated to assess the extent to which climate impacts on growth rates persist. Following ref. 18 , in the case that,

the implication is that impacts on the growth rate persist up to NL years after the initial shock (possibly to a weaker or a stronger extent), whereas if

then the initial impact on the growth rate is recovered after NL years and the effect is only one on the level of output. However, we note that such approaches are limited by the fact that, when including an insufficient number of lags to detect a recovery of the growth rates, one may find equation ( 6 ) to be satisfied and incorrectly assume that a change in climatic conditions affects the growth rate indefinitely. In practice, given a limited record of historical data, including too few lags to confidently conclude in an infinitely persistent impact on the growth rate is likely, particularly over the long timescales over which future climate damages are often projected 2 , 24 . To avoid this issue, we instead begin our analysis with a model for which the level of output, lgrp r , y , depends on the level of a climate variable, C r , y :

Given the non-stationarity of the level of output, we follow the literature 19 and estimate such an equation in first-differenced form as,

which we refer to as a model of ‘pure level effects’ in the main text. This model constitutes a baseline specification in which a permanent change in the climate variable produces an instantaneous impact on the growth rate and a permanent effect only on the level of output. By including lagged variables in this specification,

we are able to test whether the impacts on the growth rate persist any further than instantaneously by evaluating whether α L > 0 are statistically significantly different from zero. Even though this framework is also limited by the possibility of including too few lags, the choice of a baseline model specification in which impacts on the growth rate do not persist means that, in the case of including too few lags, the framework reverts to the baseline specification of level effects. As such, this framework is conservative with respect to the persistence of impacts and the magnitude of future damages. It naturally avoids assumptions of infinite persistence and we are able to interpret any persistence that we identify with equation ( 9 ) as a lower bound on the extent of climate impact persistence on growth rates. See the main text for further discussion of this specification choice, in particular about its conservative nature compared with previous literature estimates, such as refs. 2 , 18 .

We allow the response to climatic changes to vary across regions, using interactions of the climate variables with historical average (1979–2019) climatic conditions reflecting heterogenous effects identified in previous work 7 , 8 . Following this previous work, the moderating variables of these interaction terms constitute the historical average of either the variable itself or of the seasonal temperature difference, ${\hat{T}}_{r}$ , or annual mean temperature, ${\bar{T}}_{r}$ , in the case of daily temperature variability 7 and extreme daily rainfall, respectively 8 .

The resulting regression equation with N and M lagged variables, respectively, reads:

in which Δlgrp r , y is the annual, regional GRPpc growth rate, measured as the first difference of the logarithm of real GRPpc, following previous work 2 , 3 , 7 , 8 , 18 , 19 . Fixed-effects regressions were run using the fixest package in R (ref. 61 ).

Estimates of the coefficients of interest α i , L are shown in Extended Data Fig. 1 for N = M = 10 lags and for our preferred choice of the number of lags in Supplementary Figs. 1 – 3 . In Extended Data Fig. 1 , errors are shown clustered at the regional level, but for the construction of damage projections, we block-bootstrap the regressions by region 1,000 times to provide a range of parameter estimates with which to sample the projection uncertainty (following refs. 2 , 31 ).

Spatial-lag model

In Supplementary Fig. 14 , we present the results from a spatial-lag model that explores the potential for climate impacts to ‘spill over’ into spatially neighbouring regions. We measure the distance between centroids of each pair of sub-national regions and construct spatial lags that take the average of the first-differenced climate variables and their interaction terms over neighbouring regions that are at distances of 0–500, 500–1,000, 1,000–1,500 and 1,500–2000 km (spatial lags, ‘SL’, 1 to 4). For simplicity, we then assess a spatial-lag model without temporal lags to assess spatial spillovers of contemporaneous climate impacts. This model takes the form:

in which SL indicates the spatial lag of each climate variable and interaction term. In Supplementary Fig. 14 , we plot the cumulative marginal effect of each climate variable at different baseline climate conditions by summing the coefficients for each climate variable and interaction term, for example, for average temperature impacts as:

These cumulative marginal effects can be regarded as the overall spatially dependent impact to an individual region given a one-unit shock to a climate variable in that region and all neighbouring regions at a given value of the moderating variable of the interaction term.

Constructing projections of economic damage from future climate change

We construct projections of future climate damages by applying the coefficients estimated in equation ( 10 ) and shown in Supplementary Tables 2 – 4 (when including only lags with statistically significant effects in specifications that limit overfitting; see Supplementary Methods Section 1 ) to projections of future climate change from the CMIP-6 models. Year-on-year changes in each primary climate variable of interest are calculated to reflect the year-to-year variations used in the empirical models. 30-year moving averages of the moderating variables of the interaction terms are calculated to reflect the long-term average of climatic conditions that were used for the moderating variables in the empirical models. By using moving averages in the projections, we account for the changing vulnerability to climate shocks based on the evolving long-term conditions (Supplementary Figs. 10 and 11 show that the results are robust to the precise choice of the window of this moving average). Although these climate variables are not differenced, the fact that the bias-adjusted climate models reproduce observed climatological patterns across regions for these moderating variables very accurately (Supplementary Table 6 ) with limited spread across models (<3%) precludes the possibility that any considerable bias or uncertainty is introduced by this methodological choice. However, we impose caps on these moderating variables at the 95th percentile at which they were observed in the historical data to prevent extrapolation of the marginal effects outside the range in which the regressions were estimated. This is a conservative choice that limits the magnitude of our damage projections.

Time series of primary climate variables and moderating climate variables are then combined with estimates of the empirical model parameters to evaluate the regression coefficients in equation ( 10 ), producing a time series of annual GRPpc growth-rate reductions for a given emission scenario, climate model and set of empirical model parameters. The resulting time series of growth-rate impacts reflects those occurring owing to future climate change. By contrast, a future scenario with no climate change would be one in which climate variables do not change (other than with random year-to-year fluctuations) and hence the time-averaged evaluation of equation ( 10 ) would be zero. Our approach therefore implicitly compares the future climate-change scenario to this no-climate-change baseline scenario.

The time series of growth-rate impacts owing to future climate change in region r and year y , δ r , y , are then added to the future baseline growth rates, π r , y (in log-diff form), obtained from the SSP2 scenario to yield trajectories of damaged GRPpc growth rates, ρ r , y . These trajectories are aggregated over time to estimate the future trajectory of GRPpc with future climate impacts:

in which GRPpc r , y =2020 is the initial log level of GRPpc. We begin damage estimates in 2020 to reflect the damages occurring since the end of the period for which we estimate the empirical models (1979–2019) and to match the timing of mitigation-cost estimates from most IAMs (see below).

For each emission scenario, this procedure is repeated 1,000 times while randomly sampling from the selection of climate models, the selection of empirical models with different numbers of lags (shown in Supplementary Figs. 1 – 3 and Supplementary Tables 2 – 4 ) and bootstrapped estimates of the regression parameters. The result is an ensemble of future GRPpc trajectories that reflect uncertainty from both physical climate change and the structural and sampling uncertainty of the empirical models.

Estimates of mitigation costs

We obtain IPCC estimates of the aggregate costs of emission mitigation from the AR6 Scenario Explorer and Database hosted by IIASA 23 . Specifically, we search the AR6 Scenarios Database World v1.1 for IAMs that provided estimates of global GDP and population under both a SSP2 baseline and a SSP2-RCP2.6 scenario to maintain consistency with the socio-economic and emission scenarios of the climate damage projections. We find five IAMs that provide data for these scenarios, namely, MESSAGE-GLOBIOM 1.0, REMIND-MAgPIE 1.5, AIM/GCE 2.0, GCAM 4.2 and WITCH-GLOBIOM 3.1. Of these five IAMs, we use the results only from the first three that passed the IPCC vetting procedure for reproducing historical emission and climate trajectories. We then estimate global mitigation costs as the percentage difference in global per capita GDP between the SSP2 baseline and the SSP2-RCP2.6 emission scenario. In the case of one of these IAMs, estimates of mitigation costs begin in 2020, whereas in the case of two others, mitigation costs begin in 2010. The mitigation cost estimates before 2020 in these two IAMs are mostly negligible, and our choice to begin comparison with damage estimates in 2020 is conservative with respect to the relative weight of climate damages compared with mitigation costs for these two IAMs.

Data availability

Data on economic production and ERA-5 climate data are publicly available at https://doi.org/10.5281/zenodo.4681306 (ref. 62 ) and https://www.ecmwf.int/en/forecasts/datasets/reanalysis-datasets/era5 , respectively. Data on mitigation costs are publicly available at https://data.ene.iiasa.ac.at/ar6/#/downloads . Processed climate and economic data, as well as all other necessary data for reproduction of the results, are available at the public repository https://doi.org/10.5281/zenodo.10562951 (ref. 63 ).

Code availability

All code necessary for reproduction of the results is available at the public repository https://doi.org/10.5281/zenodo.10562951 (ref. 63 ).

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Acknowledgements

We gratefully acknowledge financing from the Volkswagen Foundation and the Deutsche Gesellschaft für Internationale Zusammenarbeit (GIZ) GmbH on behalf of the Government of the Federal Republic of Germany and Federal Ministry for Economic Cooperation and Development (BMZ).

Open access funding provided by Potsdam-Institut für Klimafolgenforschung (PIK) e.V.

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Extended data figures and tables

Extended data fig. 1 constraining the persistence of historical climate impacts on economic growth rates..

The results of a panel-based fixed-effects distributed lag model for the effects of annual mean temperature ( a ), daily temperature variability ( b ), total annual precipitation ( c ), the number of wet days ( d ) and extreme daily precipitation ( e ) on sub-national economic growth rates. Point estimates show the effects of a 1 °C or one standard deviation increase (for temperature and precipitation variables, respectively) at the lower quartile, median and upper quartile of the relevant moderating variable (green, orange and purple, respectively) at different lagged periods after the initial shock (note that these are not cumulative effects). Climate variables are used in their first-differenced form (see main text for discussion) and the moderating climate variables are the annual mean temperature, seasonal temperature difference, total annual precipitation, number of wet days and annual mean temperature, respectively, in panels a – e (see Methods for further discussion). Error bars show the 95% confidence intervals having clustered standard errors by region. The within-region R 2 , Bayesian and Akaike information criteria for the model are shown at the top of the figure. This figure shows results with ten lags for each variable to demonstrate the observed levels of persistence, but our preferred specifications remove later lags based on the statistical significance of terms shown above and the information criteria shown in Extended Data Fig. 2 . The resulting models without later lags are shown in Supplementary Figs. 1 – 3 .

Extended Data Fig. 2 Incremental lag-selection procedure using information criteria and within-region R 2 .

Starting from a panel-based fixed-effects distributed lag model estimating the effects of climate on economic growth using the real historical data (as in equation ( 4 )) with ten lags for all climate variables (as shown in Extended Data Fig. 1 ), lags are incrementally removed for one climate variable at a time. The resulting Bayesian and Akaike information criteria are shown in a – e and f – j , respectively, and the within-region R 2 and number of observations in k – o and p – t , respectively. Different rows show the results when removing lags from different climate variables, ordered from top to bottom as annual mean temperature, daily temperature variability, total annual precipitation, the number of wet days and extreme annual precipitation. Information criteria show minima at approximately four lags for precipitation variables and ten to eight for temperature variables, indicating that including these numbers of lags does not lead to overfitting. See Supplementary Table 1 for an assessment using information criteria to determine whether including further climate variables causes overfitting.

Extended Data Fig. 3 Damages in our preferred specification that provides a robust lower bound on the persistence of climate impacts on economic growth versus damages in specifications of pure growth or pure level effects.

Estimates of future damages as shown in Fig. 1 but under the emission scenario RCP8.5 for three separate empirical specifications: in orange our preferred specification, which provides an empirical lower bound on the persistence of climate impacts on economic growth rates while avoiding assumptions of infinite persistence (see main text for further discussion); in purple a specification of ‘pure growth effects’ in which the first difference of climate variables is not taken and no lagged climate variables are included (the baseline specification of ref. 2 ); and in pink a specification of ‘pure level effects’ in which the first difference of climate variables is taken but no lagged terms are included.

Extended Data Fig. 4 Climate changes in different variables as a function of historical interannual variability.

Changes in each climate variable of interest from 1979–2019 to 2035–2065 under the high-emission scenario SSP5-RCP8.5, expressed as a percentage of the historical variability of each measure. Historical variability is estimated as the standard deviation of each detrended climate variable over the period 1979–2019 during which the empirical models were identified (detrending is appropriate because of the inclusion of region-specific linear time trends in the empirical models). See Supplementary Fig. 13 for changes expressed in standard units. Data on national administrative boundaries are obtained from the GADM database version 3.6 and are freely available for academic use ( https://gadm.org/ ).

Extended Data Fig. 5 Contribution of different climate variables to overall committed damages.

a , Climate damages in 2049 when using empirical models that account for all climate variables, changes in annual mean temperature only or changes in both annual mean temperature and one other climate variable (daily temperature variability, total annual precipitation, the number of wet days and extreme daily precipitation, respectively). b , The cumulative marginal effects of an increase in annual mean temperature of 1 °C, at different baseline temperatures, estimated from empirical models including all climate variables or annual mean temperature only. Estimates and uncertainty bars represent the median and 95% confidence intervals obtained from 1,000 block-bootstrap resamples from each of three different empirical models using eight, nine or ten lags of temperature terms.

Extended Data Fig. 6 The difference in committed damages between the upper and lower quartiles of countries when ranked by GDP and cumulative historical emissions.

Quartiles are defined using a population weighting, as are the average committed damages across each quartile group. The violin plots indicate the distribution of differences between quartiles across the two extreme emission scenarios (RCP2.6 and RCP8.5) and the uncertainty sampling procedure outlined in Methods , which accounts for uncertainty arising from the choice of lags in the empirical models, uncertainty in the empirical model parameter estimates, as well as the climate model projections. Bars indicate the median, as well as the 10th and 90th percentiles and upper and lower sixths of the distribution reflecting the very likely and likely ranges following the likelihood classification adopted by the IPCC.

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Kotz, M., Levermann, A. & Wenz, L. The economic commitment of climate change. Nature 628 , 551–557 (2024). https://doi.org/10.1038/s41586-024-07219-0

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Received : 25 January 2023

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Published : 17 April 2024

Issue Date : 18 April 2024

DOI : https://doi.org/10.1038/s41586-024-07219-0

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How the American middle class has changed in the past five decades

The middle class, once the economic stratum of a clear majority of American adults, has steadily contracted in the past five decades. The share of adults who live in middle-class households fell from 61% in 1971 to 50% in 2021, according to a new Pew Research Center analysis of government data.

From 2020: Are you in the American middle class? Find out with our income calculator

A bar chart showing that the share of adults in U.S. middle class has decreased considerably since 1971

The shrinking of the middle class has been accompanied by an increase in the share of adults in the upper-income tier – from 14% in 1971 to 21% in 2021 – as well as an increase in the share who are in the lower-income tier, from 25% to 29%. These changes have occurred gradually, as the share of adults in the middle class decreased in each decade from 1971 to 2011, but then held steady through 2021.

The analysis below presents seven facts about how the economic status of the U.S. middle class and that of America’s major demographic groups have changed since 1971. A related analysis examines the impact of the coronavirus pandemic on the financial well-being of households in the lower-, middle- and upper-income tiers, with comparisons to the Great Recession era. (In the source data for both analyses, demographic figures refer to the 1971-2021 period, while income figures refer to the 1970-2020 period. Thus, the shares of adults in an income tier are based on their household incomes in the previous year.)

This report analyzes data from the Annual Social and Economic Supplements (ASEC) of the Current Population Survey (CPS) to study how the economic status of the American middle class has changed since 1971. It also examines the movement of demographic groups in and out of the American middle class and across lower- and upper-income tiers from 1971 to 2021.

The CPS is the U.S. government’s official source for monthly estimates of unemployment ; the ASEC, conducted in March each year, is the official source for its estimates of income and poverty . The COVID-19 outbreak has affected data collection efforts by the U.S. government in its surveys, limiting in-person data collection and affecting the response rate. It is possible that some measures of economic outcomes and how they vary across demographic groups are affected by these changes in data collection. This report makes use of updated weights released by the Census Bureau to correct for nonresponse in 2019, 2020 and 2021.

In this analysis, “middle-income” adults in 2021 are those with an annual household income that was two-thirds to double the national median income in 2020, after incomes have been adjusted for household size, or about $52,000 to $156,000 annually in 2020 dollars for a household of three. “Lower-income” adults have household incomes less than $52,000 and “upper-income” adults have household incomes greater than $156,000.

The income it takes to be middle income varies by household size, with smaller households requiring less to support the same lifestyle as larger households. The boundaries of the income tiers also vary across years with changes in the national median income. Read the methodology for more details.

The terms “middle income” and “middle class” are used interchangeably in this analysis for the sake of exposition. But being middle class can refer to more than just income, be it the level of education, the type of profession, economic security, home ownership, or one’s social and political values. Class also could simply be a matter of self-identification.

Household incomes have risen considerably since 1970, but those of middle-class households have not climbed nearly as much as those of upper-income households. The median income of middle-class households in 2020 was 50% greater than in 1970 ($90,131 vs. $59,934), as measured in 2020 dollars. These gains were realized slowly, but for the most part steadily, with the exception of the period from 2000 to 2010, the so-called “ lost decade ,” when incomes fell across the board.

A bar chart showing that incomes rose the most for upper-income households in U.S. from 1970 to 2020

The median income for lower-income households grew more slowly than that of middle-class households, increasing from $20,604 in 1970 to $29,963 in 2020, or 45%.

The rise in income from 1970 to 2020 was steepest for upper-income households. Their median income increased 69% during that timespan, from $130,008 to $219,572.

As a result of these changes, the gap in the incomes of upper-income and other households also increased. In 2020, the median income of upper-income households was 7.3 times that of lower-income households, up from 6.3 in 1970. The median income of upper-income households was 2.4 times that of middle-income households in 2020, up from 2.2 in 1970.

A line graph showing that the share of aggregate income held by the U.S. middle class has plunged since 1970

The share of aggregate U.S. household income held by the middle class has fallen steadily since 1970. The widening of the income gap and the shrinking of the middle class has led to a steady decrease in the share of U.S. aggregate income held by middle-class households. In 1970, adults in middle-income households accounted for 62% of aggregate income, a share that fell to 42% in 2020.

Meanwhile, the share of aggregate income accounted for by upper-income households has increased steadily, from 29% in 1970 to 50% in 2020. Part of this increase reflects the rising share of adults who are in the upper-income tier.

The share of U.S. aggregate income held by lower-income households edged down from 10% to 8% over these five decades, even though the proportion of adults living in lower-income households increased over this period.

Older Americans and Black adults made the greatest progress up the income ladder from 1971 to 2021. Among adults overall, the share who were in the upper-income tier increased from 14% in 1971 to 21% in 2021, or by 7 percentage points. Meanwhile, the share in the lower-income tier increased from 25% to 29%, or by 4 points. On balance, this represented a net gain of 3 percentage points in income status for all adults.

A bar chart showing that Black adults and those older or married saw some of the biggest gains in income status from 1971 to 2021

Those ages 65 and older made the most notable progress up the income ladder from 1971 to 2021. They increased their share in the upper-income tier while reducing their share in the lower-income tier, resulting in a net gain of 25 points. Progress among adults 65 and older was likely driven by an increase in labor force participation , rising educational levels and by the role of Social Security payments in reducing poverty.

Black adults, as well as married men and women, were also among the biggest gainers from 1971 to 2021, with net increases ranging from 12 to 14 percentage points.

On the other hand, not having at least a bachelor’s degree resulted in a notable degree of economic regression over this period. Adults with a high school diploma or less education, as well as those with some college experience but no degree, saw sizable increases in their shares in the lower-income tier in the past five decades. Although no single group of adults by education category moved up the income ladder from 1971 to 2021, adults overall realized gains by boosting their education levels . The share of adults 25 and older who had completed at least four years of college stood at 38% in 2021, compared with only 11% in 1971.

Progress up the income ladder for a demographic group does not necessarily signal its economic status in comparison with other groups at a given point in time. For example, in 2021, adults ages 65 and older and Black adults were still more likely than many other groups to be lower income, and less likely to be middle or upper income.

Married adults and those in multi-earner households made more progress up the income ladder from 1971 to 2021 than their immediate counterparts. Generally, partnered adults have better outcomes on a range of economic outcomes than the unpartnered. One reason is that marriage is increasingly linked to educational attainment , which bears fruit in terms of higher incomes.

A bar chart showing that U.S. adults who are married or in households with more than one earner are more likely to be upper income

Married men and women were distributed across the income tiers identically to each other in both 1971 and 2021. Both groups nearly doubled their shares in the upper-income tier in the past five decades, from 14% in 1971 to 27% in 2021. And neither group experienced an increase in the share in the lower-income tier.

Unmarried men and women were much more likely than their married counterparts to be in the lower-income tier in 2021. And unmarried men, in particular, experienced a sizable increase in their share in the lower-income tier from 1971 t0 2021 and a similarly large decrease in their share in the middle-income tier. Nonetheless, unmarried men are less likely than unmarried women to be lower income and more likely to be middle income.

Adults in households with more than one earner fare much better economically than adults in households with only one earner. In 2021, some 20% of adults in multi-earner households were in the lower-income tier, compared with 53% of adults in single-earner households. Also, adults in multi-earner households were more than twice as likely as adults in single-earner households to be in the upper-income tier in 2021. In the long haul, adults in single-earner households are among the groups who slid down the income ladder the most from 1971 to 2021.

A bar chart showing that Black and Hispanic adults, women are more likely to be lower income

Despite progress, Black and Hispanic adults trail behind other groups in their economic status. Although Black adults made some of the biggest strides up the income tiers from 1971 to 2021, they, along with Hispanic adults, are more likely to be in the lower-income tier than are White or Asian adults. About 40% of both Black and Hispanic adults were lower income in 2021, compared with 24% of White adults and 22% of Asian adults.

Black adults are the only major racial and ethnic group that did not experience a decrease in its middle-class share, which stood at 47% in 2021, about the same as in 1971. White adults are the only group in which more than half (52%) lived in middle-class households in 2021, albeit after declining from 63% in 1971. At the top end, only about one-in-ten Black and Hispanic adults were upper income in 2021, compared with one-in-four or more White and Asian adults.

The relative economic status of men and women has changed little from 1971 to 2021. Both experienced similar percentage point increases in the shares in the lower- and upper-income tiers, and both saw double-digit decreases in the shares who are middle class. Women remained more likely than men to live in lower-income households in 2021 (31% vs. 26%).

A bar chart showing that despite gains, older adults in the U.S. remain most likely to be lower income

Adults 65 and older continue to lag economically, despite decades of progress. The share of adults ages 65 and older in the lower-income tier fell from 54% in 1971 to 37% in 2021. Their share in the middle class rose from 39% to 47% and their share in the upper-income tier increased from 7% to 16%. However, adults 65 and older are the only age group in which more than one-in-three adults are in lower-income households, and they are much less likely than adults ages 30 to 44 – as well as those ages 45 to 64 – to be in the upper-income tier.

All other age groups experienced an increase in the shares who are lower income from 1971 to 2021, as well as a decrease in the shares who are middle income. But they also saw increases in the shares who are upper income. Among adults ages 30 to 44, for instance, the share in upper-income households almost doubled, from 12% in 1971 to 21% in 2021.

A bar chart showing that about four-in-ten college-educated adults in the U.S. are in the upper-income tier

There is a sizable and growing income gap between adults with a bachelor’s degree and those with lower levels of education. In 2021, about four-in-ten adults with at least a bachelor’s degree (39%) were in the upper-income tier, compared with 16% or less among those without a bachelor’s degree. The share of adults in the upper-income tier with at least a bachelor’s degree edged up from 1971 to 2021, while the share without a bachelor’s degree either edged down or held constant.

About half or a little more of adults with either some college education or a high school diploma only were in the middle class in 2021. But these two groups, along with those with less than a high school education, experienced notable drops in their middle class shares from 1971 to 2021 – and notable increases in the shares in the lower-income tier. In 2021, about four-in-ten adults with only a high school diploma or its equivalent (39%) were in the lower-income tier, about double the share in 1971.

Note: Here is the methodology for this analysis.

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The hardships and dreams of asian americans living in poverty, a booming u.s. stock market doesn’t benefit all racial and ethnic groups equally, black americans’ views on success in the u.s., wealth surged in the pandemic, but debt endures for poorer black and hispanic families, most popular.

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ABOUT PEW RESEARCH CENTER Pew Research Center is a nonpartisan fact tank that informs the public about the issues, attitudes and trends shaping the world. It conducts public opinion polling, demographic research, media content analysis and other empirical social science research. Pew Research Center does not take policy positions. It is a subsidiary of The Pew Charitable Trusts .

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What is Empirical Research? Definition, Methods, Examples

What is Empirical Research?

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Qualitative vs. Quantitative Research

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Empirical Research Data Analysis

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Raising awareness of uncertain choices in empirical data analysis: A teaching concept toward replicable research practices

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