research that is usually based on numerical measurements

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research that is usually based on numerical measurements

Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques. Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon.

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Muijs, Daniel. Doing Quantitative Research in Education with SPSS . 2nd edition. London: SAGE Publications, 2010.

Characteristics

Goal in conducting quantitative research study is to determine the relationship between one thing [an independent variable] and another [a dependent or outcome variable] within a population. Quantitative research designs are either descriptive [subjects usually measured once] or experimental [subjects measured before and after a treatment]. A descriptive study establishes only associations between variables; an experimental study establishes causality.

Quantitative research deals in numbers, logic, and an objective stance. Quantitative research focuses on numeric and unchanging data and detailed, convergent reasoning rather than divergent reasoning [i.e., the generation of a variety of ideas about a research problem in a spontaneous, free-flowing manner].

Its main characteristics are:

The data is usually gathered using structured research instruments.
The results are based on larger sample sizes that are representative of the population.
The research study can usually be replicated or repeated, given its high reliability.
Researcher has a clearly defined research question to which objective answers are sought.
All aspects of the study are carefully designed before data is collected.
Data are in the form of numbers and statistics, often arranged in tables, charts, figures, or other non-textual forms.
Project can be used to generalize concepts more widely, predict future results, or investigate causal relationships.
Researcher uses tools, such as questionnaires or computer software, to collect numerical data.

The overarching aim of a quantitative research study is to classify features, count them, and construct statistical models in an attempt to explain what is observed.

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Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques . Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon.

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Characteristics of Quantitative Research

Your goal in conducting quantitative research study is to determine the relationship between one thing [an independent variable] and another [a dependent or outcome variable] within a population. Quantitative research designs are either descriptive [subjects usually measured once] or experimental [subjects measured before and after a treatment]. A descriptive study establishes only associations between variables; an experimental study establishes causality.

Its main characteristics are :

The data is usually gathered using structured research instruments.
The results are based on larger sample sizes that are representative of the population.
The research study can usually be replicated or repeated, given its high reliability.
Researcher has a clearly defined research question to which objective answers are sought.
All aspects of the study are carefully designed before data is collected.
Data are in the form of numbers and statistics, often arranged in tables, charts, figures, or other non-textual forms.
Project can be used to generalize concepts more widely, predict future results, or investigate causal relationships.
Researcher uses tools, such as questionnaires or computer software, to collect numerical data.

The overarching aim of a quantitative research study is to classify features, count them, and construct statistical models in an attempt to explain what is observed.

Things to keep in mind when reporting the results of a study using quantitative methods :

Explain the data collected and their statistical treatment as well as all relevant results in relation to the research problem you are investigating. Interpretation of results is not appropriate in this section.
Report unanticipated events that occurred during your data collection. Explain how the actual analysis differs from the planned analysis. Explain your handling of missing data and why any missing data does not undermine the validity of your analysis.
Explain the techniques you used to "clean" your data set.
Choose a minimally sufficient statistical procedure ; provide a rationale for its use and a reference for it. Specify any computer programs used.
Describe the assumptions for each procedure and the steps you took to ensure that they were not violated.
When using inferential statistics , provide the descriptive statistics, confidence intervals, and sample sizes for each variable as well as the value of the test statistic, its direction, the degrees of freedom, and the significance level [report the actual p value].
Avoid inferring causality , particularly in nonrandomized designs or without further experimentation.
Use tables to provide exact values ; use figures to convey global effects. Keep figures small in size; include graphic representations of confidence intervals whenever possible.
Always tell the reader what to look for in tables and figures .

NOTE: When using pre-existing statistical data gathered and made available by anyone other than yourself [e.g., government agency], you still must report on the methods that were used to gather the data and describe any missing data that exists and, if there is any, provide a clear explanation why the missing data does not undermine the validity of your final analysis.

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Quantitative Research Methods. Writing@CSU. Colorado State University; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Basic Research Design for Quantitative Studies

Before designing a quantitative research study, you must decide whether it will be descriptive or experimental because this will dictate how you gather, analyze, and interpret the results. A descriptive study is governed by the following rules: subjects are generally measured once; the intention is to only establish associations between variables; and, the study may include a sample population of hundreds or thousands of subjects to ensure that a valid estimate of a generalized relationship between variables has been obtained. An experimental design includes subjects measured before and after a particular treatment, the sample population may be very small and purposefully chosen, and it is intended to establish causality between variables. Introduction The introduction to a quantitative study is usually written in the present tense and from the third person point of view. It covers the following information:

Identifies the research problem -- as with any academic study, you must state clearly and concisely the research problem being investigated.
Reviews the literature -- review scholarship on the topic, synthesizing key themes and, if necessary, noting studies that have used similar methods of inquiry and analysis. Note where key gaps exist and how your study helps to fill these gaps or clarifies existing knowledge.
Describes the theoretical framework -- provide an outline of the theory or hypothesis underpinning your study. If necessary, define unfamiliar or complex terms, concepts, or ideas and provide the appropriate background information to place the research problem in proper context [e.g., historical, cultural, economic, etc.].

Methodology The methods section of a quantitative study should describe how each objective of your study will be achieved. Be sure to provide enough detail to enable the reader can make an informed assessment of the methods being used to obtain results associated with the research problem. The methods section should be presented in the past tense.

Study population and sampling -- where did the data come from; how robust is it; note where gaps exist or what was excluded. Note the procedures used for their selection;
Data collection – describe the tools and methods used to collect information and identify the variables being measured; describe the methods used to obtain the data; and, note if the data was pre-existing [i.e., government data] or you gathered it yourself. If you gathered it yourself, describe what type of instrument you used and why. Note that no data set is perfect--describe any limitations in methods of gathering data.
Data analysis -- describe the procedures for processing and analyzing the data. If appropriate, describe the specific instruments of analysis used to study each research objective, including mathematical techniques and the type of computer software used to manipulate the data.

Results The finding of your study should be written objectively and in a succinct and precise format. In quantitative studies, it is common to use graphs, tables, charts, and other non-textual elements to help the reader understand the data. Make sure that non-textual elements do not stand in isolation from the text but are being used to supplement the overall description of the results and to help clarify key points being made. Further information about how to effectively present data using charts and graphs can be found here .

Statistical analysis -- how did you analyze the data? What were the key findings from the data? The findings should be present in a logical, sequential order. Describe but do not interpret these trends or negative results; save that for the discussion section. The results should be presented in the past tense.

Discussion Discussions should be analytic, logical, and comprehensive. The discussion should meld together your findings in relation to those identified in the literature review, and placed within the context of the theoretical framework underpinning the study. The discussion should be presented in the present tense.

Interpretation of results -- reiterate the research problem being investigated and compare and contrast the findings with the research questions underlying the study. Did they affirm predicted outcomes or did the data refute it?
Description of trends, comparison of groups, or relationships among variables -- describe any trends that emerged from your analysis and explain all unanticipated and statistical insignificant findings.
Discussion of implications – what is the meaning of your results? Highlight key findings based on the overall results and note findings that you believe are important. How have the results helped fill gaps in understanding the research problem?
Limitations -- describe any limitations or unavoidable bias in your study and, if necessary, note why these limitations did not inhibit effective interpretation of the results.

Conclusion End your study by to summarizing the topic and provide a final comment and assessment of the study.

Summary of findings – synthesize the answers to your research questions. Do not report any statistical data here; just provide a narrative summary of the key findings and describe what was learned that you did not know before conducting the study.
Recommendations – if appropriate to the aim of the assignment, tie key findings with policy recommendations or actions to be taken in practice.
Future research – note the need for future research linked to your study’s limitations or to any remaining gaps in the literature that were not addressed in your study.

Black, Thomas R. Doing Quantitative Research in the Social Sciences: An Integrated Approach to Research Design, Measurement and Statistics . London: Sage, 1999; Gay,L. R. and Peter Airasain. Educational Research: Competencies for Analysis and Applications . 7th edition. Upper Saddle River, NJ: Merril Prentice Hall, 2003; Hector, Anestine. An Overview of Quantitative Research in Composition and TESOL . Department of English, Indiana University of Pennsylvania; Hopkins, Will G. “Quantitative Research Design.” Sportscience 4, 1 (2000); "A Strategy for Writing Up Research Results. The Structure, Format, Content, and Style of a Journal-Style Scientific Paper." Department of Biology. Bates College; Nenty, H. Johnson. "Writing a Quantitative Research Thesis." International Journal of Educational Science 1 (2009): 19-32; Ouyang, Ronghua (John). Basic Inquiry of Quantitative Research . Kennesaw State University.

Strengths of Using Quantitative Methods

Quantitative researchers try to recognize and isolate specific variables contained within the study framework, seek correlation, relationships and causality, and attempt to control the environment in which the data is collected to avoid the risk of variables, other than the one being studied, accounting for the relationships identified.

Among the specific strengths of using quantitative methods to study social science research problems:

Allows for a broader study, involving a greater number of subjects, and enhancing the generalization of the results;
Allows for greater objectivity and accuracy of results. Generally, quantitative methods are designed to provide summaries of data that support generalizations about the phenomenon under study. In order to accomplish this, quantitative research usually involves few variables and many cases, and employs prescribed procedures to ensure validity and reliability;
Applying well established standards means that the research can be replicated, and then analyzed and compared with similar studies;
You can summarize vast sources of information and make comparisons across categories and over time; and,
Personal bias can be avoided by keeping a 'distance' from participating subjects and using accepted computational techniques .

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Limitations of Using Quantitative Methods

Quantitative methods presume to have an objective approach to studying research problems, where data is controlled and measured, to address the accumulation of facts, and to determine the causes of behavior. As a consequence, the results of quantitative research may be statistically significant but are often humanly insignificant.

Some specific limitations associated with using quantitative methods to study research problems in the social sciences include:

Quantitative data is more efficient and able to test hypotheses, but may miss contextual detail;
Uses a static and rigid approach and so employs an inflexible process of discovery;
The development of standard questions by researchers can lead to "structural bias" and false representation, where the data actually reflects the view of the researcher instead of the participating subject;
Results provide less detail on behavior, attitudes, and motivation;
Researcher may collect a much narrower and sometimes superficial dataset;
Results are limited as they provide numerical descriptions rather than detailed narrative and generally provide less elaborate accounts of human perception;
The research is often carried out in an unnatural, artificial environment so that a level of control can be applied to the exercise. This level of control might not normally be in place in the real world thus yielding "laboratory results" as opposed to "real world results"; and,
Preset answers will not necessarily reflect how people really feel about a subject and, in some cases, might just be the closest match to the preconceived hypothesis.

Research Tip

Finding Examples of How to Apply Different Types of Research Methods

SAGE publications is a major publisher of studies about how to design and conduct research in the social and behavioral sciences. Their SAGE Research Methods Online and Cases database includes contents from books, articles, encyclopedias, handbooks, and videos covering social science research design and methods including the complete Little Green Book Series of Quantitative Applications in the Social Sciences and the Little Blue Book Series of Qualitative Research techniques. The database also includes case studies outlining the research methods used in real research projects. This is an excellent source for finding definitions of key terms and descriptions of research design and practice, techniques of data gathering, analysis, and reporting, and information about theories of research [e.g., grounded theory]. The database covers both qualitative and quantitative research methods as well as mixed methods approaches to conducting research.

SAGE Research Methods Online and Cases

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Home » Quantitative Data – Types, Methods and Examples

Quantitative Data – Types, Methods and Examples

Table of Contents

Quantitative Data

Definition:

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

Quantitative Data Types

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

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

Quantitative Data Collection Methods

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

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

Quantitative Data Analysis Methods

There are several methods for analyzing quantitative data, including:

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

Quantitative Data Formats

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

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

Quantitative Data Gathering Guide

Here is a basic guide for gathering quantitative data:

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

Examples of Quantitative Data

Here are some examples of quantitative data:

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

Applications of Quantitative Data

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

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

Purpose of Quantitative Data

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

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

When to use Quantitative Data

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

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

Characteristics of Quantitative Data

Quantitative data is characterized by several key features, including:

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

Advantages of Quantitative Data

Some advantages of quantitative data are:

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

Limitations of Quantitative Data

Some Limitations of Quantitative Data are as follows:

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

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Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques . Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon.

Characteristics of Quantitative Research

Quantitative research deals in numbers, logic, and an objective stance. Quantitative research focuses on numberic and unchanging data and detailed, convergent reasoning rather than divergent reasoning [i.e., the generation of a variety of ideas about a research problem in a spontaneous, free-flowing manner].

Its main characteristics are :

The data is usually gathered using structured research instruments.
The results are based on larger sample sizes that are representative of the population.
The research study can usually be replicated or repeated, given its high reliability.
Researcher has a clearly defined research question to which objective answers are sought.
All aspects of the study are carefully designed before data is collected.
Data are in the form of numbers and statistics, often arranged in tables, charts, figures, or other non-textual forms.
Project can be used to generalize concepts more widely, predict future results, or investigate causal relationships.
Researcher uses tools, such as questionnaires or computer software, to collect numerical data.

The overarching aim of a quantitative research study is to classify features, count them, and construct statistical models in an attempt to explain what is observed.

Things to keep in mind when reporting the results of a study using quantiative methods :

Explain the data collected and their statistical treatment as well as all relevant results in relation to the research problem you are investigating. Interpretation of results is not appropriate in this section.
Report unanticipated events that occurred during your data collection. Explain how the actual analysis differs from the planned analysis. Explain your handling of missing data and why any missing data does not undermine the validity of your analysis.
Explain the techniques you used to "clean" your data set.
Choose a minimally sufficient statistical procedure ; provide a rationale for its use and a reference for it. Specify any computer programs used.
Describe the assumptions for each procedure and the steps you took to ensure that they were not violated.
When using inferential statistics , provide the descriptive statistics, confidence intervals, and sample sizes for each variable as well as the value of the test statistic, its direction, the degrees of freedom, and the significance level [report the actual p value].
Avoid inferring causality , particularly in nonrandomized designs or without further experimentation.
Use tables to provide exact values ; use figures to convey global effects. Keep figures small in size; include graphic representations of confidence intervals whenever possible.
Always tell the reader what to look for in tables and figures .

NOTE: When using pre-existing statistical data gathered and made available by anyone other than yourself [e.g., government agency], you still must report on the methods that were used to gather the data and describe any missing data that exists and, if there is any, provide a clear explanation why the missing datat does not undermine the validity of your final analysis.

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Quantitative Research Methods . Writing@CSU. Colorado State University; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Basic Research Designs for Quantitative Studies

Identifies the research problem -- as with any academic study, you must state clearly and concisely the research problem being investigated.
Reviews the literature -- review scholarship on the topic, synthesizing key themes and, if necessary, noting studies that have used similar methods of inquiry and analysis. Note where key gaps exist and how your study helps to fill these gaps or clarifies existing knowledge.
Describes the theoretical framework -- provide an outline of the theory or hypothesis underpinning your study. If necessary, define unfamiliar or complex terms, concepts, or ideas and provide the appropriate background information to place the research problem in proper context [e.g., historical, cultural, economic, etc.].

Study population and sampling -- where did the data come from; how robust is it; note where gaps exist or what was excluded. Note the procedures used for their selection;
Data collection – describe the tools and methods used to collect information and identify the variables being measured; describe the methods used to obtain the data; and, note if the data was pre-existing [i.e., government data] or you gathered it yourself. If you gathered it yourself, describe what type of instrument you used and why. Note that no data set is perfect--describe any limitations in methods of gathering data.
Data analysis -- describe the procedures for processing and analyzing the data. If appropriate, describe the specific instruments of analysis used to study each research objective, including mathematical techniques and the type of computer software used to manipulate the data.

Statistical analysis -- how did you analyze the data? What were the key findings from the data? The findings should be present in a logical, sequential order. Describe but do not interpret these trends or negative results; save that for the discussion section. The results should be presented in the past tense.

Interpretation of results -- reiterate the research problem being investigated and compare and contrast the findings with the research questions underlying the study. Did they affirm predicted outcomes or did the data refute it?
Description of trends, comparison of groups, or relationships among variables -- describe any trends that emerged from your analysis and explain all unanticipated and statistical insignificant findings.
Discussion of implications – what is the meaning of your results? Highlight key findings based on the overall results and note findings that you believe are important. How have the results helped fill gaps in understanding the research problem?
Limitations -- describe any limitations or unavoidable bias in your study and, if necessary, note why these limitations did not inhibit effective interpretation of the results.

Conclusion End your study by to summarizing the topic and provide a final comment and assessment of the study.

Summary of findings – synthesize the answers to your research questions. Do not report any statistical data here; just provide a narrative summary of the key findings and describe what was learned that you did not know before conducting the study.
Recommendations – if appropriate to the aim of the assignment, tie key findings with policy recommendations or actions to be taken in practice.
Future research – note the need for future research linked to your study’s limitations or to any remaining gaps in the literature that were not addressed in your study.

Black, Thomas R. Doing Quantitative Research in the Social Sciences: An Integrated Approach to Research Design, Measurement and Statistics . London: Sage, 1999; Gay,L. R. and Peter Airasain. Educational Research: Competencies for Analysis and Applications . 7th edition. Upper Saddle River, NJ: Merril Prentice Hall, 2003; Hector, Anestine. An Overview of Quantitative Research in Compostion and TESOL . Department of English, Indiana University of Pennsylvania; Hopkins, Will G. “Quantitative Research Design.” Sportscience 4, 1 (2000); A Strategy for Writing Up Research Results . The Structure, Format, Content, and Style of a Journal-Style Scientific Paper. Department of Biology. Bates College; Nenty, H. Johnson. "Writing a Quantitative Research Thesis." International Journal of Educational Science 1 (2009): 19-32; Ouyang, Ronghua (John). Basic Inquiry of Quantitative Research . Kennesaw State University.

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Measurements in quantitative research: how to select and report on research instruments

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1 Department of Acute and Tertiary Care in the School of Nursing, University of Pittsburgh in Pennsylvania.
PMID: 24969252
DOI: 10.1188/14.ONF.431-433

Measures exist to numerically represent degrees of attributes. Quantitative research is based on measurement and is conducted in a systematic, controlled manner. These measures enable researchers to perform statistical tests, analyze differences between groups, and determine the effectiveness of treatments. If something is not measurable, it cannot be tested.

Keywords: measurements; quantitative research; reliability; validity.

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Review Article
Published: 01 June 2023

Data, measurement and empirical methods in the science of science

Lu Liu 1 , 2 , 3 , 4 ,
Benjamin F. Jones ORCID: orcid.org/0000-0001-9697-9388 1 , 2 , 3 , 5 , 6 ,
Brian Uzzi ORCID: orcid.org/0000-0001-6855-2854 1 , 2 , 3 &
Dashun Wang ORCID: orcid.org/0000-0002-7054-2206 1 , 2 , 3 , 7

Nature Human Behaviour volume 7 , pages 1046–1058 ( 2023 ) Cite this article

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The advent of large-scale datasets that trace the workings of science has encouraged researchers from many different disciplinary backgrounds to turn scientific methods into science itself, cultivating a rapidly expanding ‘science of science’. This Review considers this growing, multidisciplinary literature through the lens of data, measurement and empirical methods. We discuss the purposes, strengths and limitations of major empirical approaches, seeking to increase understanding of the field’s diverse methodologies and expand researchers’ toolkits. Overall, new empirical developments provide enormous capacity to test traditional beliefs and conceptual frameworks about science, discover factors associated with scientific productivity, predict scientific outcomes and design policies that facilitate scientific progress.

SciSciNet: A large-scale open data lake for the science of science research

A dataset for measuring the impact of research data and their curation

Envisioning a “science diplomacy 2.0”: on data, global challenges, and multi-layered networks

Scientific advances are a key input to rising standards of living, health and the capacity of society to confront grand challenges, from climate change to the COVID-19 pandemic 1 , 2 , 3 . A deeper understanding of how science works and where innovation occurs can help us to more effectively design science policy and science institutions, better inform scientists’ own research choices, and create and capture enormous value for science and humanity. Building on these key premises, recent years have witnessed substantial development in the ‘science of science’ 4 , 5 , 6 , 7 , 8 , 9 , which uses large-scale datasets and diverse computational toolkits to unearth fundamental patterns behind scientific production and use.

The idea of turning scientific methods into science itself is long-standing. Since the mid-20th century, researchers from different disciplines have asked central questions about the nature of scientific progress and the practice, organization and impact of scientific research. Building on these rich historical roots, the field of the science of science draws upon many disciplines, ranging from information science to the social, physical and biological sciences to computer science, engineering and design. The science of science closely relates to several strands and communities of research, including metascience, scientometrics, the economics of science, research on research, science and technology studies, the sociology of science, metaknowledge and quantitative science studies 5 . There are noticeable differences between some of these communities, mostly around their historical origins and the initial disciplinary composition of researchers forming these communities. For example, metascience has its origins in the clinical sciences and psychology, and focuses on rigour, transparency, reproducibility and other open science-related practices and topics. The scientometrics community, born in library and information sciences, places a particular emphasis on developing robust and responsible measures and indicators for science. Science and technology studies engage the history of science and technology, the philosophy of science, and the interplay between science, technology and society. The science of science, which has its origins in physics, computer science and sociology, takes a data-driven approach and emphasizes questions on how science works. Each of these communities has made fundamental contributions to understanding science. While they differ in their origins, these differences pale in comparison to the overarching, common interest in understanding the practice of science and its societal impact.

Three major developments have encouraged rapid advances in the science of science. The first is in data 9 : modern databases include millions of research articles, grant proposals, patents and more. This windfall of data traces scientific activity in remarkable detail and at scale. The second development is in measurement: scholars have used data to develop many new measures of scientific activities and examine theories that have long been viewed as important but difficult to quantify. The third development is in empirical methods: thanks to parallel advances in data science, network science, artificial intelligence and econometrics, researchers can study relationships, make predictions and assess science policy in powerful new ways. Together, new data, measurements and methods have revealed fundamental new insights about the inner workings of science and scientific progress itself.

With multiple approaches, however, comes a key challenge. As researchers adhere to norms respected within their disciplines, their methods vary, with results often published in venues with non-overlapping readership, fragmenting research along disciplinary boundaries. This fragmentation challenges researchers’ ability to appreciate and understand the value of work outside of their own discipline, much less to build directly on it for further investigations.

Recognizing these challenges and the rapidly developing nature of the field, this paper reviews the empirical approaches that are prevalent in this literature. We aim to provide readers with an up-to-date understanding of the available datasets, measurement constructs and empirical methodologies, as well as the value and limitations of each. Owing to space constraints, this Review does not cover the full technical details of each method, referring readers to related guides to learn more. Instead, we will emphasize why a researcher might favour one method over another, depending on the research question.

Beyond a positive understanding of science, a key goal of the science of science is to inform science policy. While this Review mainly focuses on empirical approaches, with its core audience being researchers in the field, the studies reviewed are also germane to key policy questions. For example, what is the appropriate scale of scientific investment, in what directions and through what institutions 10 , 11 ? Are public investments in science aligned with public interests 12 ? What conditions produce novel or high-impact science 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 ? How do the reward systems of science influence the rate and direction of progress 13 , 21 , 22 , 23 , 24 , and what governs scientific reproducibility 25 , 26 , 27 ? How do contributions evolve over a scientific career 28 , 29 , 30 , 31 , 32 , and how may diversity among scientists advance scientific progress 33 , 34 , 35 , among other questions relevant to science policy 36 , 37 .

Overall, this review aims to facilitate entry to science of science research, expand researcher toolkits and illustrate how diverse research approaches contribute to our collective understanding of science. Section 2 reviews datasets and data linkages. Section 3 reviews major measurement constructs in the science of science. Section 4 considers a range of empirical methods, focusing on one study to illustrate each method and briefly summarizing related examples and applications. Section 5 concludes with an outlook for the science of science.

Historically, data on scientific activities were difficult to collect and were available in limited quantities. Gathering data could involve manually tallying statistics from publications 38 , 39 , interviewing scientists 16 , 40 , or assembling historical anecdotes and biographies 13 , 41 . Analyses were typically limited to a specific domain or group of scientists. Today, massive datasets on scientific production and use are at researchers’ fingertips 42 , 43 , 44 . Armed with big data and advanced algorithms, researchers can now probe questions previously not amenable to quantification and with enormous increases in scope and scale, as detailed below.

Publication datasets cover papers from nearly all scientific disciplines, enabling analyses of both general and domain-specific patterns. Commonly used datasets include the Web of Science (WoS), PubMed, CrossRef, ORCID, OpenCitations, Dimensions and OpenAlex. Datasets incorporating papers’ text (CORE) 45 , 46 , 47 , data entities (DataCite) 48 , 49 and peer review reports (Publons) 33 , 50 , 51 have also become available. These datasets further enable novel measurement, for example, representations of a paper’s content 52 , 53 , novelty 15 , 54 and interdisciplinarity 55 .

Notably, databases today capture more diverse aspects of science beyond publications, offering a richer and more encompassing view of research contexts and of researchers themselves (Fig. 1 ). For example, some datasets trace research funding to the specific publications these investments support 56 , 57 , allowing high-scale studies of the impact of funding on productivity and the return on public investment. Datasets incorporating job placements 58 , 59 , curriculum vitae 21 , 59 and scientific prizes 23 offer rich quantitative evidence on the social structure of science. Combining publication profiles with mentorship genealogies 60 , 61 , dissertations 34 and course syllabi 62 , 63 provides insights on mentoring and cultivating talent.

This figure presents commonly used data types in science of science research, information contained in each data type and examples of data sources. Datasets in the science of science research have not only grown in scale but have also expanded beyond publications to integrate upstream funding investments and downstream applications that extend beyond science itself.

Finally, today’s scope of data extends beyond science to broader aspects of society. Altmetrics 64 captures news media and social media mentions of scientific articles. Other databases incorporate marketplace uses of science, including through patents 10 , pharmaceutical clinical trials and drug approvals 65 , 66 . Policy documents 67 , 68 help us to understand the role of science in the halls of government 69 and policy making 12 , 68 .

While datasets of the modern scientific enterprise have grown exponentially, they are not without limitations. As is often the case for data-driven research, drawing conclusions from specific data sources requires scrutiny and care. Datasets are typically based on published work, which may favour easy-to-publish topics over important ones (the streetlight effect) 70 , 71 . The publication of negative results is also rare (the file drawer problem) 72 , 73 . Meanwhile, English language publications account for over 90% of articles in major data sources, with limited coverage of non-English journals 74 . Publication datasets may also reflect biases in data collection across research institutions or demographic groups. Despite the open science movement, many datasets require paid subscriptions, which can create inequality in data access. Creating more open datasets for the science of science, such as OpenAlex, may not only improve the robustness and replicability of empirical claims but also increase entry to the field.

As today’s datasets become larger in scale and continue to integrate new dimensions, they offer opportunities to unveil the inner workings and external impacts of science in new ways. They can enable researchers to reach beyond previous limitations while conducting original studies of new and long-standing questions about the sciences.

Measurement

Here we discuss prominent measurement approaches in the science of science, including their purposes and limitations.

Modern publication databases typically include data on which articles and authors cite other papers and scientists. These citation linkages have been used to engage core conceptual ideas in scientific research. Here we consider two common measures based on citation information: citation counts and knowledge flows.

First, citation counts are commonly used indicators of impact. The term ‘indicator’ implies that it only approximates the concept of interest. A citation count is defined as how many times a document is cited by subsequent documents and can proxy for the importance of research papers 75 , 76 as well as patented inventions 77 , 78 , 79 . Rather than treating each citation equally, measures may further weight the importance of each citation, for example by using the citation network structure to produce centrality 80 , PageRank 81 , 82 or Eigenfactor indicators 83 , 84 .

Citation-based indicators have also faced criticism 84 , 85 . Citation indicators necessarily oversimplify the construct of impact, often ignoring heterogeneity in the meaning and use of a particular reference, the variations in citation practices across fields and institutional contexts, and the potential for reputation and power structures in science to influence citation behaviour 86 , 87 . Researchers have started to understand more nuanced citation behaviours ranging from negative citations 86 to citation context 47 , 88 , 89 . Understanding what a citation actually measures matters in interpreting and applying many research findings in the science of science. Evaluations relying on citation-based indicators rather than expert judgements raise questions regarding misuse 90 , 91 , 92 . Given the importance of developing indicators that can reliably quantify and evaluate science, the scientometrics community has been working to provide guidance for responsible citation practices and assessment 85 .

Second, scientists use citations to trace knowledge flows. Each citation in a paper is a link to specific previous work from which we can proxy how new discoveries draw upon existing ideas 76 , 93 and how knowledge flows between fields of science 94 , 95 , research institutions 96 , regions and nations 97 , 98 , 99 , and individuals 81 . Combinations of citation linkages can also approximate novelty 15 , disruptiveness 17 , 100 and interdisciplinarity 55 , 95 , 101 , 102 . A rapidly expanding body of work further examines citations to scientific articles from other domains (for example, patents, clinical drug trials and policy documents) to understand the applied value of science 10 , 12 , 65 , 66 , 103 , 104 , 105 .

Individuals

Analysing individual careers allows researchers to answer questions such as: How do we quantify individual scientific productivity? What is a typical career lifecycle? How are resources and credits allocated across individuals and careers? A scholar’s career can be examined through the papers they publish 30 , 31 , 106 , 107 , 108 , with attention to career progression and mobility, publication counts and citation impact, as well as grant funding 24 , 109 , 110 and prizes 111 , 112 , 113 ,

Studies of individual impact focus on output, typically approximated by the number of papers a researcher publishes and citation indicators. A popular measure for individual impact is the h -index 114 , which takes both volume and per-paper impact into consideration. Specifically, a scientist is assigned the largest value h such that they have h papers that were each cited at least h times. Later studies build on the idea of the h -index and propose variants to address limitations 115 , these variants ranging from emphasizing highly cited papers in a career 116 , to field differences 117 and normalizations 118 , to the relative contribution of an individual in collaborative works 119 .

To study dynamics in output over the lifecycle, individuals can be studied according to age, career age or the sequence of publications. A long-standing literature has investigated the relationship between age and the likelihood of outstanding achievement 28 , 106 , 111 , 120 , 121 . Recent studies further decouple the relationship between age, publication volume and per-paper citation, and measure the likelihood of producing highly cited papers in the sequence of works one produces 30 , 31 .

As simple as it sounds, representing careers using publication records is difficult. Collecting the full publication list of a researcher is the foundation to study individuals yet remains a key challenge, requiring name disambiguation techniques to match specific works to specific researchers. Although algorithms are increasingly capable at identifying millions of career profiles 122 , they vary in accuracy and robustness. ORCID can help to alleviate the problem by offering researchers the opportunity to create, maintain and update individual profiles themselves, and it goes beyond publications to collect broader outputs and activities 123 . A second challenge is survivorship bias. Empirical studies tend to focus on careers that are long enough to afford statistical analyses, which limits the applicability of the findings to scientific careers as a whole. A third challenge is the breadth of scientists’ activities, where focusing on publications ignores other important contributions such as mentorship and teaching, service (for example, refereeing papers, reviewing grant proposals and editing journals) or leadership within their organizations. Although researchers have begun exploring these dimensions by linking individual publication profiles with genealogical databases 61 , 124 , dissertations 34 , grants 109 , curriculum vitae 21 and acknowledgements 125 , scientific careers beyond publication records remain under-studied 126 , 127 . Lastly, citation-based indicators only serve as an approximation of individual performance with similar limitations as discussed above. The scientific community has called for more appropriate practices 85 , 128 , ranging from incorporating expert assessment of research contributions to broadening the measures of impact beyond publications.

Over many decades, science has exhibited a substantial and steady shift away from solo authorship towards coauthorship, especially among highly cited works 18 , 129 , 130 . In light of this shift, a research field, the science of team science 131 , 132 , has emerged to study the mechanisms that facilitate or hinder the effectiveness of teams. Team size can be proxied by the number of coauthors on a paper, which has been shown to predict distinctive types of advance: whereas larger teams tend to develop ideas, smaller teams tend to disrupt current ways of thinking 17 . Team characteristics can be inferred from coauthors’ backgrounds 133 , 134 , 135 , allowing quantification of a team’s diversity in terms of field, age, gender or ethnicity. Collaboration networks based on coauthorship 130 , 136 , 137 , 138 , 139 offer nuanced network-based indicators to understand individual and institutional collaborations.

However, there are limitations to using coauthorship alone to study teams 132 . First, coauthorship can obscure individual roles 140 , 141 , 142 , which has prompted institutional responses to help to allocate credit, including authorship order and individual contribution statements 56 , 143 . Second, coauthorship does not reflect the complex dynamics and interactions between team members that are often instrumental for team success 53 , 144 . Third, collaborative contributions can extend beyond coauthorship in publications to include members of a research laboratory 145 or co-principal investigators (co-PIs) on a grant 146 . Initiatives such as CRediT may help to address some of these issues by recording detailed roles for each contributor 147 .

Institutions

Research institutions, such as departments, universities, national laboratories and firms, encompass wider groups of researchers and their corresponding outputs. Institutional membership can be inferred from affiliations listed on publications or patents 148 , 149 , and the output of an institution can be aggregated over all its affiliated researchers 150 . Institutional research information systems (CRIS) contain more comprehensive research outputs and activities from employees.

Some research questions consider the institution as a whole, investigating the returns to research and development investment 104 , inequality of resource allocation 22 and the flow of scientists 21 , 148 , 149 . Other questions focus on institutional structures as sources of research productivity by looking into the role of peer effects 125 , 151 , 152 , 153 , how institutional policies impact research outcomes 154 , 155 and whether interdisciplinary efforts foster innovation 55 . Institution-oriented measurement faces similar limitations as with analyses of individuals and teams, including name disambiguation for a given institution and the limited capacity of formal publication records to characterize the full range of relevant institutional outcomes. It is also unclear how to allocate credit among multiple institutions associated with a paper. Moreover, relevant institutional employees extend beyond publishing researchers: interns, technicians and administrators all contribute to research endeavours 130 .

In sum, measurements allow researchers to quantify scientific production and use across numerous dimensions, but they also raise questions of construct validity: Does the proposed metric really reflect what we want to measure? Testing the construct’s validity is important, as is understanding a construct’s limits. Where possible, using alternative measurement approaches, or qualitative methods such as interviews and surveys, can improve measurement accuracy and the robustness of findings.

Empirical methods

In this section, we review two broad categories of empirical approaches (Table 1 ), each with distinctive goals: (1) to discover, estimate and predict empirical regularities; and (2) to identify causal mechanisms. For each method, we give a concrete example to help to explain how the method works, summarize related work for interested readers, and discuss contributions and limitations.

Descriptive and predictive approaches

Empirical regularities and generalizable facts.

The discovery of empirical regularities in science has had a key role in driving conceptual developments and the directions of future research. By observing empirical patterns at scale, researchers unveil central facts that shape science and present core features that theories of scientific progress and practice must explain. For example, consider citation distributions. de Solla Price first proposed that citation distributions are fat-tailed 39 , indicating that a few papers have extremely high citations while most papers have relatively few or even no citations at all. de Solla Price proposed that citation distribution was a power law, while researchers have since refined this view to show that the distribution appears log-normal, a nearly universal regularity across time and fields 156 , 157 . The fat-tailed nature of citation distributions and its universality across the sciences has in turn sparked substantial theoretical work that seeks to explain this key empirical regularity 20 , 156 , 158 , 159 .

Empirical regularities are often surprising and can contest previous beliefs of how science works. For example, it has been shown that the age distribution of great achievements peaks in middle age across a wide range of fields 107 , 121 , 160 , rejecting the common belief that young scientists typically drive breakthroughs in science. A closer look at the individual careers also indicates that productivity patterns vary widely across individuals 29 . Further, a scholar’s highest-impact papers come at a remarkably constant rate across the sequence of their work 30 , 31 .

The discovery of empirical regularities has had important roles in shaping beliefs about the nature of science 10 , 45 , 161 , 162 , sources of breakthrough ideas 15 , 163 , 164 , 165 , scientific careers 21 , 29 , 126 , 127 , the network structure of ideas and scientists 23 , 98 , 136 , 137 , 138 , 139 , 166 , gender inequality 57 , 108 , 126 , 135 , 143 , 167 , 168 , and many other areas of interest to scientists and science institutions 22 , 47 , 86 , 97 , 102 , 105 , 134 , 169 , 170 , 171 . At the same time, care must be taken to ensure that findings are not merely artefacts due to data selection or inherent bias. To differentiate meaningful patterns from spurious ones, it is important to stress test the findings through different selection criteria or across non-overlapping data sources.

Regression analysis

When investigating correlations among variables, a classic method is regression, which estimates how one set of variables explains variation in an outcome of interest. Regression can be used to test explicit hypotheses or predict outcomes. For example, researchers have investigated whether a paper’s novelty predicts its citation impact 172 . Adding additional control variables to the regression, one can further examine the robustness of the focal relationship.

Although regression analysis is useful for hypothesis testing, it bears substantial limitations. If the question one wishes to ask concerns a ‘causal’ rather than a correlational relationship, regression is poorly suited to the task as it is impossible to control for all the confounding factors. Failing to account for such ‘omitted variables’ can bias the regression coefficient estimates and lead to spurious interpretations. Further, regression models often have low goodness of fit (small R 2 ), indicating that the variables considered explain little of the outcome variation. As regressions typically focus on a specific relationship in simple functional forms, regressions tend to emphasize interpretability rather than overall predictability. The advent of predictive approaches powered by large-scale datasets and novel computational techniques offers new opportunities for modelling complex relationships with stronger predictive power.

Mechanistic models

Mechanistic modelling is an important approach to explaining empirical regularities, drawing from methods primarily used in physics. Such models predict macro-level regularities of a system by modelling micro-level interactions among basic elements with interpretable and modifiable formulars. While theoretical by nature, mechanistic models in the science of science are often empirically grounded, and this approach has developed together with the advent of large-scale, high-resolution data.

Simplicity is the core value of a mechanistic model. Consider for example, why citations follow a fat-tailed distribution. de Solla Price modelled the citing behaviour as a cumulative advantage process on a growing citation network 159 and found that if the probability a paper is cited grows linearly with its existing citations, the resulting distribution would follow a power law, broadly aligned with empirical observations. The model is intentionally simplified, ignoring myriad factors. Yet the simple cumulative advantage process is by itself sufficient in explaining a power law distribution of citations. In this way, mechanistic models can help to reveal key mechanisms that can explain observed patterns.

Moreover, mechanistic models can be refined as empirical evidence evolves. For example, later investigations showed that citation distributions are better characterized as log-normal 156 , 173 , prompting researchers to introduce a fitness parameter to encapsulate the inherent differences in papers’ ability to attract citations 174 , 175 . Further, older papers are less likely to be cited than expected 176 , 177 , 178 , motivating more recent models 20 to introduce an additional aging effect 179 . By combining the cumulative advantage, fitness and aging effects, one can already achieve substantial predictive power not just for the overall properties of the system but also the citation dynamics of individual papers 20 .

In addition to citations, mechanistic models have been developed to understand the formation of collaborations 136 , 180 , 181 , 182 , 183 , knowledge discovery and diffusion 184 , 185 , topic selection 186 , 187 , career dynamics 30 , 31 , 188 , 189 , the growth of scientific fields 190 and the dynamics of failure in science and other domains 178 .

At the same time, some observers have argued that mechanistic models are too simplistic to capture the essence of complex real-world problems 191 . While it has been a cornerstone for the natural sciences, representing social phenomena in a limited set of mathematical equations may miss complexities and heterogeneities that make social phenomena interesting in the first place. Such concerns are not unique to the science of science, as they represent a broader theme in computational social sciences 192 , 193 , ranging from social networks 194 , 195 to human mobility 196 , 197 to epidemics 198 , 199 . Other observers have questioned the practical utility of mechanistic models and whether they can be used to guide decisions and devise actionable policies. Nevertheless, despite these limitations, several complex phenomena in the science of science are well captured by simple mechanistic models, showing a high degree of regularity beneath complex interacting systems and providing powerful insights about the nature of science. Mixing such modelling with other methods could be particularly fruitful in future investigations.

Machine learning

The science of science seeks in part to forecast promising directions for scientific research 7 , 44 . In recent years, machine learning methods have substantially advanced predictive capabilities 200 , 201 and are playing increasingly important parts in the science of science. In contrast to the previous methods, machine learning does not emphasize hypotheses or theories. Rather, it leverages complex relationships in data and optimizes goodness of fit to make predictions and categorizations.

Traditional machine learning models include supervised, semi-supervised and unsupervised learning. The model choice depends on data availability and the research question, ranging from supervised models for citation prediction 202 , 203 to unsupervised models for community detection 204 . Take for example mappings of scientific knowledge 94 , 205 , 206 . The unsupervised method applies network clustering algorithms to map the structures of science. Related visualization tools make sense of clusters from the underlying network, allowing observers to see the organization, interactions and evolution of scientific knowledge. More recently, supervised learning, and deep neural networks in particular, have witnessed especially rapid developments 207 . Neural networks can generate high-dimensional representations of unstructured data such as images and texts, which encode complex properties difficult for human experts to perceive.

Take text analysis as an example. A recent study 52 utilizes 3.3 million paper abstracts in materials science to predict the thermoelectric properties of materials. The intuition is that the words currently used to describe a material may predict its hitherto undiscovered properties (Fig. 2 ). Compared with a random material, the materials predicted by the model are eight times more likely to be reported as thermoelectric in the next 5 years, suggesting that machine learning has the potential to substantially speed up knowledge discovery, especially as data continue to grow in scale and scope. Indeed, predicting the direction of new discoveries represents one of the most promising avenues for machine learning models, with neural networks being applied widely to biology 208 , physics 209 , 210 , mathematics 211 , chemistry 212 , medicine 213 and clinical applications 214 . Neural networks also offer a quantitative framework to probe the characteristics of creative products ranging from scientific papers 53 , journals 215 , organizations 148 , to paintings and movies 32 . Neural networks can also help to predict the reproducibility of papers from a variety of disciplines at scale 53 , 216 .

This figure illustrates the word2vec skip-gram methods 52 , where the goal is to predict useful properties of materials using previous scientific literature. a , The architecture and training process of the word2vec skip-gram model, where the 3-layer, fully connected neural network learns the 200-dimensional representation (hidden layer) from the sparse vector for each word and its context in the literature (input layer). b , The top two principal components of the word embedding. Materials with similar features are close in the 2D space, allowing prediction of a material’s properties. Different targeted words are shown in different colours. Reproduced with permission from ref. 52 , Springer Nature Ltd.

While machine learning can offer high predictive accuracy, successful applications to the science of science face challenges, particularly regarding interpretability. Researchers may value transparent and interpretable findings for how a given feature influences an outcome, rather than a black-box model. The lack of interpretability also raises concerns about bias and fairness. In predicting reproducible patterns from data, machine learning models inevitably include and reproduce biases embedded in these data, often in non-transparent ways. The fairness of machine learning 217 is heavily debated in applications ranging from the criminal justice system to hiring processes. Effective and responsible use of machine learning in the science of science therefore requires thoughtful partnership between humans and machines 53 to build a reliable system accessible to scrutiny and modification.

Causal approaches

The preceding methods can reveal core facts about the workings of science and develop predictive capacity. Yet, they fail to capture causal relationships, which are particularly useful in assessing policy interventions. For example, how can we test whether a science policy boosts or hinders the performance of individuals, teams or institutions? The overarching idea of causal approaches is to construct some counterfactual world where two groups are identical to each other except that one group experiences a treatment that the other group does not.

Towards causation

Before engaging in causal approaches, it is useful to first consider the interpretative challenges of observational data. As observational data emerge from mechanisms that are not fully known or measured, an observed correlation may be driven by underlying forces that were not accounted for in the analysis. This challenge makes causal inference fundamentally difficult in observational data. An awareness of this issue is the first step in confronting it. It further motivates intermediate empirical approaches, including the use of matching strategies and fixed effects, that can help to confront (although not fully eliminate) the inference challenge. We first consider these approaches before turning to more fully causal methods.

Matching. Matching utilizes rich information to construct a control group that is similar to the treatment group on as many observable characteristics as possible before the treatment group is exposed to the treatment. Inferences can then be made by comparing the treatment and the matched control groups. Exact matching applies to categorical values, such as country, gender, discipline or affiliation 35 , 218 . Coarsened exact matching considers percentile bins of continuous variables and matches observations in the same bin 133 . Propensity score matching estimates the probability of receiving the ‘treatment’ on the basis of the controlled variables and uses the estimates to match treatment and control groups, which reduces the matching task from comparing the values of multiple covariates to comparing a single value 24 , 219 . Dynamic matching is useful for longitudinally matching variables that change over time 220 , 221 .

Fixed effects. Fixed effects are a powerful and now standard tool in controlling for confounders. A key requirement for using fixed effects is that there are multiple observations on the same subject or entity (person, field, institution and so on) 222 , 223 , 224 . The fixed effect works as a dummy variable that accounts for the role of any fixed characteristic of that entity. Consider the finding where gender-diverse teams produce higher-impact papers than same-gender teams do 225 . A confounder may be that individuals who tend to write high-impact papers may also be more likely to work in gender-diverse teams. By including individual fixed effects, one accounts for any fixed characteristics of individuals (such as IQ, cultural background or previous education) that might drive the relationship of interest.

In sum, matching and fixed effects methods reduce potential sources of bias in interpreting relationships between variables. Yet, confounders may persist in these studies. For instance, fixed effects do not control for unobserved factors that change with time within the given entity (for example, access to funding or new skills). Identifying casual effects convincingly will then typically require distinct research methods that we turn to next.

Quasi-experiments

Researchers in economics and other fields have developed a range of quasi-experimental methods to construct treatment and control groups. The key idea here is exploiting randomness from external events that differentially expose subjects to a particular treatment. Here we review three quasi-experimental methods: difference-in-differences, instrumental variables and regression discontinuity (Fig. 3 ).

a – c , This figure presents illustrations of ( a ) differences-in-differences, ( b ) instrumental variables and ( c ) regression discontinuity methods. The solid line in b represents causal links and the dashed line represents the relationships that are not allowed, if the IV method is to produce causal inference.

Difference-in-differences. Difference-in-difference regression (DiD) investigates the effect of an unexpected event, comparing the affected group (the treated group) with an unaffected group (the control group). The control group is intended to provide the counterfactual path—what would have happened were it not for the unexpected event. Ideally, the treated and control groups are on virtually identical paths before the treatment event, but DiD can also work if the groups are on parallel paths (Fig. 3a ). For example, one study 226 examines how the premature death of superstar scientists affects the productivity of their previous collaborators. The control group are collaborators of superstars who did not die in the time frame. The two groups do not show significant differences in publications before a death event, yet upon the death of a star scientist, the treated collaborators on average experience a 5–8% decline in their quality-adjusted publication rates compared with the control group. DiD has wide applicability in the science of science, having been used to analyse the causal effects of grant design 24 , access costs to previous research 155 , 227 , university technology transfer policies 154 , intellectual property 228 , citation practices 229 , evolution of fields 221 and the impacts of paper retractions 230 , 231 , 232 . The DiD literature has grown especially rapidly in the field of economics, with substantial recent refinements 233 , 234 .

Instrumental variables. Another quasi-experimental approach utilizes ‘instrumental variables’ (IV). The goal is to determine the causal influence of some feature X on some outcome Y by using a third, instrumental variable. This instrumental variable is a quasi-random event that induces variation in X and, except for its impact through X , has no other effect on the outcome Y (Fig. 3b ). For example, consider a study of astronomy that seeks to understand how telescope time affects career advancement 235 . Here, one cannot simply look at the correlation between telescope time and career outcomes because many confounds (such as talent or grit) may influence both telescope time and career opportunities. Now consider the weather as an instrumental variable. Cloudy weather will, at random, reduce an astronomer’s observational time. Yet, the weather on particular nights is unlikely to correlate with a scientist’s innate qualities. The weather can then provide an instrumental variable to reveal a causal relationship between telescope time and career outcomes. Instrumental variables have been used to study local peer effects in research 151 , the impact of gender composition in scientific committees 236 , patents on future innovation 237 and taxes on inventor mobility 238 .

Regression discontinuity. In regression discontinuity, policies with an arbitrary threshold for receiving some benefit can be used to construct treatment and control groups (Fig. 3c ). Take the funding paylines for grant proposals as an example. Proposals with scores increasingly close to the payline are increasingly similar in their both observable and unobservable characteristics, yet only those projects with scores above the payline receive the funding. For example, a study 110 examines the effect of winning an early-career grant on the probability of winning a later, mid-career grant. The probability has a discontinuous jump across the initial grant’s payline, providing the treatment and control groups needed to estimate the causal effect of receiving a grant. This example utilizes the ‘sharp’ regression discontinuity that assumes treatment status to be fully determined by the cut-off. If we assume treatment status is only partly determined by the cut-off, we can use ‘fuzzy’ regression discontinuity designs. Here the probability of receiving a grant is used to estimate the future outcome 11 , 110 , 239 , 240 , 241 .

Although quasi-experiments are powerful tools, they face their own limitations. First, these approaches identify causal effects within a specific context and often engage small numbers of observations. How representative the samples are for broader populations or contexts is typically left as an open question. Second, the validity of the causal design is typically not ironclad. Researchers usually conduct different robustness checks to verify whether observable confounders have significant differences between the treated and control groups, before treatment. However, unobservable features may still differ between treatment and control groups. The quality of instrumental variables and the specific claim that they have no effect on the outcome except through the variable of interest, is also difficult to assess. Ultimately, researchers must rely partly on judgement to tell whether appropriate conditions are met for causal inference.

This section emphasized popular econometric approaches to causal inference. Other empirical approaches, such as graphical causal modelling 242 , 243 , also represent an important stream of work on assessing causal relationships. Such approaches usually represent causation as a directed acyclic graph, with nodes as variables and arrows between them as suspected causal relationships. In the science of science, the directed acyclic graph approach has been applied to quantify the causal effect of journal impact factor 244 and gender or racial bias 245 on citations. Graphical causal modelling has also triggered discussions on strengths and weaknesses compared to the econometrics methods 246 , 247 .

Experiments

In contrast to quasi-experimental approaches, laboratory and field experiments conduct direct randomization in assigning treatment and control groups. These methods engage explicitly in the data generation process, manipulating interventions to observe counterfactuals. These experiments are crafted to study mechanisms of specific interest and, by designing the experiment and formally randomizing, can produce especially rigorous causal inference.

Laboratory experiments. Laboratory experiments build counterfactual worlds in well-controlled laboratory environments. Researchers randomly assign participants to the treatment or control group and then manipulate the laboratory conditions to observe different outcomes in the two groups. For example, consider laboratory experiments on team performance and gender composition 144 , 248 . The researchers randomly assign participants into groups to perform tasks such as solving puzzles or brainstorming. Teams with a higher proportion of women are found to perform better on average, offering evidence that gender diversity is causally linked to team performance. Laboratory experiments can allow researchers to test forces that are otherwise hard to observe, such as how competition influences creativity 249 . Laboratory experiments have also been used to evaluate how journal impact factors shape scientists’ perceptions of rewards 250 and gender bias in hiring 251 .

Laboratory experiments allow for precise control of settings and procedures to isolate causal effects of interest. However, participants may behave differently in synthetic environments than in real-world settings, raising questions about the generalizability and replicability of the results 252 , 253 , 254 . To assess causal effects in real-world settings, researcher use randomized controlled trials.

Randomized controlled trials. A randomized controlled trial (RCT), or field experiment, is a staple for causal inference across a wide range of disciplines. RCTs randomly assign participants into the treatment and control conditions 255 and can be used not only to assess mechanisms but also to test real-world interventions such as policy change. The science of science has witnessed growing use of RCTs. For instance, a field experiment 146 investigated whether lower search costs for collaborators increased collaboration in grant applications. The authors randomly allocated principal investigators to face-to-face sessions in a medical school, and then measured participants’ chance of writing a grant proposal together. RCTs have also offered rich causal insights on peer review 256 , 257 , 258 , 259 , 260 and gender bias in science 261 , 262 , 263 .

While powerful, RCTs are difficult to conduct in the science of science, mainly for two reasons. The first concerns potential risks in a policy intervention. For instance, while randomizing funding across individuals could generate crucial causal insights for funders, it may also inadvertently harm participants’ careers 264 . Second, key questions in the science of science often require a long-time horizon to trace outcomes, which makes RCTs costly. It also raises the difficulty of replicating findings. A relative advantage of the quasi-experimental methods discussed earlier is that one can identify causal effects over potentially long periods of time in the historical record. On the other hand, quasi-experiments must be found as opposed to designed, and they often are not available for many questions of interest. While the best approaches are context dependent, a growing community of researchers is building platforms to facilitate RCTs for the science of science, aiming to lower their costs and increase their scale. Performing RCTs in partnership with science institutions can also contribute to timely, policy-relevant research that may substantially improve science decision-making and investments.

Research in the science of science has been empowered by the growth of high-scale data, new measurement approaches and an expanding range of empirical methods. These tools provide enormous capacity to test conceptual frameworks about science, discover factors impacting scientific productivity, predict key scientific outcomes and design policies that better facilitate future scientific progress. A careful appreciation of empirical techniques can help researchers to choose effective tools for questions of interest and propel the field. A better and broader understanding of these methodologies may also build bridges across diverse research communities, facilitating communication and collaboration, and better leveraging the value of diverse perspectives. The science of science is about turning scientific methods on the nature of science itself. The fruits of this work, with time, can guide researchers and research institutions to greater progress in discovery and understanding across the landscape of scientific inquiry.

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Acknowledgements

The authors thank all members of the Center for Science of Science and Innovation (CSSI) for invaluable comments. This work was supported by the Air Force Office of Scientific Research under award number FA9550-19-1-0354, National Science Foundation grant SBE 1829344, and the Alfred P. Sloan Foundation G-2019-12485.

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Liu, L., Jones, B.F., Uzzi, B. et al. Data, measurement and empirical methods in the science of science. Nat Hum Behav 7 , 1046–1058 (2023). https://doi.org/10.1038/s41562-023-01562-4

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PMC10506897

Conducting and Writing Quantitative and Qualitative Research

Edward barroga.

1 Department of Medical Education, Showa University School of Medicine, Tokyo, Japan.

Glafera Janet Matanguihan

2 Department of Biological Sciences, Messiah University, Mechanicsburg, PA, USA.

Atsuko Furuta

Makiko arima, shizuma tsuchiya, chikako kawahara, yusuke takamiya.

Comprehensive knowledge of quantitative and qualitative research systematizes scholarly research and enhances the quality of research output. Scientific researchers must be familiar with them and skilled to conduct their investigation within the frames of their chosen research type. When conducting quantitative research, scientific researchers should describe an existing theory, generate a hypothesis from the theory, test their hypothesis in novel research, and re-evaluate the theory. Thereafter, they should take a deductive approach in writing the testing of the established theory based on experiments. When conducting qualitative research, scientific researchers raise a question, answer the question by performing a novel study, and propose a new theory to clarify and interpret the obtained results. After which, they should take an inductive approach to writing the formulation of concepts based on collected data. When scientific researchers combine the whole spectrum of inductive and deductive research approaches using both quantitative and qualitative research methodologies, they apply mixed-method research. Familiarity and proficiency with these research aspects facilitate the construction of novel hypotheses, development of theories, or refinement of concepts.

Graphical Abstract

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Object name is jkms-38-e291-abf001.jpg

INTRODUCTION

Novel research studies are conceptualized by scientific researchers first by asking excellent research questions and developing hypotheses, then answering these questions by testing their hypotheses in ethical research. 1 , 2 , 3 Before they conduct novel research studies, scientific researchers must possess considerable knowledge of both quantitative and qualitative research. 2

In quantitative research, researchers describe existing theories, generate and test a hypothesis in novel research, and re-evaluate existing theories deductively based on their experimental results. 1 , 4 , 5 In qualitative research, scientific researchers raise and answer research questions by performing a novel study, then propose new theories by clarifying their results inductively. 1 , 6

RATIONALE OF THIS ARTICLE

When researchers have a limited knowledge of both research types and how to conduct them, this can result in substandard investigation. Researchers must be familiar with both types of research and skilled to conduct their investigations within the frames of their chosen type of research. Thus, meticulous care is needed when planning quantitative and qualitative research studies to avoid unethical research and poor outcomes.

Understanding the methodological and writing assumptions 7 , 8 underpinning quantitative and qualitative research, especially by non-Anglophone researchers, is essential for their successful conduct. Scientific researchers, especially in the academe, face pressure to publish in international journals 9 where English is the language of scientific communication. 10 , 11 In particular, non-Anglophone researchers face challenges related to linguistic, stylistic, and discourse differences. 11 , 12 Knowing the assumptions of the different types of research will help clarify research questions and methodologies, easing the challenge and help.

SEARCH FOR RELEVANT ARTICLES

To identify articles relevant to this topic, we adhered to the search strategy recommended by Gasparyan et al. 7 We searched through PubMed, Scopus, Directory of Open Access Journals, and Google Scholar databases using the following keywords: quantitative research, qualitative research, mixed-method research, deductive reasoning, inductive reasoning, study design, descriptive research, correlational research, experimental research, causal-comparative research, quasi-experimental research, historical research, ethnographic research, meta-analysis, narrative research, grounded theory, phenomenology, case study, and field research.

AIMS OF THIS ARTICLE

This article aims to provide a comparative appraisal of qualitative and quantitative research for scientific researchers. At present, there is still a need to define the scope of qualitative research, especially its essential elements. 13 Consensus on the critical appraisal tools to assess the methodological quality of qualitative research remains lacking. 14 Framing and testing research questions can be challenging in qualitative research. 2 In the healthcare system, it is essential that research questions address increasingly complex situations. Therefore, research has to be driven by the kinds of questions asked and the corresponding methodologies to answer these questions. 15 The mixed-method approach also needs to be clarified as this would appear to arise from different philosophical underpinnings. 16

This article also aims to discuss how particular types of research should be conducted and how they should be written in adherence to international standards. In the US, Europe, and other countries, responsible research and innovation was conceptualized and promoted with six key action points: engagement, gender equality, science education, open access, ethics and governance. 17 , 18 International ethics standards in research 19 as well as academic integrity during doctoral trainings are now integral to the research process. 20

POTENTIAL BENEFITS FROM THIS ARTICLE

This article would be beneficial for researchers in further enhancing their understanding of the theoretical, methodological, and writing aspects of qualitative and quantitative research, and their combination.

Moreover, this article reviews the basic features of both research types and overviews the rationale for their conduct. It imparts information on the most common forms of quantitative and qualitative research, and how they are carried out. These aspects would be helpful for selecting the optimal methodology to use for research based on the researcher’s objectives and topic.

This article also provides information on the strengths and weaknesses of quantitative and qualitative research. Such information would help researchers appreciate the roles and applications of both research types and how to gain from each or their combination. As different research questions require different types of research and analyses, this article is anticipated to assist researchers better recognize the questions answered by quantitative and qualitative research.

Finally, this article would help researchers to have a balanced perspective of qualitative and quantitative research without considering one as superior to the other.

TYPES OF RESEARCH

Research can be classified into two general types, quantitative and qualitative. 21 Both types of research entail writing a research question and developing a hypothesis. 22 Quantitative research involves a deductive approach to prove or disprove the hypothesis that was developed, whereas qualitative research involves an inductive approach to create a hypothesis. 23 , 24 , 25 , 26

In quantitative research, the hypothesis is stated before testing. In qualitative research, the hypothesis is developed through inductive reasoning based on the data collected. 27 , 28 For types of data and their analysis, qualitative research usually includes data in the form of words instead of numbers more commonly used in quantitative research. 29

Quantitative research usually includes descriptive, correlational, causal-comparative / quasi-experimental, and experimental research. 21 On the other hand, qualitative research usually encompasses historical, ethnographic, meta-analysis, narrative, grounded theory, phenomenology, case study, and field research. 23 , 25 , 28 , 30 A summary of the features, writing approach, and examples of published articles for each type of qualitative and quantitative research is shown in Table 1 . 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 , 39 , 40 , 41 , 42 , 43

Research	Type	Methodology feature	Research writing pointers	Example of published article
Quantitative	Descriptive research	Describes status of identified variable to provide systematic information about phenomenon	Explain how a situation, sample, or variable was examined or observed as it occurred without investigator interference	Östlund AS, Kristofferzon ML, Häggström E, Wadensten B. Primary care nurses’ performance in motivational interviewing: a quantitative descriptive study. 2015;16(1):89.
	Descriptive research
	Correlational research	Determines and interprets extent of relationship between two or more variables using statistical data	Describe the establishment of reliability and validity, converging evidence, relationships, and predictions based on statistical data	Díaz-García O, Herranz Aguayo I, Fernández de Castro P, Ramos JL. Lifestyles of Spanish elders from supervened SARS-CoV-2 variant onwards: A correlational research on life satisfaction and social-relational praxes. 2022;13:948745.
	Correlational research
	Causal-comparative/Quasi-experimental research	Establishes cause-effect relationships among variables	Write about comparisons of the identified control groups exposed to the treatment variable with unexposed groups	: Sharma MK, Adhikari R. Effect of school water, sanitation, and hygiene on health status among basic level students in Nepal. Environ Health Insights 2022;16:11786302221095030.
		Uses non-randomly assigned groups where it is not logically feasible to conduct a randomized controlled trial	Provide clear descriptions of the causes determined after making data analyses and conclusions, and known and unknown variables that could potentially affect the outcome
				[The study applies a causal-comparative research design]
				: Tuna F, Tunçer B, Can HB, Süt N, Tuna H. Immediate effect of Kinesio taping® on deep cervical flexor endurance: a non-controlled, quasi-experimental pre-post quantitative study. 2022;40(6):528-35.

	Experimental research	Establishes cause-effect relationship among group of variables making up a study using scientific method	Describe how an independent variable was manipulated to determine its effects on dependent variables	Hyun C, Kim K, Lee S, Lee HH, Lee J. Quantitative evaluation of the consciousness level of patients in a vegetative state using virtual reality and an eye-tracking system: a single-case experimental design study. 2022;32(10):2628-45.
	Experimental research		Explain the random assignments of subjects to experimental treatments
Qualitative	Historical research	Describes past events, problems, issues, and facts	Write the research based on historical reports	Silva Lima R, Silva MA, de Andrade LS, Mello MA, Goncalves MF. Construction of professional identity in nursing students: qualitative research from the historical-cultural perspective. 2020;28:e3284.
	Historical research	Describes past events, problems, issues, and facts	Write the research based on historical reports
	Ethnographic research	Develops in-depth analytical descriptions of current systems, processes, and phenomena or understandings of shared beliefs and practices of groups or culture	Compose a detailed report of the interpreted data	Gammeltoft TM, Huyền Diệu BT, Kim Dung VT, Đức Anh V, Minh Hiếu L, Thị Ái N. Existential vulnerability: an ethnographic study of everyday lives with diabetes in Vietnam. 2022;29(3):271-88.
	Ethnographic research		Compose a detailed report of the interpreted data
	Meta-analysis	Accumulates experimental and correlational results across independent studies using statistical method	Specify the topic, follow reporting guidelines, describe the inclusion criteria, identify key variables, explain the systematic search of databases, and detail the data extraction	Oeljeklaus L, Schmid HL, Kornfeld Z, Hornberg C, Norra C, Zerbe S, et al. Therapeutic landscapes and psychiatric care facilities: a qualitative meta-analysis. 2022;19(3):1490.
	Meta-analysis
	Narrative research	Studies an individual and gathers data by collecting stories for constructing a narrative about the individual’s experiences and their meanings	Write an in-depth narration of events or situations focused on the participants	Anderson H, Stocker R, Russell S, Robinson L, Hanratty B, Robinson L, et al. Identity construction in the very old: a qualitative narrative study. 2022;17(12):e0279098.
	Narrative research
	Grounded theory	Engages in inductive ground-up or bottom-up process of generating theory from data	Write the research as a theory and a theoretical model.	Amini R, Shahboulaghi FM, Tabrizi KN, Forouzan AS. Social participation among Iranian community-dwelling older adults: a grounded theory study. 2022;11(6):2311-9.
	Grounded theory		Describe data analysis procedure about theoretical coding for developing hypotheses based on what the participants say
	Phenomenology	Attempts to understand subjects’ perspectives	Write the research report by contextualizing and reporting the subjects’ experiences	Green G, Sharon C, Gendler Y. The communication challenges and strength of nurses’ intensive corona care during the two first pandemic waves: a qualitative descriptive phenomenology study. 2022;10(5):837.
	Phenomenology	Attempts to understand subjects’ perspectives
	Case study	Analyzes collected data by detailed identification of themes and development of narratives written as in-depth study of lessons from case	Write the report as an in-depth study of possible lessons learned from the case	Horton A, Nugus P, Fortin MC, Landsberg D, Cantarovich M, Sandal S. Health system barriers and facilitators to living donor kidney transplantation: a qualitative case study in British Columbia. 2022;10(2):E348-56.
	Case study
	Field research	Directly investigates and extensively observes social phenomenon in natural environment without implantation of controls or experimental conditions	Describe the phenomenon under the natural environment over time	Buus N, Moensted M. Collectively learning to talk about personal concerns in a peer-led youth program: a field study of a community of practice. 2022;30(6):e4425-32.
	Field research

QUANTITATIVE RESEARCH

Deductive approach.

The deductive approach is used to prove or disprove the hypothesis in quantitative research. 21 , 25 Using this approach, researchers 1) make observations about an unclear or new phenomenon, 2) investigate the current theory surrounding the phenomenon, and 3) hypothesize an explanation for the observations. Afterwards, researchers will 4) predict outcomes based on the hypotheses, 5) formulate a plan to test the prediction, and 6) collect and process the data (or revise the hypothesis if the original hypothesis was false). Finally, researchers will then 7) verify the results, 8) make the final conclusions, and 9) present and disseminate their findings ( Fig. 1A ).

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Types of quantitative research

The common types of quantitative research include (a) descriptive, (b) correlational, c) experimental research, and (d) causal-comparative/quasi-experimental. 21

Descriptive research is conducted and written by describing the status of an identified variable to provide systematic information about a phenomenon. A hypothesis is developed and tested after data collection, analysis, and synthesis. This type of research attempts to factually present comparisons and interpretations of findings based on analyses of the characteristics, progression, or relationships of a certain phenomenon by manipulating the employed variables or controlling the involved conditions. 44 Here, the researcher examines, observes, and describes a situation, sample, or variable as it occurs without investigator interference. 31 , 45 To be meaningful, the systematic collection of information requires careful selection of study units by precise measurement of individual variables 21 often expressed as ranges, means, frequencies, and/or percentages. 31 , 45 Descriptive statistical analysis using ANOVA, Student’s t -test, or the Pearson coefficient method has been used to analyze descriptive research data. 46

Correlational research is performed by determining and interpreting the extent of a relationship between two or more variables using statistical data. This involves recognizing data trends and patterns without necessarily proving their causes. The researcher studies only the data, relationships, and distributions of variables in a natural setting, but does not manipulate them. 21 , 45 Afterwards, the researcher establishes reliability and validity, provides converging evidence, describes relationship, and makes predictions. 47

Experimental research is usually referred to as true experimentation. The researcher establishes the cause-effect relationship among a group of variables making up a study using the scientific method or process. This type of research attempts to identify the causal relationships between variables through experiments by arbitrarily controlling the conditions or manipulating the variables used. 44 The scientific manuscript would include an explanation of how the independent variable was manipulated to determine its effects on the dependent variables. The write-up would also describe the random assignments of subjects to experimental treatments. 21

Causal-comparative/quasi-experimental research closely resembles true experimentation but is conducted by establishing the cause-effect relationships among variables. It may also be conducted to establish the cause or consequences of differences that already exist between, or among groups of individuals. 48 This type of research compares outcomes between the intervention groups in which participants are not randomized to their respective interventions because of ethics- or feasibility-related reasons. 49 As in true experiments, the researcher identifies and measures the effects of the independent variable on the dependent variable. However, unlike true experiments, the researchers do not manipulate the independent variable.

In quasi-experimental research, naturally formed or pre-existing groups that are not randomly assigned are used, particularly when an ethical, randomized controlled trial is not feasible or logical. 50 The researcher identifies control groups as those which have been exposed to the treatment variable, and then compares these with the unexposed groups. The causes are determined and described after data analysis, after which conclusions are made. The known and unknown variables that could still affect the outcome are also included. 7

QUALITATIVE RESEARCH

Inductive approach.

Qualitative research involves an inductive approach to develop a hypothesis. 21 , 25 Using this approach, researchers answer research questions and develop new theories, but they do not test hypotheses or previous theories. The researcher seldom examines the effectiveness of an intervention, but rather explores the perceptions, actions, and feelings of participants using interviews, content analysis, observations, or focus groups. 25 , 45 , 51

Distinctive features of qualitative research

Qualitative research seeks to elucidate about the lives of people, including their lived experiences, behaviors, attitudes, beliefs, personality characteristics, emotions, and feelings. 27 , 30 It also explores societal, organizational, and cultural issues. 30 This type of research provides a good story mimicking an adventure which results in a “thick” description that puts readers in the research setting. 52

The qualitative research questions are open-ended, evolving, and non-directional. 26 The research design is usually flexible and iterative, commonly employing purposive sampling. The sample size depends on theoretical saturation, and data is collected using in-depth interviews, focus groups, and observations. 27

In various instances, excellent qualitative research may offer insights that quantitative research cannot. Moreover, qualitative research approaches can describe the ‘lived experience’ perspectives of patients, practitioners, and the public. 53 Interestingly, recent developments have looked into the use of technology in shaping qualitative research protocol development, data collection, and analysis phases. 54

Qualitative research employs various techniques, including conversational and discourse analysis, biographies, interviews, case-studies, oral history, surveys, documentary and archival research, audiovisual analysis, and participant observations. 26

Conducting qualitative research

To conduct qualitative research, investigators 1) identify a general research question, 2) choose the main methods, sites, and subjects, and 3) determine methods of data documentation access to subjects. Researchers also 4) decide on the various aspects for collecting data (e.g., questions, behaviors to observe, issues to look for in documents, how much (number of questions, interviews, or observations), 5) clarify researchers’ roles, and 6) evaluate the study’s ethical implications in terms of confidentiality and sensitivity. Afterwards, researchers 7) collect data until saturation, 8) interpret data by identifying concepts and theories, and 9) revise the research question if necessary and form hypotheses. In the final stages of the research, investigators 10) collect and verify data to address revisions, 11) complete the conceptual and theoretical framework to finalize their findings, and 12) present and disseminate findings ( Fig. 1B ).

Types of qualitative research

The different types of qualitative research include (a) historical research, (b) ethnographic research, (c) meta-analysis, (d) narrative research, (e) grounded theory, (f) phenomenology, (g) case study, and (h) field research. 23 , 25 , 28 , 30

Historical research is conducted by describing past events, problems, issues, and facts. The researcher gathers data from written or oral descriptions of past events and attempts to recreate the past without interpreting the events and their influence on the present. 6 Data is collected using documents, interviews, and surveys. 55 The researcher analyzes these data by describing the development of events and writes the research based on historical reports. 2

Ethnographic research is performed by observing everyday life details as they naturally unfold. 2 It can also be conducted by developing in-depth analytical descriptions of current systems, processes, and phenomena or by understanding the shared beliefs and practices of a particular group or culture. 21 The researcher collects extensive narrative non-numerical data based on many variables over an extended period, in a natural setting within a specific context. To do this, the researcher uses interviews, observations, and active participation. These data are analyzed by describing and interpreting them and developing themes. A detailed report of the interpreted data is then provided. 2 The researcher immerses himself/herself into the study population and describes the actions, behaviors, and events from the perspective of someone involved in the population. 23 As examples of its application, ethnographic research has helped to understand a cultural model of family and community nursing during the coronavirus disease 2019 outbreak. 56 It has also been used to observe the organization of people’s environment in relation to cardiovascular disease management in order to clarify people’s real expectations during follow-up consultations, possibly contributing to the development of innovative solutions in care practices. 57

Meta-analysis is carried out by accumulating experimental and correlational results across independent studies using a statistical method. 21 The report is written by specifying the topic and meta-analysis type. In the write-up, reporting guidelines are followed, which include description of inclusion criteria and key variables, explanation of the systematic search of databases, and details of data extraction. Meta-analysis offers in-depth data gathering and analysis to achieve deeper inner reflection and phenomenon examination. 58

Narrative research is performed by collecting stories for constructing a narrative about an individual’s experiences and the meanings attributed to them by the individual. 9 It aims to hear the voice of individuals through their account or experiences. 17 The researcher usually conducts interviews and analyzes data by storytelling, content review, and theme development. The report is written as an in-depth narration of events or situations focused on the participants. 2 , 59 Narrative research weaves together sequential events from one or two individuals to create a “thick” description of a cohesive story or narrative. 23 It facilitates understanding of individuals’ lives based on their own actions and interpretations. 60

Grounded theory is conducted by engaging in an inductive ground-up or bottom-up strategy of generating a theory from data. 24 The researcher incorporates deductive reasoning when using constant comparisons. Patterns are detected in observations and then a working hypothesis is created which directs the progression of inquiry. The researcher collects data using interviews and questionnaires. These data are analyzed by coding the data, categorizing themes, and describing implications. The research is written as a theory and theoretical models. 2 In the write-up, the researcher describes the data analysis procedure (i.e., theoretical coding used) for developing hypotheses based on what the participants say. 61 As an example, a qualitative approach has been used to understand the process of skill development of a nurse preceptor in clinical teaching. 62 A researcher can also develop a theory using the grounded theory approach to explain the phenomena of interest by observing a population. 23

Phenomenology is carried out by attempting to understand the subjects’ perspectives. This approach is pertinent in social work research where empathy and perspective are keys to success. 21 Phenomenology studies an individual’s lived experience in the world. 63 The researcher collects data by interviews, observations, and surveys. 16 These data are analyzed by describing experiences, examining meanings, and developing themes. The researcher writes the report by contextualizing and reporting the subjects’ experience. This research approach describes and explains an event or phenomenon from the perspective of those who have experienced it. 23 Phenomenology understands the participants’ experiences as conditioned by their worldviews. 52 It is suitable for a deeper understanding of non-measurable aspects related to the meanings and senses attributed by individuals’ lived experiences. 60

Case study is conducted by collecting data through interviews, observations, document content examination, and physical inspections. The researcher analyzes the data through a detailed identification of themes and the development of narratives. The report is written as an in-depth study of possible lessons learned from the case. 2

Field research is performed using a group of methodologies for undertaking qualitative inquiries. The researcher goes directly to the social phenomenon being studied and observes it extensively. In the write-up, the researcher describes the phenomenon under the natural environment over time with no implantation of controls or experimental conditions. 45

DIFFERENCES BETWEEN QUANTITATIVE AND QUALITATIVE RESEARCH

Scientific researchers must be aware of the differences between quantitative and qualitative research in terms of their working mechanisms to better understand their specific applications. This knowledge will be of significant benefit to researchers, especially during the planning process, to ensure that the appropriate type of research is undertaken to fulfill the research aims.

In terms of quantitative research data evaluation, four well-established criteria are used: internal validity, external validity, reliability, and objectivity. 23 The respective correlating concepts in qualitative research data evaluation are credibility, transferability, dependability, and confirmability. 30 Regarding write-up, quantitative research papers are usually shorter than their qualitative counterparts, which allows the latter to pursue a deeper understanding and thus producing the so-called “thick” description. 29

Interestingly, a major characteristic of qualitative research is that the research process is reversible and the research methods can be modified. This is in contrast to quantitative research in which hypothesis setting and testing take place unidirectionally. This means that in qualitative research, the research topic and question may change during literature analysis, and that the theoretical and analytical methods could be altered during data collection. 44

Quantitative research focuses on natural, quantitative, and objective phenomena, whereas qualitative research focuses on social, qualitative, and subjective phenomena. 26 Quantitative research answers the questions “what?” and “when?,” whereas qualitative research answers the questions “why?,” “how?,” and “how come?.” 64

Perhaps the most important distinction between quantitative and qualitative research lies in the nature of the data being investigated and analyzed. Quantitative research focuses on statistical, numerical, and quantitative aspects of phenomena, and employ the same data collection and analysis, whereas qualitative research focuses on the humanistic, descriptive, and qualitative aspects of phenomena. 26 , 28

Structured versus unstructured processes

The aims and types of inquiries determine the difference between quantitative and qualitative research. In quantitative research, statistical data and a structured process are usually employed by the researcher. Quantitative research usually suggests quantities (i.e., numbers). 65 On the other hand, researchers typically use opinions, reasons, verbal statements, and an unstructured process in qualitative research. 63 Qualitative research is more related to quality or kind. 65

In quantitative research, the researcher employs a structured process for collecting quantifiable data. Often, a close-ended questionnaire is used wherein the response categories for each question are designed in which values can be assigned and analyzed quantitatively using a common scale. 66 Quantitative research data is processed consecutively from data management, then data analysis, and finally to data interpretation. Data should be free from errors and missing values. In data management, variables are defined and coded. In data analysis, statistics (e.g., descriptive, inferential) as well as central tendency (i.e., mean, median, mode), spread (standard deviation), and parameter estimation (confidence intervals) measures are used. 67

In qualitative research, the researcher uses an unstructured process for collecting data. These non-statistical data may be in the form of statements, stories, or long explanations. Various responses according to respondents may not be easily quantified using a common scale. 66

Composing a qualitative research paper resembles writing a quantitative research paper. Both papers consist of a title, an abstract, an introduction, objectives, methods, findings, and discussion. However, a qualitative research paper is less regimented than a quantitative research paper. 27

Quantitative research as a deductive hypothesis-testing design

Quantitative research can be considered as a hypothesis-testing design as it involves quantification, statistics, and explanations. It flows from theory to data (i.e., deductive), focuses on objective data, and applies theories to address problems. 45 , 68 It collects numerical or statistical data; answers questions such as how many, how often, how much; uses questionnaires, structured interview schedules, or surveys 55 as data collection tools; analyzes quantitative data in terms of percentages, frequencies, statistical comparisons, graphs, and tables showing statistical values; and reports the final findings in the form of statistical information. 66 It uses variable-based models from individual cases and findings are stated in quantified sentences derived by deductive reasoning. 24

In quantitative research, a phenomenon is investigated in terms of the relationship between an independent variable and a dependent variable which are numerically measurable. The research objective is to statistically test whether the hypothesized relationship is true. 68 Here, the researcher studies what others have performed, examines current theories of the phenomenon being investigated, and then tests hypotheses that emerge from those theories. 4

Quantitative hypothesis-testing research has certain limitations. These limitations include (a) problems with selection of meaningful independent and dependent variables, (b) the inability to reflect subjective experiences as variables since variables are usually defined numerically, and (c) the need to state a hypothesis before the investigation starts. 61

Qualitative research as an inductive hypothesis-generating design

Qualitative research can be considered as a hypothesis-generating design since it involves understanding and descriptions in terms of context. It flows from data to theory (i.e., inductive), focuses on observation, and examines what happens in specific situations with the aim of developing new theories based on the situation. 45 , 68 This type of research (a) collects qualitative data (e.g., ideas, statements, reasons, characteristics, qualities), (b) answers questions such as what, why, and how, (c) uses interviews, observations, or focused-group discussions as data collection tools, (d) analyzes data by discovering patterns of changes, causal relationships, or themes in the data; and (e) reports the final findings as descriptive information. 61 Qualitative research favors case-based models from individual characteristics, and findings are stated using context-dependent existential sentences that are justifiable by inductive reasoning. 24

In qualitative research, texts and interviews are analyzed and interpreted to discover meaningful patterns characteristic of a particular phenomenon. 61 Here, the researcher starts with a set of observations and then moves from particular experiences to a more general set of propositions about those experiences. 4

Qualitative hypothesis-generating research involves collecting interview data from study participants regarding a phenomenon of interest, and then using what they say to develop hypotheses. It involves the process of questioning more than obtaining measurements; it generates hypotheses using theoretical coding. 61 When using large interview teams, the key to promoting high-level qualitative research and cohesion in large team methods and successful research outcomes is the balance between autonomy and collaboration. 69

Qualitative data may also include observed behavior, participant observation, media accounts, and cultural artifacts. 61 Focus group interviews are usually conducted, audiotaped or videotaped, and transcribed. Afterwards, the transcript is analyzed by several researchers.

Qualitative research also involves scientific narratives and the analysis and interpretation of textual or numerical data (or both), mostly from conversations and discussions. Such approach uncovers meaningful patterns that describe a particular phenomenon. 2 Thus, qualitative research requires skills in grasping and contextualizing data, as well as communicating data analysis and results in a scientific manner. The reflective process of the inquiry underscores the strengths of a qualitative research approach. 2

Combination of quantitative and qualitative research

When both quantitative and qualitative research methods are used in the same research, mixed-method research is applied. 25 This combination provides a complete view of the research problem and achieves triangulation to corroborate findings, complementarity to clarify results, expansion to extend the study’s breadth, and explanation to elucidate unexpected results. 29

Moreover, quantitative and qualitative findings are integrated to address the weakness of both research methods 29 , 66 and to have a more comprehensive understanding of the phenomenon spectrum. 66

For data analysis in mixed-method research, real non-quantitized qualitative data and quantitative data must both be analyzed. 70 The data obtained from quantitative analysis can be further expanded and deepened by qualitative analysis. 23

In terms of assessment criteria, Hammersley 71 opined that qualitative and quantitative findings should be judged using the same standards of validity and value-relevance. Both approaches can be mutually supportive. 52

Quantitative and qualitative research must be carefully studied and conducted by scientific researchers to avoid unethical research and inadequate outcomes. Quantitative research involves a deductive process wherein a research question is answered with a hypothesis that describes the relationship between independent and dependent variables, and the testing of the hypothesis. This investigation can be aptly termed as hypothesis-testing research involving the analysis of hypothesis-driven experimental studies resulting in a test of significance. Qualitative research involves an inductive process wherein a research question is explored to generate a hypothesis, which then leads to the development of a theory. This investigation can be aptly termed as hypothesis-generating research. When the whole spectrum of inductive and deductive research approaches is combined using both quantitative and qualitative research methodologies, mixed-method research is applied, and this can facilitate the construction of novel hypotheses, development of theories, or refinement of concepts.

Disclosure: The authors have no potential conflicts of interest to disclose.

Author Contributions:

Conceptualization: Barroga E, Matanguihan GJ.
Data curation: Barroga E, Matanguihan GJ, Furuta A, Arima M, Tsuchiya S, Kawahara C, Takamiya Y, Izumi M.
Formal analysis: Barroga E, Matanguihan GJ, Furuta A, Arima M, Tsuchiya S, Kawahara C.
Investigation: Barroga E, Matanguihan GJ, Takamiya Y, Izumi M.
Methodology: Barroga E, Matanguihan GJ, Furuta A, Arima M, Tsuchiya S, Kawahara C, Takamiya Y, Izumi M.
Project administration: Barroga E, Matanguihan GJ.
Resources: Barroga E, Matanguihan GJ, Furuta A, Arima M, Tsuchiya S, Kawahara C, Takamiya Y, Izumi M.
Supervision: Barroga E.
Validation: Barroga E, Matanguihan GJ, Furuta A, Arima M, Tsuchiya S, Kawahara C, Takamiya Y, Izumi M.
Visualization: Barroga E, Matanguihan GJ.
Writing - original draft: Barroga E, Matanguihan GJ.
Writing - review & editing: Barroga E, Matanguihan GJ, Furuta A, Arima M, Tsuchiya S, Kawahara C, Takamiya Y, Izumi M.

Types of data #

In empirical research, we collect and interpret data in order to answer questions about the world. “Data” in this context usually results from some form of “measurement”. The notion of measurement here is very broad – it could include familiar acts like using a ruler to measure the length of an object, but it could also include asking a human research subject a question to “measure” their attitude about some topic.

Depending on the type of measurement that is made, the resulting data value can take different forms. Here we will discuss some of the common forms that can be taken by data.

Nominal data #

A nominal measurement is one that can take on any element in a finite set of unordered values. A commonly encountered nominal measurement that arises in research involving human subjects is biological race. There are many ways of “coding” race, but all of the common ways to do this would be considered to have a nominal form. The current United States Census Bureau approach to coding race uses five categories: Asian American, Black or African American, Native Americans and Alaska Native, Native Hawaiian and Other Pacific Islander, and White American. In some settings, subjects are given the option to respond that they have two or more races, and may be given the option to not respond. Since these race categories have no meaningful ordering, this is a nominal variable. Nominal variables are sometimes called categorical , or factor-type variables.

Nominal variables often arise in research involving human subjects, where common nominal variables include race, national origin (country of birth), biological sex, marital status, and immigration status. These may be broadly termed demographic traits .

Nominal variables arise in many other settings as well:

In medicine, we may be studying people with cancer, and there are many forms of cancer; for example, cancer can be classified based on the affected organ (lung, ovary, brain, etc.).

In market research, people have brand preferences, e.g. for toothpaste.

In astronomy, there are different types of stars (brown dwarf, red dwarf, neutron, etc.).

Many nominal variables are binary , meaning that they can only take on two possible values. These arise, for example, when the variable by definition refers to the presence of absence of some trait, e.g. responses to questions such as “do you have health insurance”, or “are you married”? These are sometimes called dichotomous traits. In some cases, the dichotomy is a simplification of a more complex reality. For example, we can ask someone whether they are currently employed, which is a binary choice, or we can give them more fine-grained options such as being employed full time, employed part time, retired, etc.

Ordinal data #

An ordinal variable is one that takes on values that can be ordered, but are not quantifiable to arbitrarily high precision. A common ordinal variable is educational attainment. This variable is often coded as (1) did not complete high school, (2) graduated from high school, (3) completed some college, (4) graduated from college, (5) completed some advanced or professional training beyond college. Note that in this setting, a person belongs to the highest level that is applicable, so that a person who completed college is in group (4) even though they also have a high school degree. Unlike a nominal variable, which cannot be ordered, there is a meaningful ordering for variables such as educational attainment.

Another common example of an ordinal variable would be a rating scale – suppose for example that patients with an injury are asked to rate their pain on a scale from 1 (least pain) to 10 (greatest pain). A very famous form of ordinal value is the five-point “Likert scale” used in questionnaires: the respondent is given a statement about a topic and can respond whether they “strongly agree”, “somewhat agree”, “neither agree nor disagree”, “somewhat disagree”, or “strongly disagree” with the statement.

A key property of an ordinal value is that the increments between adjacent categories cannot always be taken to have equal magnitudes. For example, we do not know whether the difference between “neither agree nor disagree” and “somewhat disagree” is equivalent to the difference between “somewhat disagree” and “strongly disagree”, even though these are both pairs of adjacent categories.

Quantitative data #

A “quantitative” measurement is one that can be made to very high accuracy on a numerical scale. Physical measurements such as length and weight are usually quantitative. A quantitative variable will usually have “units” associated with it, for example when measuring length the units may be centimeters. Income and age are two other measurements that would generally be considered to be quantitative, with units potentially being dollars and years, respectively.

Quantitative data are generally seen as containing more information than ordinal data, partly because they are generally measured to high precision, and also because unlike ordinal data, the presence of measurement units give a precise meaning to differences along the measurement scale. The difference between 5cm and 4cm, and the difference between 7cm and 6cm are both 1cm. On the other hand, as noted above, on a 10 point ordinal scale the difference between 5 and 4 may not convey the same meaning as the difference between 7 and 6, even though they are both one point differences.

Interval and ratio scales #

Sometimes, people refer to quantitative data as having an interval scale , and/or a ratio scale . An interval scale is one in which it makes sense to subtract two values, and a ratio scale is one in which it makes sense to divide two values. Most quantitative data have an interval scale, but it is not always the case that the scale of a quantitative variable is a ratio scale.

For example, suppose we are measuring temperature in degrees Fahrenheit, and we observe on a particular day that Cleveland and Atlanta reach high temperatures of 25 and 50 degrees, respectively. As an interval scale, it makes sense to subtract the two measurements and state that the Atlanta is 25 degrees warmer than the Cleveland. However it generally does not make sense to state that Atlanta is twice as warm as Cleveland based on Fahrenheit measurements. The origin (0 degree point) for Fahrenheit temperature is 32 degrees below the freezing point of water, which is a somewhat arbitrary value. To state that “Atlanta is twice as warm as Cleveland” would mean that Atlanta is twice as far from 0F compared to Cleveland, which is technically true but arguably not very meaningful. If we were to work on the centigrade scale, and we observe on a given day that the temperature in Atlanta is 20 degrees centigrade, and the temperature in Cleveland is 10 degrees centigrade, then we can make a stronger case for the scale having a ratio interpretation, since 0C is the freezing point of water, which has important real-world consequences.

Through this example, we can see that whether a scale is an interval and/or a ratio scale is somewhat a matter of judgment. The key thing to keep in mind at this point is that some pairs of quantitative variables can be compared through differences, some through ratios, and sometimes both type of comparisons make sense.

Practical considerations #

The typology described above is often useful, but in practice we encounter cases where it is ambiguous what type of data we have. We give examples of such ambiguous cases below. The key thing to keep in mind is that these terms are meant to help us communicate about our data. In some settings, terms such as “ordinal” or “ratio” may have unclear meanings. In that case, simply don’t use them in that setting.

For example, we might represent a person’s employment status with five levels: (i) employed full-time, (ii) employed part time, looking for full-time work, (iii) employed part time, not looking for full-time work, (iv) not employed, looking for work, (v) not employed, not looking for work. These could be treated as nominal, but alternatively, we could view this as an ordered spectrum in which (i) represents the greatest participation (desired or achieved) in the workforce, and (v) represents the least participation in the workforce. Thus, this variable could be viewed as either ordinal or nominal.

Considering educational attainment, we could code this variable as the number of years of schooling a person has completed. This could be taken to be quantitative, with units of years. However, it could also be considered to be ordinal. One reason to consider it as ordinal would be that it is much less common to have a partial year of schooling than to have a full year of schooling, and a person who completes, say, 11.5 years of schooling does not necessarily gain half of the benefit of their incomplete 12th year of schooling compared to someone with 12 full years of schooling. In other words, this scale is primarily discrete with whole-year increments, rather than being continuous with arbitrarily-fine increments.

Yet another type of ambiguity arises when we consider quantitative data. This type of data arises from measurements that are made at high precision, and are treated as real numbers. However, in practice every quantitative measurement has limited, finite precision due to the limitations of our measurement systems. For example, a digital scale may read out only to 1/100 of a gram. In some cases, a “quantitative” measurement made with very low precision might best be treated as ordinal.

When we consider the impact or consequences of changes in a variable’s value, we see that just because a variable is quantitative does not mean that every increment on its scale has the same consequences. For example, comparing temperatures of 33C to 30C, and 43C to 40C both result in a 3C difference of temperature. However, it may be argued that we care about a variable such as temperature only to the extent that it relates to something else that directly impacts us. For example, the “heat index” aims to reflect the comfort or discomfort that humans feel in environments with different temperatures. It takes account of the fact that a one degree change in temperature in a low humidity setting gives a lower perceived increase in heat than a one degree change in temperature in a high humidity setting. Thus, with respect to heat as perceived through the heat index, the temperature scale may not be an interval scale after all, since a fixed difference, say of 3 degrees C, does not always have the same impact on our preception of temperature.

Another useful example is the relationship between wealth and health. Wealth can be taken as a quantitative variable, defined to be the financial resources of an individual or family. In one sense, wealth is certainly an interval and a ratio scale. If one person has wealth of $400K, and another person has wealth of $100K, then the first person can buy $300K more stuff than the second person, suggesting that wealth is an interval scale. It is also true that the first person can buy four times more stuff than the second person, suggesting that wealth is a ratio scale. However, if we are focusing on wealth as it relates to health, then the first person may not tend to be any healthier than the second person. Both of these individuals have relatively high wealth compared to the population as a whole. It is well-established that both within and between countries, wealthier people tend to be healthier and live longer. But this effect is largely seen when contrasting the poorest individuals to individuals who are closer to the median, rather than contrasting wealthy to very wealthy individuals.

In summary, keep in mind that the purpose of the terms discussed here is to help us communicate, and we should not worry too much about the ambiguous cases. Instead, use these terms when it makes sense to do so, and avoid them in cases where it is not helpful.

Understanding qualitative measurement: The what, why, and how

Last updated

30 January 2024

Reviewed by

You’ll need to collect data to determine the success of any project, from product launches to employee culture initiatives. How that data is collected is just as important as what it reveals.

There are many ways to gather and analyze data, from in-person interviews to emailed surveys. Qualitative research focuses on telling a story with the information collected, while quantitative research involves collecting, analyzing, and presenting hard datasets.

Data gathered through qualitative measurement describes traits or characteristics. You can collect it in different ways, including interviews and observation, and it can be in the form of descriptive words.

While gathering and analyzing data through qualitative measurement can be challenging, especially if you’re working with limited resources or a smaller team, the insights you get at the end of the project are often well worth the effort.

What is qualitative measurement?

Qualitative measures can be particularly helpful in understanding how a phenomenon or action affects individuals and groups.

Why is qualitative data important?

Through data, you can understand how to better serve your customers and employees and anticipate shifts in your business.

The data will provide a deeper understanding of your customers, empowering you to make decisions that positively benefit your company in the long run. Qualitative data helps you see patterns and trends so you can make actionable changes. It can also answer questions posed by your project so you can provide company stakeholders with helpful information and insights.

How to collect qualitative data

Your ideal method for collecting qualitative data will depend on the resources you have at your disposal, the size of your team, and your project’s timeline.

You might select one method or a mixture of several. For instance, you could opt to send out surveys following a focus group session to receive additional feedback on one or two specific areas of interest.

Analyze your available resources and discuss options with project stakeholders before committing to one particular plan.

The following are some examples of the methods you could use:

Individual interviews

In-depth interviews are one of the most popular methods of collecting qualitative data. They are usually conducted in person, but you could also use video software.

During interviews, a researcher asks the person questions, logging their answers as they go.

Focus groups

Focus groups are a powerful way to observe and document a group of people, making them a common method for collecting qualitative data. They provide researchers with a direct way to interact with participants, listening to them while they share their insights and experiences and recording responses without the interference of software or third-party systems.

However, while focus groups and interviews are two of the most popular methods, they might not be right for every situation or company.

Direct observation

Direct observation allows researchers to see participants in their natural setting, offering an intriguing “real-life” angle to data collection . This method can provide rich, detailed information about the individuals or groups you are studying.

You can conduct surveys in person or online through web software or email. They can also be as detailed or general as your project requires. To get the most information from your surveys, use open-ended questions that encourage respondents to share their thoughts and opinions on the subject.

Diaries and journals

Product launches or employee experience initiatives are two examples of projects that could benefit from diaries and journals as a form of qualitative data gathering.

Diaries and journals enable participants to record their thoughts and feelings on a particular topic. By later examining the diary entries, project managers and stakeholders can better understand their reactions and opinions on the project and the questions asked.

Examples of qualitative data

Qualitative data is non-numeric information. It’s descriptive, often including adjectives to paint a picture of a situation or object. Qualitative data can be used to describe a person or place, as you can see in the examples below:

The employee prefers black coffee to sweet beverages.

The cat is black and fluffy.

The brown leather couch is worn and faded.

There are many ways to collate qualitative data, but remember to use appropriate language when communicating it to other project stakeholders. Qualitative data isn’t flowery, but neither does it shy away from descriptors to comprehensively paint a picture.

How to measure qualitative data

To measure qualitative data, define a clear project scope ahead of time. Know what questions you want answered and what people you need to speak to to make that happen. While not every result can be tallied, by understanding the questions and project scope well in advance, you’ll be better prepared to analyze what you’re querying.

Define the method you wish to use for your project. Whether you opt for surveys, focus groups, or a mixture of methods, employ the approach that will yield the most valuable data.

Work within your means and be realistic about the resources you can dedicate to data collection. For example, if you only have one or two employees to dedicate to the project, don’t commit to multiple focus group meetings with large groups of participants, as it might not be feasible.

What’s the difference between qualitative and quantitative measurements?

Qualitative measurements are descriptive. You can’t measure them with a ruler, scale, or other numeric value, nor can you express them with a numeric value.

In contrast, quantitative measurements are numeric in nature and can be counted.

When to use qualitative vs. quantitative measurements

Both qualitative and quantitative measurements can be valuable. Which to use greatly depends on the nature of your project.

If you’re looking to confirm a theory, such as determining which variety of body butter was sold most during a specific month, quantitative measurements will likely give you the answers you need.

To learn more about concepts and experiences, such as which advertising campaign your target customers prefer, opt for qualitative measurement.

You don’t have to commit to one or the other exclusively. Many businesses use a mixed-method approach to research, combining elements of both quantitative and qualitative measurements. Know the questions you want to answer and proceed accordingly with what makes the most sense for your goals.

What are the best ways to communicate qualitative data?

Communicating the qualitative data you’ve gathered can be tricky. The information is subjective, and many project stakeholders or other involved parties may have an easier time understanding and reacting to numeric data.

To effectively communicate qualitative data, you’ll need to create a compelling storyline that offers context and relevant details.

It can also help to describe the data collection method you used. This not only helps set the stage for your story but gives those listening insight into research methodologies they may be unfamiliar with.

Finally, allow plenty of time for questions. Regardless of whether you’re speaking to your company’s CEO or a fellow project manager, you should be prepared to respond to questions with additional, relevant information.

How can qualitative measurement be expressed through data?

Qualitative data is non-numeric. It is most often expressed through descriptions since it is surveyed or observed rather than counted.

Challenges associated with qualitative measurement

Any in-depth study or research project requires a time commitment. Depending on the research method you employ, other resources might be required. For instance, you might need to compensate the participants of a focus group in some way.

The time and resources required to undertake qualitative measurement could make it prohibitive for many companies, especially small ones with only a few employees. Outsourcing can also be expensive.

Conducting a cost–benefit analysis could help you decide if qualitative measurement is a worthwhile undertaking or one that should be delayed as you plan and prepare.

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What Is Qualitative Research? | Methods & Examples

What Is Qualitative Research? | Methods & Examples

Published on June 19, 2020 by Pritha Bhandari . Revised on June 22, 2023.

Qualitative research involves collecting and analyzing non-numerical data (e.g., text, video, or audio) to understand concepts, opinions, or experiences. It can be used to gather in-depth insights into a problem or generate new ideas for research.

Qualitative research is the opposite of quantitative research , which involves collecting and analyzing numerical data for statistical analysis.

Qualitative research is commonly used in the humanities and social sciences, in subjects such as anthropology, sociology, education, health sciences, history, etc.

How does social media shape body image in teenagers?
How do children and adults interpret healthy eating in the UK?
What factors influence employee retention in a large organization?
How is anxiety experienced around the world?
How can teachers integrate social issues into science curriculums?

Approaches to qualitative research, qualitative research methods, qualitative data analysis, advantages of qualitative research, disadvantages of qualitative research, other interesting articles, frequently asked questions about qualitative research.

Qualitative research is used to understand how people experience the world. While there are many approaches to qualitative research, they tend to be flexible and focus on retaining rich meaning when interpreting data.

Common approaches include grounded theory, ethnography , action research , phenomenological research, and narrative research. They share some similarities, but emphasize different aims and perspectives.

Qualitative research approaches
Approach	What does it involve?
Grounded theory	Researchers collect rich data on a topic of interest and develop theories .
	Researchers immerse themselves in groups or organizations to understand their cultures.
Action research	Researchers and participants collaboratively link theory to practice to drive social change.
Phenomenological research	Researchers investigate a phenomenon or event by describing and interpreting participants’ lived experiences.
Narrative research	Researchers examine how stories are told to understand how participants perceive and make sense of their experiences.

Note that qualitative research is at risk for certain research biases including the Hawthorne effect , observer bias , recall bias , and social desirability bias . While not always totally avoidable, awareness of potential biases as you collect and analyze your data can prevent them from impacting your work too much.

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Each of the research approaches involve using one or more data collection methods . These are some of the most common qualitative methods:

Observations: recording what you have seen, heard, or encountered in detailed field notes.
Interviews: personally asking people questions in one-on-one conversations.
Focus groups: asking questions and generating discussion among a group of people.
Surveys : distributing questionnaires with open-ended questions.
Secondary research: collecting existing data in the form of texts, images, audio or video recordings, etc.
You take field notes with observations and reflect on your own experiences of the company culture.
You distribute open-ended surveys to employees across all the company’s offices by email to find out if the culture varies across locations.
You conduct in-depth interviews with employees in your office to learn about their experiences and perspectives in greater detail.

Qualitative researchers often consider themselves “instruments” in research because all observations, interpretations and analyses are filtered through their own personal lens.

For this reason, when writing up your methodology for qualitative research, it’s important to reflect on your approach and to thoroughly explain the choices you made in collecting and analyzing the data.

Qualitative data can take the form of texts, photos, videos and audio. For example, you might be working with interview transcripts, survey responses, fieldnotes, or recordings from natural settings.

Most types of qualitative data analysis share the same five steps:

Prepare and organize your data. This may mean transcribing interviews or typing up fieldnotes.
Review and explore your data. Examine the data for patterns or repeated ideas that emerge.
Develop a data coding system. Based on your initial ideas, establish a set of codes that you can apply to categorize your data.
Assign codes to the data. For example, in qualitative survey analysis, this may mean going through each participant’s responses and tagging them with codes in a spreadsheet. As you go through your data, you can create new codes to add to your system if necessary.
Identify recurring themes. Link codes together into cohesive, overarching themes.

There are several specific approaches to analyzing qualitative data. Although these methods share similar processes, they emphasize different concepts.

Qualitative data analysis
Approach	When to use	Example
	To describe and categorize common words, phrases, and ideas in qualitative data.	A market researcher could perform content analysis to find out what kind of language is used in descriptions of therapeutic apps.
	To identify and interpret patterns and themes in qualitative data.	A psychologist could apply thematic analysis to travel blogs to explore how tourism shapes self-identity.
	To examine the content, structure, and design of texts.	A media researcher could use textual analysis to understand how news coverage of celebrities has changed in the past decade.
	To study communication and how language is used to achieve effects in specific contexts.	A political scientist could use discourse analysis to study how politicians generate trust in election campaigns.

Qualitative research often tries to preserve the voice and perspective of participants and can be adjusted as new research questions arise. Qualitative research is good for:

Flexibility

The data collection and analysis process can be adapted as new ideas or patterns emerge. They are not rigidly decided beforehand.

Natural settings

Data collection occurs in real-world contexts or in naturalistic ways.

Meaningful insights

Detailed descriptions of people’s experiences, feelings and perceptions can be used in designing, testing or improving systems or products.

Generation of new ideas

Open-ended responses mean that researchers can uncover novel problems or opportunities that they wouldn’t have thought of otherwise.

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Researchers must consider practical and theoretical limitations in analyzing and interpreting their data. Qualitative research suffers from:

Unreliability

The real-world setting often makes qualitative research unreliable because of uncontrolled factors that affect the data.

Subjectivity

Due to the researcher’s primary role in analyzing and interpreting data, qualitative research cannot be replicated . The researcher decides what is important and what is irrelevant in data analysis, so interpretations of the same data can vary greatly.

Limited generalizability

Small samples are often used to gather detailed data about specific contexts. Despite rigorous analysis procedures, it is difficult to draw generalizable conclusions because the data may be biased and unrepresentative of the wider population .

Labor-intensive

Although software can be used to manage and record large amounts of text, data analysis often has to be checked or performed manually.

If you want to know more about statistics , methodology , or research bias , make sure to check out some of our other articles with explanations and examples.

Chi square goodness of fit test
Degrees of freedom
Null hypothesis
Discourse analysis
Control groups
Mixed methods research
Non-probability sampling
Quantitative research
Inclusion and exclusion criteria

Research bias

Rosenthal effect
Implicit bias
Cognitive bias
Selection bias
Negativity bias
Status quo bias

Quantitative research deals with numbers and statistics, while qualitative research deals with words and meanings.

Quantitative methods allow you to systematically measure variables and test hypotheses . Qualitative methods allow you to explore concepts and experiences in more detail.

There are five common approaches to qualitative research :

Grounded theory involves collecting data in order to develop new theories.
Ethnography involves immersing yourself in a group or organization to understand its culture.
Narrative research involves interpreting stories to understand how people make sense of their experiences and perceptions.
Phenomenological research involves investigating phenomena through people’s lived experiences.
Action research links theory and practice in several cycles to drive innovative changes.

Data collection is the systematic process by which observations or measurements are gathered in research. It is used in many different contexts by academics, governments, businesses, and other organizations.

There are various approaches to qualitative data analysis , but they all share five steps in common:

Prepare and organize your data.
Review and explore your data.
Develop a data coding system.
Assign codes to the data.
Identify recurring themes.

The specifics of each step depend on the focus of the analysis. Some common approaches include textual analysis , thematic analysis , and discourse analysis .

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JSmol Viewer

Improving error estimates for evaluating satellite-based atmospheric co 2 measurement concepts through numerical simulations.

1. Introduction

2. materials and methods, 2.1. instrumental concept, 2.2. bayesian estimation, 2.3. direct and inverse radiative transfer modelling, 2.4. modis data, 2.5. definition of the case database.

CO 2 concentration: 394.88 ppm and CH 4 concentration: 1850 ppb;
Viewing zenith angle: nadir.
Cirrus: cases with no cirrus, cases with one cirrus layer in the [394.5; 438.0] hPa layer with a cloud top height (CTH) of 8 km, and cases with one cirrus layer in the [247.87; 275.95] hPa layer with a CTH of 12 km (cir100 in OPAC model); The cloud optical depth (COD) is 0.05 or 0.10 at 1.064 μm.
Aerosols: cases with an aerosol layer with an AOD of 0.05 or 0.15 at 1.064 μm. according to Figure 7 , either according to the fine mode: OPAC MITR00 model (mineral transport—desert) in the layer [705.0; 783.0] hPa (at an altitude of about 3 km), or according to the coarse mode: OPAC WASO70 (water soluble—continental) or SOOT00 (soot) in the layer [848.69; 1013.25] hPa (at an altitude of about 1.5 km).
Albedo: 3 values per frequency bands: SWIR 0.02, 0.15, or 0.30 and NIR 0.06, 0.3, or 0.5 according to the global distribution observed by MODIS.
Sun zenith angle: 0°, 50°, or 70.
Atmospheric profiles (defined for 20 pressure levels), three from TIGR database: Trop1—tropical, very hot and very humid; Trop3—tropical, hot and moderately humid; and MidLat2—temperate, more or less hot and moderately humid.

3.1. Generation of XCO 2 Errors

3.2. predictor and predictant selection for random error, 3.3. averaging kernel, 3.4. mapping of the co 2 errors using modis data, 4. discussion, 4.1. two-step procedure relevance, 4.2. random error and cavk versus effective error, 4.3. random error maps, 5. conclusions and perspectives, author contributions, data availability statement, acknowledgments, conflicts of interest, abbreviations.

AEMS	Atmospheric Environment Monitoring Satellite
ALB	ALBedo
ANR	Agence Nationale pour la Recherche
AOD	Aerosol Optical Depth
AVK	AVeraging Kernel
BLUE	Best Linear Unbiased Estimator
CAVK	Column AVeraging Kernel
CNES	Centre National d’Etudes Spatiales
CNSA	Chinese National Space Administration
COD	Cirrus Optical Depth
CO2M	Copernicus Carbon Dioxide Monitoring Mission
CTH	Cirrus Top Height
ESA	European Space Agency
ISRF	Instrumental Spectral Response Function
JAXA	Japanese Aerospace eXploration Agency
FWHM	Full Width at Half Maximum
GEISA	Gestion et Etudes des Informations Spectroscopiques Atmosphériques
GHG	GreenHouse Gas
GOSAT	Greenhouse gas Observation SATellite
IPDA	Integrated Path Differential Absorption
LIDORT	LInearised Discrete Ordinate Radiative Transfer
LMD	Laboratoire de Météorologie Dynamique
LSCE	Laboratoire des Sciences du Climat et de l’Environnement
MITR	MIneral TRansported
MODIS	Moderate Resolution Imaging Spectroradiometer
MRD	Mission Requirements Document
NASA	National Aeronautics and Space Administration
NIR	Near InfraRed
OCO	Orbital Carbon Observatory
SNR	Signal-to-Noise ratio
SWIR	Short-Wave InfraRed
SZA	Sun Zenith Angle
TAS	Thales Alenia Space
TCCON	Total Carbon Column Observing Network
TIGR	Thermodynamic Initial Guess Retrieval
TRACE	TRAcking Carbon Emission
VZA	Viewing Zenith Angle
WASO	WAter SOluble
4A/OP	Automated Atmospheric Absorption Atlas/OPerational version
5AI	Adaptable 4A Inversion

Appendix A. Prerequisites for an Optimal Two-Step Procedure

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Click here to enlarge figure

	Band		ISRF FWHM	Sampling Step	Number of Samples
		)			Number of Samples
NIR	747–773	12,936–13,387	0.12	0.04	651
SWIR1	1590–1675	5970–6289	0.30	0.10	851
SWIR2	1990–2095	4773–5025	0.35	0.1166	901

Luminance in		SWIR2	SWIR1	NIR
/sr/nm		SWIR2	SWIR1	NIR
Threshold	A	11.010 × 10	9.24 × 10	1.84 × 10
	B	146.78513 × 10	134.34701 × 10	7.04246 × 10
Intermediate	A	16.3 × 10	13.70 × 10	2.96 × 10
	B	146.78603 × 10	134.34702 × 10	10.56227 × 10
Goal	A	23.7 × 10	19.50 × 10	3.72 × 10
	B	307.04588 × 10	283.37915 × 10	15.33655 × 10

SNR	SWIR2	SWIR1	NIR

Photons/s/cm /sr/nm
Goal	321/498	768/492	854/473
Intermediate	293/442	673/443	763/424
Threshold	217/337	528/338	601/333
CarbonSat	205/—–	323/—–	334/—–
CO2M	—–/400	—–/400	—–/330

Noise Level
Noise Level
Threshold	−2.8210	1.3141	6.6354	−5.3900	0.57202
Intermediate	−6.6441	1.1260	10.720	−6.7136	0.91118
Goal	−7.4981	1.8386	12.284	−7.4414	0.95628

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Silveira, B.B.; Cassé, V.; Chomette, O.; Crevoisier, C. Improving Error Estimates for Evaluating Satellite-Based Atmospheric CO 2 Measurement Concepts through Numerical Simulations. Remote Sens. 2024 , 16 , 2452. https://doi.org/10.3390/rs16132452

Silveira BB, Cassé V, Chomette O, Crevoisier C. Improving Error Estimates for Evaluating Satellite-Based Atmospheric CO 2 Measurement Concepts through Numerical Simulations. Remote Sensing . 2024; 16(13):2452. https://doi.org/10.3390/rs16132452

Silveira, Bruna Barbosa, Vincent Cassé, Olivier Chomette, and Cyril Crevoisier. 2024. "Improving Error Estimates for Evaluating Satellite-Based Atmospheric CO 2 Measurement Concepts through Numerical Simulations" Remote Sensing 16, no. 13: 2452. https://doi.org/10.3390/rs16132452

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Organizing Your Social Sciences Research Paper: Quantitative Methods

Purpose of Guide
Writing a Research Proposal
Design Flaws to Avoid
Independent and Dependent Variables
Narrowing a Topic Idea
Broadening a Topic Idea
The Research Problem/Question
Academic Writing Style
Choosing a Title
Making an Outline
Paragraph Development
The C.A.R.S. Model
Background Information
Theoretical Framework
Citation Tracking
Evaluating Sources
Reading Research Effectively
Primary Sources
Secondary Sources
What Is Scholarly vs. Popular?
Is it Peer-Reviewed?
Qualitative Methods
Quantitative Methods
Common Grammar Mistakes
Writing Concisely
Avoiding Plagiarism [linked guide]
Annotated Bibliography
Grading Someone Else's Paper

Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques . Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon.

Characteristics of Quantitative Research

Your goal in conducting quantitative research study is to determine the relationship between one thing [an independent variable] and another [a dependent or outcome variable] within a population. Quantitative research designs may or may not establish causality. Quantitative research deals in numbers, logic, and an objective stance. Quantitative research focuses on numeric and unchanging data and detailed, convergent reasoning rather than divergent reasoning [i.e., the generation of a variety of ideas about a research problem in a spontaneous, free-flowing manner].

Its main characteristics are :

The data is usually gathered using structured research instruments.
The results are based on larger sample sizes that are representative of the population.
The research study can usually be replicated or repeated, given its high reliability.
Researcher has a clearly defined research question to which objective answers are sought.
All aspects of the study are carefully designed before data is collected.
Data are in the form of numbers and statistics, often arranged in tables, charts, figures, or other non-textual forms.
Project can be used to generalize concepts more widely, predict future results, or investigate causal relationships.
Researcher uses tools, such as questionnaires or computer software, to collect numerical data.

The overarching aim of a quantitative research study is to classify features, count them, and construct statistical models in an attempt to explain what is observed.

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Quantitative Research Methods . Writing@CSU. Colorado State University; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Basic Research Design for Quantitative Studies

Identifies the research problem -- as with any academic study, you must state clearly and concisely the research problem being investigated.
Reviews the literature -- review scholarship on the topic, synthesizing key themes and, if necessary, noting studies that have used similar methods of inquiry and analysis. Note where key gaps exist and how your study helps to fill these gaps or clarifies existing knowledge.
Describes the theoretical framework -- provide an outline of the theory or hypothesis underpinning your study. If necessary, define unfamiliar or complex terms, concepts, or ideas and provide the appropriate background information to place the research problem in proper context [e.g., historical, cultural, economic, etc.].

Study population and sampling -- where did the data come from; how robust is it; note where gaps exist or what was excluded. Note the procedures used for their selection;
Data collection – describe the tools and methods used to collect information and identify the variables being measured; describe the methods used to obtain the data; and, note if the data was pre-existing [i.e., government data] or you gathered it yourself. If you gathered it yourself, describe what type of instrument you used and why. Note that no data set is perfect--describe any limitations in methods of gathering data.
Data analysis -- describe the procedures for processing and analyzing the data. If appropriate, describe the specific instruments of analysis used to study each research objective, including mathematical techniques and the type of computer software used to manipulate the data.

Strengths of Using Quantitative Methods

Among the specific strengths of using quantitative methods to study social science research problems:

Allows for a broader study, involving a greater number of subjects, and enhancing the generalization of the results;
Allows for greater objectivity and accuracy of results. Generally, quantitative methods are designed to provide summaries of data that support generalizations about the phenomenon under study. In order to accomplish this, quantitative research usually involves few variables and many cases, and employs prescribed procedures to ensure validity and reliability;
Applying well establshed standards means that the research can be replicated, and then analyzed and compared with similar studies;
You can summarize vast sources of information and make comparisons across categories and over time; and,
Personal bias can be avoided by keeping a 'distance' from participating subjects and using accepted computational techniques .

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Limitations of Using Quantiative Methods

Some specific limitations associated with using quantitative methods to study research problems in the social sciences include:

Quantitative data is more efficient and able to test hypotheses, but may miss contextual detail;
Uses a static and rigid approach and so employs an inflexible process of discovery;
The development of standard questions by researchers can lead to "structural bias" and false representation, where the data actually reflects the view of the researcher instead of the participating subject;
Results provide less detail on behavior, attitudes, and motivation;
Researcher may collect a much narrower and sometimes superficial dataset;
Results are limited as they provide numerical descriptions rather than detailed narrative and generally provide less elaborate accounts of human perception;
The research is often carried out in an unnatural, artificial environment so that a level of control can be applied to the exercise. This level of control might not normally be in place in the real world thus yielding "laboratory results" as opposed to "real world results"; and,
Preset answers will not necessarily reflect how people really feel about a subject and, in some cases, might just be the closest match to the preconceived hypothesis.

Need Help Locating Statistics?

Resources for locating data and statistics can be found here:

Statistics & Data Research Guide

Research Tip

Finding Examples of How to Apply Different Types of Research Methods

SAGE Research Methods Online and Cases

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Experimental and numerical characterization of a flexible strain sensor based on polydimethylsiloxane polymeric network and MWCNT’s

Original Paper
Open access
Published: 05 July 2024
Volume 31 , article number 211 , ( 2024 )

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Nadia A. Vázquez-Torres 1 na1 ,
Jorge A. Benítez-Martínez 1 na1 ,
Juan R. Vélez-Cordero 2 na1 &
Francisco M. Sánchez-Arévalo ORCID: orcid.org/0000-0003-4369-1262 1 na1

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We demonstrated the feasibility of obtaining a low-cost, flexible strain sensor by spraying a conductive thin layer of MWCNT’s over an S-pattern embedded within a PDMS matrix. The final composite conforms a dog bone-shaped tensile specimen intended to measure the strain associated with a human wrist extension movement. Our sensor works with a combination of different mechanisms, such as piezoresistivity and tunneling, which depend on the level and repetitions of loads applied to the sensor. According to the reported elongation ratios, these sensors can detect large strains, up to 40%, for several uniaxial loading-unloading cycles. This makes them useful for human skin strain measurements.

Graphical abstract

Stretchable strain sensor facilely fabricated based on multi-wall carbon nanotube composites with excellent performance

Highly Sensitive Flexible Strain Sensor Based on a Double-percolation Structured Elastic Fiber of Carbon Nanotube (CNT)/Styrene Butadiene Styrene (SBS) @ Thermoplastic Polyurethane (TPU) for Human Motion and Tactile Recognition

Nanoarchitectonics with MWCNT and Ecoflex film for flexible strain sensors: wide linear range for wearable applications and monitoring of pressure distribution

Avoid common mistakes on your manuscript.

Introduction

Nowadays, many people worldwide have demonstrated the need to know their personal records regarding health, sports performance, or even the combination of both during sports training routines. This has been possible due to the implementation of ergonomic devices based on electronic materials and sensing technology innovations. Some representative utilities of these devices are, for example, human motion monitoring [ 1 , 2 ], healthcare [ 3 ], gesture recognition [ 4 ], tactile sensors [ 5 ], and even the development of soft robots with sensory capabilities [ 5 , 6 ]. To develop these types of sensors, different fabrication methods have been used such as 3D printing [ 7 ], coating, spinning, chemical vapor deposition, lithography technologies, laser ablation and transfer methods [ 4 , 8 , 9 ]. Now it is known that depending on several factors such as the synthesis method, structural design, the conductive particles and their guest polymeric matrix, the flexible strain sensors’ working mechanisms could be due to piezoresistive effects, geometric effects, crack propagation, disconnection, tunneling effect or a combination of some of them [ 4 , 10 ].

It is clear that the interest in flexible strain sensors is increasing nowadays, and a notable number of works have studied the development, characterization and application of different types/shapes and measurement mechanisms of such sensors [ 4 , 11 ]. Flexible strain sensors are usually made of elastomer, like PDMS, and different conductive particles such as platinum [ 12 ], gold [ 13 ], carbon black [ 14 ], graphene/graphene oxide [ 15 , 16 ], carbon nanotubes[ 17 , 18 ], multiwalled carbon nanotubes [ 8 , 9 ] or a combination of some of them like carbon nanotubes with graphene[ 19 ], palladium with graphene oxide [ 16 ], or carbon nanotubes with Mxene [ 20 ]. Besides PDMS, other polymeric matrices have been explored as well to develop these strain sensors, including natural fibers such as cotton coated with a composite based on PTFE/water, Capstone ST-110 with carbon nanotubes [ 21 ] or even medical elastic bands coated with self-segregated carbon nanotubes [ 18 ]. The variety of applications achieved by these flexible sensors are large, some notable examples are: gas selectivity and separation [ 14 ], compressive, shear, and torsional load sensors [ 12 ], motion detection of human joints, facial gesture [ 8 , 13 , 17 , 19 ] and medical signals during sport training routines on humans, [ 20 ] among others.

Although significant advances have recently been made in the development and application of flexible strain sensors, there still remains the need to understand their work mechanism and consequently improve their stability, sensitivity, response time and sensing range of these sensors based on PDMS and conductive nanoparticles. A considerable cumulus of work has been addressed to study different types of flexible strain sensors. To the best of our knowledge, nobody has studied experimentally and numerically the electrical and mechanical responses of a flexible strain sensor based on a carpet of conductive MWCNT’s deposited over a S-shaped pattern within a PDMS matrix. Therefore, the main purpose of this work was to generate a free-standing MWCNT’s S-pattern as a conductive circuit embedded between PDMS layers to obtain a low-cost, flexible strain sensor which will be experimentally and numerically evaluated to get a better understanding of its mechanical and electrical behaviors under cycling uniaxial loads.

Materials and methods

Dow Corning Sylgard 184 Poly(dimethylsiloxane) (PDMS) in a 10:1 ratio was used as the flexible polymeric base of the strain sensor. Multi-walled carbon nanotubes (MWCNT’s) 6-9 nm in diameter and 5 $\mu $ m of length were used to fabricate the conductive pattern of the sensors (MWCNT’s were purchased from Sigma Aldrich, St. Louis, MO, USA, CAS:308068-56-6). Both PDMS and MWCNT’s were used as received.

fabrication of the flexible strain sensor

The explanation of the fabrication protocol is illustrated in Fig. 1 . Using the Sylgard 184 kit, the PDMS part A (pre-polymer) and PDMS part B (curing reagent) were weighted, preserving a 10:1 ratio. Then parts A and B were mechanically stirred for 5 minutes at room temperature. The mixture was degassed in a vacuum chamber having a pressure of -67 kPa for 25 minutes at room temperature. Subsequently, the mixture was poured into a PLA 3D-printed mold with a specific geometry following the D1708 ASTM standard. The PLA mold was previously supported and fixed on glass using double-sided adhesive tape. The mixture within the mold was cured in an oven at 60 $^\circ $ C for 90 minutes. Then the cured samples exhibiting the geometry of a dog-bone-shaped specimen (with thickness around 500 $\mu $ m) were carefully detached and transferred to another but deeper 3D-printed PLA molds. Next, we put over the first layer of the dog-bone-shaped PDMS a mask made of adhesive vinyl having the same dog-bone shape but now including a centered hollow channel with an S-pattern. This pattern works as a strain gage. The masks were fabricated using the laser cutting module of the ZMorph FAB multifunctional. Later, 1 mg of MWCNT’s were dissolved in 10 mL of isopropyl alcohol and sonicated for 5 minutes; subsequently, this dissolution was poured into an Iwata airbrush (HP-C NCE model). Then, 1mL of the MWCNT’s dissolution was sprayed on the PDMS surface, with the mask and the airbrush connected to an oil-free air compressor working at 138 kPa. Thus, after 100 cycles of deposition, a conductive S-pattern of MWCNT’s was obtained. After total evaporation of the isopropyl alcohol, we carefully detached the vinyl mask. Next, the conductive MWCNT path terminals were connected to two adhesive carbon tape strips, which were later used to monitor the electrical resistance. After this, a second layer of PDMS was collocated on top of the first layer, sandwiching the MWCNT’s thin path. This was done by pouring liquid PDMS (10:1 ratio) into the mold, covering the first cured PDMS layer, the MWCNT conductive pattern, and carbon strips. Finally, the whole set was cured (temperature 60 $^\circ $ C for 90 minutes) to encapsulate the MWCNT’s conductive path with the reticulated elastomer, the former being the active part of the flexible strain sensor.

Flexible strain sensor fabrication process. The rectangle made with the blue dashed line depicts the PDMS 10:1 ratio preparation and the process of obtaining the test sample in a dog bone shape. Besides, here we show the process of deposition of MWCNT’s to get the conductive strain gage pattern of the sensor

Uniaxial tensile assays

The uniaxial tensile assays were conducted in a custom-designed mechanical tester. It consists of a load frame, a motorized linear stage (model MTS50-Z8 from Thorlabs), a miniature load cell with a capacity of 111 N (model 31 series from Honeywell), and PLA 3D-printed grips. The load frame was fabricated in 28 mm squared aluminum profiles which were vertically fixed on an aluminum breadboard (MBH3060/M 300x600 mm from Thorlabs). The MTS50-Z8 was used as a mechanical actuator providing controlled displacement ranging from 0-50 mm, and it was mounted on the vertical profiles. The upper grip was coupled to the MTS50-Z8 mechanical actuator by L-Type support. Meanwhile, the load cell and lower grip were mounted in a transversal squared aluminum profile which was also fixed to the vertical profiles. The mechanical actuator, the load cell, and the grips were carefully aligned, preserving a vertical axial axis. The flexible strain sensor was fixed between the grips, and its carbon strips were connected to a Tektronix multimeter model DMM4050 in order to register the electrical resistance changes as the uniaxial load acts on the flexible strain sensor. Notice that a second multimeter (HP model 34401A) was used to acquire the conditioned and amplified load cell signal. Thus, time, displacement, and force data were acquired synchronously by using a virtual instrument specially programmed in LabVIEW, which involves the control of the MTS50-Z8 mechanical actuator and the acquisition of the signals during the experiment.

The elastic constants of the flexible strain sensor made of PDMS were determined by non-linear fitting of the stress as a function of the elongation ratio data that were obtained from the uniaxial tensile experiments. The non-linear mechanical response of PDMS required the use of Ogden’s model [ 22 ] to mimic the mechanical behavior of the sensor. Hence the stress ( $\sigma $ ) is determined with Eq. 1 . Here $\lambda $ is the elongation ratio calculated from engineering strain ( $\varepsilon $ ) as $\lambda =\varepsilon +1$ ; meanwhile, $\mu _{i}$ and $\alpha _{i}$ are constants that are used to calculate the shear elastic modulus ( G ) through the Eq. 2 . The index ( n ) indicates the order of Ogden’s model. Assuming that PDMS presents a rubber-like mechanical behavior and has a Poisson ratio of $\nu =0.5$ , the following relation between elastic constants can be used: E= 2G(1+ $\nu $ ), giving Eq. 3 .

Once the elastic modulus was first determined by single load uniaxial tensile assay, uniaxial tensile load/unload cycles were applied. The first three cycles were applied using three different elongation ratios (1.25, 1.35, and 1.45) to observe the sensors’ initial mechanical and electrical behavior. The following seven cycles reached an elongation ratio of 1.45. After these 10 cumulative cycles, the next 10 cycles were applied using a 1.45 elongation ratio. This was done to register the influence of cycles on the mechanical and electrical behavior of the flexible strain sensors. To complement the experiments, numerical simulations were conducted to distinguish between the macroscopic (changes in gage’s geometry) and micro/nanoscopic (nanotube orientation changes, tunneling) effects on the electrical resistance changes. To capture the orientation of the nanotubes, we used simple theoretical concepts such as the order parameter [ 23 ] and a straightforward equation of state based on the macroscopic strain $\varepsilon $ . These theoretical concepts are discussed in the results section.

Numerical simulations

Numerical simulations were conducted in COMSOL Multiphysics to know the exact ohmic resistance due to geometrical changes (increase in length and decrease of cross-section) of the MWCNT S-pattern. The 3D geometry of the uniaxial test samples, following the D1708 ASTM standard, was used here. The numerical version of the sensor was made of 14,000 triangular prism elements, and a dedicated spiral-shaped channel was computationally made to simulate the path of MWCNT. Besides, the elastic constants determined for PDMS in uniaxial tensile assays were used in the simulations. Since PDMS is highly incompressible, we choose a mixed formulation in the mechanical stress equations to avoid volumetric locking phenomena, so the deviatoric and volumetric parts of the strain were treated separately [ 24 ] (if this is not done, unrealistic lateral displacements of the whole numerical geometry in the final results are detected). We also imposed symmetry conditions on appropriate surfaces to stabilize the simulations and so only 1/8 of the whole geometry was simulated thanks to symmetry. The numerical problem is then to find the sensor’s equilibrium stress field given a uniaxial displacement ${\textbf {u}}$ on the axial faces. The central equation to solve is the conservation of momentum expressed as:

where the deformation tensor is $F={\textbf {I}}+\nabla {\textbf {u}}$ and the stress $\mathbb {S}=\partial {W}/\partial {\mathcal {C}}$ (second Piola-Kirchhoff stress tensor) is obtained by deriving the strain energy function W with respect to the conjugate of $\mathbb {S}$ , that is, the Green-Lagrange strain $\mathcal {C}$ . The strain energy function is, in turn, defined in terms of the principal stretch elongation ratios, according to Ogden [ 22 ]. In Ogden’s model, W is written as:

where $\lambda _{j}$ are the principal stretch elongation ratios, K is the bulk modulus, $J=det(F)$ and $\overline{\lambda }_{j}=J^{-1/3}\lambda _{j}$ . The derivatives with respect to $\mathcal {C}$ can be worked out using the chain rule and the following expressions:

where $\hat{{\textbf {N}}}_{i}$ are the eigenvectors of each principal stretch elongation ratio.

Notice that since in the numerical simulations we obtain the full stress field inside the sensor and on its boundaries, an average procedure has to be done in order to compare the numerical values with the single stress value obtained experimentally. The experimental stress is calculated through the load cell transducer values divided by the sample’s transversal cross-section area, as previously described in the uniaxial tensile assays section.

Morphological and structural analysis of the strain sensors

Figure 2 shows the main features of the resistive-strain gage sensor based on a MWCNT’s S-pattern embedded within PDMS. Figure 2 a) depicts the shape of the sensor; its design was based on the D1708 ASTM standard that contemplates the well-known dog-bone shape of a uniaxial tensile specimen. Thus, the specimen’s length, width, and thickness were 38, 15 and 2 mm, respectively, while the radius of curvature was 5 mm and the distance between grips was 22 mm. The width of the MWCNT’s resistive pattern was 500 ±25 $\mu $ m according to the clamp rake tool from the measurements performed with vision assistant software (NI); in addition, it was corroborated through optical microscopy as shown in Fig. 2 b). The thickness of the MWCNT’s resistive pattern was measured through atomic force microscopy, as shown in Fig. 2 c). The average value of the thickness was 1.1 ±0.2 $\mu $ m and the average of the Root Mean Square roughness (Sq) value was 320 nm. Once the AFM measurements were conducted, the resistive MWCNT’s S-pattern was embedded within PDMS with carbon-tape strips added as connectors for electrical measurements with a multimeter. The initial values of the resistance of the MWCNT’s S-pattern averaged $R_{0}=877\pm 180 k\Omega $ . Here the difference of the resistance initial values between samples could be associated with the density, dispersion, and orientation of the MWCNT’s along the MWCNT’s S-pattern. The individual values of the electrical resistance in 4 different fabricated sensors are shown in Fig. 2 d).

Main physical features of the embedded MWCNT’s circuit path within a PDMS uniaxial tensile sample. a) Digital image analysis to determine the width of the MWCNT’s circuit path, b) Top view of the MWCNT’s circuit path within a PDMS uniaxial tensile sample obtained by optical microscopy. c) AFM image showing the border of the MWCNT’s circuit path sprayed on PDMS membrane and d) Initial values of electrical resistance for different fabricated sensors

Mechanical and electrical response under uniaxial tensile load

The mechanical and electrical behavior of the MWCNT’s resistive strain sensors were experimentally tested under uniaxial stress conditions. Figure 3 a) shows the mechanical response of the MWCNT’s resistive strain sensor embedded within PDMS. Here is shown that the same sensor was cycled 10 times using different elongation ratios. The three first cycles (initial cycles) were applied using $\lambda $ =1.25, $\lambda $ =1.35, and $\lambda $ =1.45; subsequently, the number of cycles increased until reached 10 cycles using an elongation ratio of $\lambda $ =1.45; their corresponding axial stress was 0.32 MPa. Regarding the mechanical response of the sensors, we observe that the PDMS presented a low non-linear behavior for the used elongation ratios, which were previously mentioned. Similar curves were obtained for three more samples; thus, the seven repetition cycles were averaged and shown in 3 b). Considering these average data, a first order Ogden model was used to obtain their mechanical models and the elastic modulus as shown in Table 1 . In these cases, we obtained an average Elastic modulus of 0.69 ±0.02 MPa. The stress vs. elongation curves demonstrate acceptable repeatability of the MWCNT’s resistive strain sensors’ mechanical response under cycling and even between samples.

Mechanical and electrical responses of the MWCNT’s resistive strain gage. a) Stress vs . elongation ratio curves after 10 cycles of load using the same specimen. b) Non-linear model fitting using a first-order Ogden’s model for different specimens, c) Electrical resistance response of the MWCNT’s resistive strain as a function of the elongation ratio showing the first 10 cycles in the same specimen, and d) Electrical resistance average behavior considering 4-10 cycles for different specimens or samples

Gage factor of PDMS-MWCNT’s resistive strain sensors. a) Gage factor for the initial slope, b) Gage factor for the final slope

Mechanical and electrical behavior of PDMS-MWCNT’s resistive strain sensors under load and unload cycling applied on the same sensor, a) Initial cycle b) cycle number 10

Now, regarding the electrical response of the PDMS-MWCNT’s resistive strain sensors, we present the curves of the changes of electrical resistance $\frac{\Delta R}{R_0}$ as a function of the elongation ratio (where $\Delta R= R-{R_0}$ ); Fig. 3 c) shows the values for each cycle using the same sensor. Here the first thing to notice is that the change in resistance $\frac{\Delta R}{R_0}$ exhibited negative values during the first cycle. In this first cycle, the MWCNT’s were disposed of/aligned according to the applied load direction. Thus, the subsequent cycles exhibited an increasing $\frac{\Delta R}{R_0}$ behavior. We have to point out that this behavior was linear until an elongation ratio ranged between 1.2-1.25. Beyond this range the slope of the $\frac{\Delta R}{R_0}$ vs. elongation ratio curves decreased. This is an interesting finding because the slope of the curves $\frac{\Delta R}{R_0}$ vs. elongation ratio is, in fact, the gage factor (GF) of the strain sensor. In view of this, the initial (with $\lambda $ between 1 and 1.25) and final (with $\lambda $ between 1.25 and 1.42) slopes of the average $\langle \frac{\Delta R}{R_0}\rangle $ (discarding cycle 1) was computed for each sensor; the averages are shown in Fig. 3 d), while the values of the slopes, or gage factors, are shown in Fig. 4 a-b) after running a linear fitting. Here, the gage factor average for the initial slope was 0.34 ±0.09 while the final slope reduced its value 4.25 times, offering an average Gage factor equal to 0.08 ±0.05. The corresponding reduction will be explained below when we discuss the simulations and present some basic theory of the phenomena involved.

Mechanical and electrical response under cyclic uniaxial tensile load

In this section, the mechanical and electrical response of PDMS-MWCNT’s resistive strain sensors under uniaxial load and unload cycling is presented. Figure 5 shows two double axes charts that relate the stress and $\frac{\Delta R}{R_0}$ as a function of the elongation ratio during mechanical cycling. In this case, Fig. 5 a) presents the cycle 1 (initial cycle) where the mechanical response of PDMS presents a hysteretic mechanical behavior; however, after the complete unloading process, the stress value returned to zero. Regarding the electrical variable, we noticed for this first cycle that the values presented a negative slope for $\frac{\Delta R}{R_0}$ , and its initial value was not recovered. Nonetheless, the negative trend for $\frac{\Delta R}{R_0}$ became positive for cycle 2 and beyond. Thus, we observed that the $\frac{\Delta R}{R_0}$ value increased as the stress and elongation ratio also increased, as shown in Fig. 5 b). In the case of the electrical response ( $\frac{\Delta R}{R_0}$ ) of the strain sensor we observe that this kind of sensors presented an hysteretic loop with a fish-shape; here the final value of $\frac{\Delta R}{R_0}$ at the end of the unloading process was different to the initial one. At this point, comparing the Figs. 5 a) and b), we assumed that MWCNT’s experienced a physical alignment due to the applied load direction, which could explain the change of behavior of the $\frac{\Delta R}{R_0}$ curves after the first cycle and beyond.

Electrical behavior of the PDMS-MWCNT’s resistive strain sensors: Sample 4, a) Electrical resistance behavior as a function of elongation ratio during 10 cycles of uniaxial tension. b) Maximum resistance value at the maximum load value for each cycle, c) $\frac{\Delta R}{R_0}$ behavior as a function of elongation ratio during 10 cycles. d) Maximum $\frac{\Delta R}{R_0}$ value at the maximum load value for each cycle

To get a better comprehension of these results, first, we have to clarify the physics behind these experiments taking into account the following points: (1) A PDMS uniaxial tensile sample, with a dogbone shape, is been deformed. The tensile sample has embedded an MWCNT’s resistive circuit in an S-gage pattern; both conform to what we have labeled as flexible PDMS-MWCNT’s resistive strain gage sensor. (2) Applying a uniaxial tensile force to the flexible sensor, the polymeric matrix based on PDMS will be deformed, presenting a non-linear -but predictable- mechanical response obeying a first-order Ogden model. (3) The MWNCT’s forming the resistive strain gage S-pattern will also suffer the transmitted deformation through the PDMS polymeric matrix. Here we have to remember that the MWCNT’s strain gage S-Pattern was deposited by using a spraying technique and adhesive masks on a PDMS surface and subsequently encapsulated with another layer of PDMS. Therefore, the MWCNT’s were confined within the polymeric matrix but they will have a certain freedom of mobility in a range defined by their geometry (average diameter and length). (4) Thus, when the sensor is uniaxially loaded, the PDMS polymeric matrix will elongate in its longitudinal direction and will contract in perpendicular directions to the longitudinal one, due to its Poisson ratio effect. (5) The current imposed stress-elongation ratio condition to the flexible PDMS matrix would be transmitted to the MWCNT’s strain gage S-Pattern; furthermore, the MWCNT’s strain gage S-Pattern would have to be deformed in the same sense, provoking a diminution of the MWCNT’s S-pattern cross-section area and therefore an increase of electrical resistance value.

Considering these 5 points, the results presented in Fig. 6 can be explained clearly. Figure 6 a) shows a representative resistance behavior as a function of the elongation ratio of the PDMS-MWCNT’s resistance strain sensors. As it was mentioned before, we realized for the first cycle that the values presented a negative slope for electrical resistance ( R ), and its initial value was not recovered. Nonetheless, the negative trend for R and $\frac{\Delta R}{R_0}$ became positive for cycle 2 and beyond, as shown in Figs. 6 a) and c). This kind of behavior was observed on cycle 2 and beyond for elongation ratios ranging between 1 and 1.25, which upon increasing the elongation ratio, an increase in resistivity was produced; however, for elongation ratios larger than 1.25 we observed that this increasing behavior suffered a change (a decrement) in its slope, as reported before in the gage factor charts (see Figs. 4 a and b). It means that the values of R and therefore $\frac{\Delta R}{R_0}$ tend to decrease at higher elongation ratios. This behavior, a priori , is contradictory to the first stage of elongation ( $\lambda $ =1-1.25); however, these results are consistent if the changes of alignment/interaction and distance between MWCNT’s are considered in the resistive response. In simple words, the flexible PDMS-MWCNT’s resistive strain gage sensor becomes more conductive for larger elongation ratios than 1.25 due to the effect of the Poisson ratio and the interaction between MWCNT’s. In these terms, we postulate that for elongation ratios higher than 1.25, the nanotubes get aligned in the direction of the application of the load; besides, the distance between them gets shorter compared to what they had in the initial loading stage. Therefore, the conjunction of these two factors will decrease the path/distance that the electrons have to travel, giving rise to the tunnel effect in the MWCNT’s neighborhood and, thus, improving the conductivity of the MWCNT’s strain gage S-Pattern and therefore decreasing the parameter $\frac{\Delta R}{R_0}$ for $1.25>\lambda $ . So far, the only way to support these arguments is our own results and the numerical simulations that will be presented later. For now, a more detailed analysis of the behavior of the electrical resistance values ( R ) and the $\frac{\Delta R}{R_0}$ values of the sensors under a greater number of cycles is presented.

Figure 6 a) shows that from cycle to cycle the electrical resistance clearly decrease. Thus, if we select the maximum value of the electrical resistance from these curves as a function of the number of cycles, an exponential decay curve is obtained as shown in Fig. 6 b); Nonetheless, if we select the same point on the elongation/resistance curves (see Fig. 6 c) but now considering the ratio $\frac{\Delta R}{R_0}$ , we obtained a constant value for those maximum $\frac{\Delta R}{R_0}$ values after a certain number of cycles, as shown Fig. 6 d). Notice that the first two points (cycles 1 and 2) correspond to lower elongation ratios; therefore, they did not reach a value close to 0.1 as the others. Our results suggest that PDMS-MWCNT’s resistive strain sensors can be trained after a certain number of mechanical load-unload cycles to improve the repeatability of the flexible strain sensors’ signal, and that it is the ratio $\frac{\Delta R}{R_0}$ the parameter that reaches a stationary value. Thus, in order to probe it, we carried out another 20 cycles more, as shown in Fig. 7 .

Extension of mechanical cycling over 20 more loading and unloading cycles. a) Electrical resistance response as a function of elongation ratio during 20 extra cycles. b) Maximum resistance value at the maximum load value for each cycle, c) $\frac{\Delta R}{R_0}$ behavior as a function of elongation ratio during 10 cycles. d) Maximum values of $\frac{\Delta R}{R_0}$ for each cycle

In this case, the load-unload cumulative cycles were registered and plotted. Figure 7 a) depicts the electrical resistance as a function of elongation ratio curves for 20 cycles more (10 cycles presented in Fig. 6 a) and other 20 cycles presented in 7 a) summing a total of 30 cycles. Here we can observe that the initial cycles of Figs. 6 a) and 7 a) presented differences between the R vs $\lambda $ loops; however, after a couple of cycles, these loops tend to present similar shapes between them and it was observed a decrease of the electrical resistance values which remained stuck between 680 and 720 k $\Omega $ . Now, considering again the maximum value of the electrical resistance during the loading process, the chart shown in Fig. 7 b) was obtained. Here, it is observed that the maximum electrical resistance values again showed an exponential decay curve. Subsequently, we performed the calculation to obtain the $\frac{\Delta R}{R_0}$ as function of elongation ratio curves, obtaining the fish shape curves for the vast majority of the cycles except for the first three cycles, see Fig. 7 c). Thus, when the maximum values of $\frac{\Delta R}{R_0}$ as function of cycles were plotted in 7 d) a trend was observed reaching a $\frac{\Delta R}{R_0}$ average value of 0.06 ±0.01. This demonstrates consistency between these electrical resistance measurements as a function of the elongation ratio, positioning PDMS-MWCNT’s composites as promising resistive strain sensors. We still have to understand the change of gage factor which is associated to the slope change of the $\frac{\Delta R}{R_0}$ vs. elongation ratio curves. Hence, numerical simulations were conducted together with some theoretical considerations.

Numerical version of the flexible strain sensor based on PDMS and MWCNT’s, a) unstrained configuration b) strained configuration, c) Scheme of two nanotubes pointing in directions ${\textbf {u}}$ , ${\textbf {u'}}$ and having a distance d . The director ${\textbf {n}}$ points to the principal strain direction, d) Stress as a function of the elongation ratio; ( $\circ $ ) experiments, (-) Ogden’s model, (- -) Mooney-Rivlin’s model. Bulk modulus K = 962 MPa, best fittings for Ogden’s model: $\mu _1$ = 0.362 MPa, $\alpha _1$ = 1.32106, for Mooney-Rivlin: C $_{10}$ = 0.2408 MPa, C $_{01}$ = -0.0437 MPa and e) Relative resistance change as a function of elongation ratio: ( $\circ $ ) experiments, dashed line: Eq. 7 , solid line: Eq. 8 with $d_{0}$ =0.1nm, dotted line: Eq. 8 with $d_{0}$ =0.2nm

Numerical simulations and theoretical considerations

As an example of the deformation states obtained numerically, Fig. 8 a-b) shows the deformation of the numerical simulated sensor before and after applying an elongation ratio of $\lambda $ =1.27. Figure 8 d) shows a representative experimental (circles) uniaxial stress progression as shown by the z-stress plot as a function of the elongation ratio and the corresponding comparison with the simulations (lines). It is important to say that since in the numerical simulations we obtained the full stress field inside and on the boundaries of the sensor, an average procedure has to be done in order to compare the numerical values with the single stretch stress value (nominal stress) given by the mechanical transducer in the experiments. In this sense, we noticed that the maximum stress obtained numerically on the axial faces had a better match. It turns out that the z-stress obtained with Ogden’s model (solid line in Fig. 8 d) had a very good match with the experimental data, but not so if we use another model such as the Mooney-Rivlin model (dashed line), which is also a popular model for hiperelasticity. This is a surprise given that both models can be fitted correctly to the same experimental data since the beginning. According to the existing literature, this apparent drawback of Mooney-Rivlin’s model has to do with the available experimental dataset used to find the model’s parameters rather than with the model itself. It has been shown that if one uses several datasets of strain progression to fit the model’s parameters, the performance of the model is substantially better (i.e., use uniaxial, biaxial, planar, bulge test, etc., rather than just one of these) [ 25 , 26 ]. OgdenÂ´s model matched the experimental data using just a uniaxial dataset to estimate its parameters can be seen as an advantage in favor to this model, after all, it has also been shown that it exhibits lower residuals in the fittings and can be applied to a wider range of strains compared to Mooney-Rivlin [ 27 ]. The insets of Fig. 8 d) show in more detail the differences between both models, revealing that Mooney-Rivlin tends to overestimate the stress in the neck region of the sensor. In any case, we insist that Mooney-Rivlin could be improved if other data sets were used in the fitting procedure rather than just uniaxial strain.

Now, to establish a clear distinction between the macroscopic/microscopic effects on the observed changes of the electrical resistance in the sensors, let’s start our analysis by assuming that the microstructure of the nanotubes does not changes at all with the strain $\varepsilon $ . This means that any change we detect in the electrical resistance R as a function of $\varepsilon $ will be of ohmic consequence, that is, will be a result of having longer conductive paths as strain increases, while having lower transversal number of paths due to transversal contraction or Poisson ratio $\nu $ . These geometrical effects are captured by Eq. 7 ,

where $l(\varepsilon )$ , $l_{o}$ are the length and initial length of the MWCNT path and $A(\varepsilon )$ and $A_{o}$ are the transverse area and initial transverse area of the path, respectively. Equation 7 is plotted in Fig. 8 e) (dashed line) and was calculated using $l(\varepsilon )$ and $A(\varepsilon )$ as determined from the numerical simulations (assuming that the thickness of the MWCNT path, $\sim 1\mu {m}$ , is kept constant). The second equivalence in Eq. 7 was corroborated ( $\nu \sim 0.5$ for PDMS) and gives the same straight dashed line in Fig. 8 e). We can immediately observe that ohm’s law gives a much higher electric resistance than that observed in the experiments; in other words, the changes in the microstructure that should be occurring as $\varepsilon $ increases must facilitate, rather than hinder, the conductive process. This is perhaps in contradiction to the general paradigm that states that strain hinders conduction and disrupts the conductive paths. Again, we insist here that the difference observed in our system is due to the fact that the MWCNT arrays form a highly concentrated path with almost negligible free volume. Therefore, in view that ohm’s law is not sufficient to explain the experimental curve, we must accept that the intrinsic resistivity $\rho $ of the MWCNT path is also changing, that is,

or that $\rho (\varepsilon )/\rho _{o}\ne 1$ . We noticed that $\rho (\varepsilon )/\rho _{o}$ should have an empirical form of

to fit a typical experimental curve, see the solid line in Fig. 8 e) for $C_{1}=-1.49$ , $C_{2}=1.19$ . What we should do now is try to obtain Eq. 9 using some first principles. As a simplistic but representative model, let us consider a pair-based interaction model or just two nanotubes (pairwise interactions) pointing in directions ${\textbf {u}}$ , ${\textbf {u'}}$ as shown in Fig. 8 c). The director ${\textbf {n}}$ is also shown and represents, for example, the direction of the principal (local) strain. At this pair interaction point of view, we can assume that the critical resistivity came from tunnel effects such as [ 28 , 29 ]

where $h=6.626\times 10^{-34}J\cdot {s}$ is Planck’s constant, e and m are the charge and mass ( $9.109\times 10^{-31}kg$ ) of the electron, $\Psi $ is the work function and $\mathcal {A}(\epsilon )$ , $d(\epsilon )$ are the overlapping area and centroid-to-centroid distance between two nanotubes, respectively. Similar to other works [ 30 , 31 ], we are going to define the inter-tube distance as

for some initial distance $d_{o}$ and Poisson lateral contraction. With this, we are indeed assuming that a high population of nanotubes accommodates as suggested in Fig. 8 c) for small strains. Now, for symmetric nanotubes, the overlapping area should be an even function of the dot product ${\textbf {u}}\cdot {\textbf {u'}}$ , that is, $\mathcal {A}\sim {LD}({\textbf {u}}\cdot {\textbf {u'}})^{2}$ , where L and D are the length and diameter of the nanotubes. At this point is convenient to recap the definition of the order parameter $\mathcal {S}$ and which is commonly used in the theory of liquid crystals. $\mathcal {S}$ is defined as: [ 23 ]

such that $\mathcal {S}=0$ ( $({\textbf {u}}\cdot {\textbf {n}})^{2}=1/3$ ) for an isotropic phase, while $\mathcal {S}=1$ ( $({\textbf {u}}\cdot {\textbf {n}})^{2}=1$ ) for a perfect nematic phase. Here $\langle ...\rangle $ indicates some orientational average over the ensemble. In view of Eq. 12 , it is convenient to approximate the area $\mathcal {A}$ as

Flexible strain sensor based on PDMS and MWCNT’s used to measure the wrist extension of a male subject, a) Image of the instrumented sensor attached on the skin b) Acquired signal registering the changes of resistance during the human wrist extension movement

where we have assumed that $\langle ({\textbf {u}}\cdot {\textbf {n}})^{2}\rangle \sim \langle ({\textbf {u}}\cdot {\textbf {u'}})^{2}\rangle $ and $\mathcal {A}_{o}\sim {LD}/3$ . By doing this we are directly relating the overlapping area with the order parameter. Now, we need to propose a state equation for $\mathcal {S}=\mathcal {S}(\epsilon )$ . In principle, the change of $\mathcal {S}$ as a function of $\epsilon $ may be a complicated function of the mechanical parameters (bending, stretching) of the nanotubes, its concentration, aspect ratio, as well as nonlinear or collective effects such as entanglement or clusterization of the nanotubes as they align towards ${\textbf {n}}$ . To keep things simple, we are going to use the fact that non-equilibrium molecular dynamics simulations [ 32 , 33 ] made of an ensemble of linear polymer melts show that the order parameter displays a saturation curve with respect to the strain. Therefore, it seems plausible to propose a general expression of the form

which represents a typical saturation behavior. Upon substituting Eqs. 11 , 13 and 14 into Eq. 10 , we can estimate the resistivity ratio as

where $\zeta =4\pi \sqrt{2m\Psi }/h$ . Upon Taylor expanding Eq. 15 up to $\mathcal {O}(\epsilon )^{2}$ we get, precisely, the polynomial form of Eq. 9 with coefficients defined as:

The theoretical black line in Fig. 8 e) is reproduced for the following choice of parameters: $\Psi =4.6eV$ , $d_{o}\sim 0.1nm$ , $k=3.7$ , $\nu =0.34$ , $\mathcal {S}_{max}=0.54$ . First of all, it was fortunate that with so few theoretical assumptions, we could obtain the correct form capable of reproducing the experimental results closely. This indicates that the rearrangements of the nanotubes are indeed changing the intrinsic conductivity in a way that favors electron tunneling, and the way this happens is by sustaining a continuous decrease of the inter-nanotube distance with the strain while increasing the overlapping area. Moreover, the selection of parameters is close to the values they are supposed to have: $\Psi =4.6eV$ is a typical value of the work function for CNT [ 34 ], while a distance of $d_{o}\sim 0.1nm$ is also of the order of the electron hopping distance (the MWCNT network we have is additionally highly concentrated). Standout the fact that for the best fit, the Poisson ratio $\nu \sim 0.34$ is closer to pristine MWCNT than to PDMS. This agrees with the fact that the MWCNT thin layer is composed mainly of nanotubes since they were not blended with uncured PDMS. Finally, the value of $\mathcal {S}_{max}\sim 0.54$ suggests that the nanotube carpet is far from rearranging into a crystalline ordered phase upon application of the strain. Now, a question arises if our model can predict negative values of $\Delta {R}/R_{o}$ as those observed in the first stretching cycles practiced on the experimental sensors. As shown in Fig. 8 e), dotted line, leaving all values fixed except that now $d_{o}=0.2nm$ (indeed a small change in the inter-tube distance) Eqs. 8 , 9 and 16 yield negative values of $\Delta {R}/R_{o}$ and a negative slope up to $\lambda =1+\epsilon \sim 1.25$ . At first sight, it seems contradictory to obtain better conduction (negative values of resistance) for higher values of the inter-tube distance. However, remember that we are calculating the relative change of R , $\Delta {R}/R_{o}$ , so in the limit $d_{o}\rightarrow 0$ the nanotubes cannot longer accommodate as $\epsilon $ increases and the intrinsic resistivity will be constant (indeed, in the limit $d_{o}\rightarrow 0$ , Eqs. 8 , 9 and 16 tend to Eq. 7 or $\rho (\epsilon )/\rho _{o}\approx 1)$ . In view of this, it seems that the cycles of expansion conducted in the experiments led to an effect of compaction in which the nanotubes re-accommodate, having each time lower values of $d_{o}$ . In summary, our working equation, Eq. 8 , is able to capture both the macroscopic geometrical ohmic changes and the micro/nanoscopic reorientations of the nanotubes in the total change of $\Delta {R}/R_{o}$ . The numerical simulations helped us to elucidate further the role specifically brought by the macroscopic geometrical changes and to establish a clear distinction between one and the other.

Biometric realization

Once the flexible strain sensors were fully electrically and mechanically characterized, then they were used to measure the strain associated with a human wrist extension movement as shown in Fig. 9 a) and b). In this chart, the change in resistance associated with wrist extension during 5 cycles is observed. The average of maximum values of $\frac{\Delta R}{R_0}$ was 0.09 $\pm {0.02}$ . It means that the flexible strain sensor was subjected to an elongation ratio close to 1.4 and suffered a normal stress close to 0.28 MPa during the cycles of wrist extension movement.

Conclusions

Low-cost, flexible strain sensors were obtained by spraying a conductive thin layer of MWCNT’s following an S-pattern embedded within the PMDS matrix exhibiting a dogbone-shaped tensile specimen, which was successfully used to measure the strain associated with a human wrist extension movement. Although significant work has been done in developing flexible strain sensors, ours is unique, as far as we know, in that it is based on standard geometry such as ASTM D1708 to minimize the effects on the mechanical behavior response of the sensor associated with its geometry. Our results demonstrated that the stress vs. elongation ratio and $\frac{\Delta R}{R_0}$ vs. elongation ratio curves presented non-linear behaviors. In this sense, the non-linear electrical response of the sensor is composed of two well-defined linear regions, the first ranging between elongation ratios of 1 to 1.25 and the second one ranging from 1.25 to 1.4. Thus, we obtained gage factors of 0.34 ±0.09 and 0.08 ±0.05, respectively. According to the reported elongation ratios and considering the definition of engineering strain, these sensors can detect large strains up to 40% for several uniaxial loading-unloading cycles. The electrical response of the sensor ( $\frac{\Delta R}{R_0}$ vs. elongation ratio curves) shows fish-shape curves, which tended to present a steady behavior after ten cycles; it suggests that MWCNT’s contained in the conductive S-pattern tend to self-accommodate according to load magnitude and direction. This assumption was proved by the simulation results and theoretical assumptions considered in this work and allowed us to clearly distinguish the role between the macroscopic geometrical effects (ohmic effects) and micro/nanoscopic effects such as tunneling effect and change of the orientation of the nanotubes in terms of the applied strain. We think this distinction is an important contribution from the point of view of the understanding of polymer/nanoparticle materials and its electrical response to mechanical deformations. At this point, we conclude that our sensor works with a combination of mechanisms, such as piezoresistive and tunneling effects, which will depend on the level of the external solicitations applied to the sensor.

Data availability

Data are contained within the article.

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Acknowledgements

This work was developed with financial support from PAPIIT DGAPA-UNAM program through grant IN101624. Nadia A. Vázquez-Torres acknowledges the support from DGAPA-UNAM postdoctoral fellowship grant. J.R. Vélez-Cordero acknowledges IxM-CONAHCyT program and financial support from grant C-554/2023. Authors also are grateful with C. A. Pereyra-Huerta for her technical assistance on sensor’s fabrication and characterization.

This work was developed with financial support from PAPIIT DGAPA-UNAM program through grants, IN101624 and IN102421.

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Nadia A. Vázquez-Torres, Jorge A. Benítez-Martínez, Juan R. Vélez-Cordero and Francisco M. Sánchez-Arévalo contributed equally to this work.

Authors and Affiliations

Instituto de Investigaciones en Materiales, Universidad Nacional Autónoma de México, Cd. Universitaria, México, 04510, CDMX, México

Nadia A. Vázquez-Torres, Jorge A. Benítez-Martínez & Francisco M. Sánchez-Arévalo

IxM-CONAHCYT, Instituto de Física, Universidad Autónoma de San Luis Potosí, 78295, San Luis Potosí, México

Juan R. Vélez-Cordero

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Conceptualization, NV, JB, and FS; methodology, NV, CP, and JB; Numerical calculations, JV; formal analysis, NV, FS, and JV; writing-original draft preparation, NV, JV, and FS; writing-review and editing, NV, JV, and FS; funding acquisition, FS.

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Vázquez-Torres, N.A., Benítez-Martínez, J.A., Vélez-Cordero, J.R. et al. Experimental and numerical characterization of a flexible strain sensor based on polydimethylsiloxane polymeric network and MWCNT’s. J Polym Res 31 , 211 (2024). https://doi.org/10.1007/s10965-024-04048-7

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A three-species model of aeolian saltation incorporating cooperative splash

Chen, Yulan
Pähtz, Thomas
Tholen, Katharina
Kroy, Klaus

Most aeolian sand transport models incorporate a so-called splash function that describes the number and velocity of particles ejected by the splash of an impacting particle. It is usually obtained from experiments or simulations in which an incident grain is shot onto a static granular packing. However, it has recently been discovered that, during aeolian sand transport, the bed cannot be considered as static, since it cannot completely recover between successive impacts. This led to a correction of the splash function accounting for cooperative effects [1], which were shown to be responsible for an anomalous third-root scaling of the sand flux with the particle-fluid density ratio s, observed in discrete-element-method-based simulations of aeolian sand transport across six orders of magnitude of s [2]. The model by [1] represents the aeolian transport layer by two species: high-energy saltons that eject low-energy reptons upon impact. While it quantitatively captures measurements and the simulated sand flux scaling, it does not recover the scaling laws of the simulated transport threshold and vertical flux at the bed. Here, we improve the model by [1] by means of a three-species saltation model. The additional species, called leapers, represent the fastest reptons, ejected by saltons in rare extreme ejection events. Together, saltons and leapers quantitatively reproduce the threshold and sand flux scaling behaviors, whereas reptons are predominantly responsible for the vertical bed surface fluxes seen in the simulations.[1] Tholen, Pähtz, Kamath, Parteli, Kroy, Anomalous scaling of aeolian sand transport reveals coupling to bed rheology, Physical Review Letters 130 (5), 058204 (2023). https://doi.org/10.1103/PhysRevLett.130.058204[2] Pähtz, Durán, Scaling laws for planetary sediment transport from DEM-RANS numerical simulations, Journal of Fluid Mechanics 963, A20 (2023). https://doi.org/10.1017/jfm.2023.343

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Numeric (Quantitative) Data: Collect your own data

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Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques . Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon.

Characteristics of Quantitative Research

Its main characteristics are :

The data is usually gathered using structured research instruments.
The results are based on larger sample sizes that are representative of the population.
The research study can usually be replicated or repeated, given its high reliability.
Researcher has a clearly defined research question to which objective answers are sought.
All aspects of the study are carefully designed before data is collected.
Data are in the form of numbers and statistics, often arranged in tables, charts, figures, or other non-textual forms.
Project can be used to generalize concepts more widely, predict future results, or investigate causal relationships.
Researcher uses tools, such as questionnaires or computer software, to collect numerical data.

The overarching aim of a quantitative research study is to classify features, count them, and construct statistical models in an attempt to explain what is observed.

Things to keep in mind when reporting the results of a study using quantitative methods :

Explain the data collected and their statistical treatment as well as all relevant results in relation to the research problem you are investigating. Interpretation of results is not appropriate in this section.
Report unanticipated events that occurred during your data collection. Explain how the actual analysis differs from the planned analysis. Explain your handling of missing data and why any missing data does not undermine the validity of your analysis.
Explain the techniques you used to "clean" your data set.
Choose a minimally sufficient statistical procedure ; provide a rationale for its use and a reference for it. Specify any computer programs used.
Describe the assumptions for each procedure and the steps you took to ensure that they were not violated.
When using inferential statistics , provide the descriptive statistics, confidence intervals, and sample sizes for each variable as well as the value of the test statistic, its direction, the degrees of freedom, and the significance level [report the actual p value].
Avoid inferring causality , particularly in nonrandomized designs or without further experimentation.
Use tables to provide exact values ; use figures to convey global effects. Keep figures small in size; include graphic representations of confidence intervals whenever possible.
Always tell the reader what to look for in tables and figures .

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Quantitative Research Methods . Writing@CSU. Colorado State University; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Basic Research Design for Quantitative Studies

Identifies the research problem -- as with any academic study, you must state clearly and concisely the research problem being investigated.
Reviews the literature -- review scholarship on the topic, synthesizing key themes and, if necessary, noting studies that have used similar methods of inquiry and analysis. Note where key gaps exist and how your study helps to fill these gaps or clarifies existing knowledge.
Describes the theoretical framework -- provide an outline of the theory or hypothesis underpinning your study. If necessary, define unfamiliar or complex terms, concepts, or ideas and provide the appropriate background information to place the research problem in proper context [e.g., historical, cultural, economic, etc.].

Study population and sampling -- where did the data come from; how robust is it; note where gaps exist or what was excluded. Note the procedures used for their selection;
Data collection – describe the tools and methods used to collect information and identify the variables being measured; describe the methods used to obtain the data; and, note if the data was pre-existing [i.e., government data] or you gathered it yourself. If you gathered it yourself, describe what type of instrument you used and why. Note that no data set is perfect--describe any limitations in methods of gathering data.
Data analysis -- describe the procedures for processing and analyzing the data. If appropriate, describe the specific instruments of analysis used to study each research objective, including mathematical techniques and the type of computer software used to manipulate the data.

Statistical analysis -- how did you analyze the data? What were the key findings from the data? The findings should be present in a logical, sequential order. Describe but do not interpret these trends or negative results; save that for the discussion section. The results should be presented in the past tense.

Interpretation of results -- reiterate the research problem being investigated and compare and contrast the findings with the research questions underlying the study. Did they affirm predicted outcomes or did the data refute it?
Description of trends, comparison of groups, or relationships among variables -- describe any trends that emerged from your analysis and explain all unanticipated and statistical insignificant findings.
Discussion of implications – what is the meaning of your results? Highlight key findings based on the overall results and note findings that you believe are important. How have the results helped fill gaps in understanding the research problem?
Limitations -- describe any limitations or unavoidable bias in your study and, if necessary, note why these limitations did not inhibit effective interpretation of the results.

Conclusion End your study by to summarizing the topic and provide a final comment and assessment of the study.

Summary of findings – synthesize the answers to your research questions. Do not report any statistical data here; just provide a narrative summary of the key findings and describe what was learned that you did not know before conducting the study.
Recommendations – if appropriate to the aim of the assignment, tie key findings with policy recommendations or actions to be taken in practice.
Future research – note the need for future research linked to your study’s limitations or to any remaining gaps in the literature that were not addressed in your study.

Strengths of Using Quantitative Methods

Among the specific strengths of using quantitative methods to study social science research problems:

Allows for a broader study, involving a greater number of subjects, and enhancing the generalization of the results;
Allows for greater objectivity and accuracy of results. Generally, quantitative methods are designed to provide summaries of data that support generalizations about the phenomenon under study. In order to accomplish this, quantitative research usually involves few variables and many cases, and employs prescribed procedures to ensure validity and reliability;
Applying well establshed standards means that the research can be replicated, and then analyzed and compared with similar studies;
You can summarize vast sources of information and make comparisons across categories and over time; and,
Personal bias can be avoided by keeping a 'distance' from participating subjects and using accepted computational techniques .

Babbie, Earl R. The Practice of Social Research . 12th ed. Belmont, CA: Wadsworth Cengage, 2010; Brians, Craig Leonard et al. Empirical Political Analysis: Quantitative and Qualitative Research Methods . 8th ed. Boston, MA: Longman, 2011; McNabb, David E. Research Methods in Public Administration and Nonprofit Management: Quantitative and Qualitative Approaches . 2nd ed. Armonk, NY: M.E. Sharpe, 2008; Singh, Kultar. Quantitative Social Research Methods . Los Angeles, CA: Sage, 2007.

Limitations of Using Quantiative Methods

Some specific limitations associated with using quantitative methods to study research problems in the social sciences include:

Quantitative data is more efficient and able to test hypotheses, but may miss contextual detail;
Uses a static and rigid approach and so employs an inflexible process of discovery;
The development of standard questions by researchers can lead to "structural bias" and false representation, where the data actually reflects the view of the researcher instead of the participating subject;
Results provide less detail on behavior, attitudes, and motivation;
Researcher may collect a much narrower and sometimes superficial dataset;
Results are limited as they provide numerical descriptions rather than detailed narrative and generally provide less elaborate accounts of human perception;
The research is often carried out in an unnatural, artificial environment so that a level of control can be applied to the exercise. This level of control might not normally be in place in the real world thus yielding "laboratory results" as opposed to "real world results"; and,
Preset answers will not necessarily reflect how people really feel about a subject and, in some cases, might just be the closest match to the preconceived hypothesis.

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What Is Quantitative Research?
Revised on June 22, 2023. Quantitative research is the process of collecting and analyzing numerical data. It can be used to find patterns and averages, make predictions, test causal relationships, and generalize results to wider populations. Quantitative research is the opposite of qualitative research, which involves collecting and analyzing ...
Quantitative Research
Quantitative Research. Quantitative research is a type of research that collects and analyzes numerical data to test hypotheses and answer research questions.This research typically involves a large sample size and uses statistical analysis to make inferences about a population based on the data collected.
Quantitative Research
Definition. Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques. Quantitative research focuses on gathering numerical data and generalizing it ...
Organizing Your Social Sciences Research Paper
Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques.Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon.
What Is Quantitative Research?
Revised on 10 October 2022. Quantitative research is the process of collecting and analysing numerical data. It can be used to find patterns and averages, make predictions, test causal relationships, and generalise results to wider populations. Quantitative research is the opposite of qualitative research, which involves collecting and ...
Quantitative Research
Quantitative research as defined in this study uses empirical assessment based on numerical measurements while qualitative methods involve the interpretation of text or other materials without relying on numerical measurement (Zikmund, Babin, Carr, & Griffin, 2013). Within the quantitative methods, survey was the most used data collection process.
Quantitative Data
Quantitative Data Types. There are two main types of quantitative data: discrete and continuous. Discrete data: Discrete data refers to numerical values that can only take on specific, distinct values. This type of data is typically represented as whole numbers and cannot be broken down into smaller units. Examples of discrete data include the ...
What is Quantitative Research?
The data is usually gathered using structured research instruments. The results are based on larger sample sizes that are representative of the population. The research study can usually be replicated or repeated, given its high reliability. Researcher has a clearly defined research question to which objective answers are sought.
Quantitative Methods
Definition. Quantitative method is the collection and analysis of numerical data to answer scientific research questions. Quantitative method is used to summarize, average, find patterns, make predictions, and test causal associations as well as generalizing results to wider populations.
Measurements in quantitative research: how to select and ...
Measures exist to numerically represent degrees of attributes. Quantitative research is based on measurement and is conducted in a systematic, controlled manner. These measures enable researchers to perform statistical tests, analyze differences between groups, and determine the effectiveness of treatments. If something is not measurable, it ...
Data, measurement and empirical methods in the science of science
Liu and coauthors review the major data sources, measures and analysis methods in the science of science, discussing how recent developments in these fields can help researchers to better predict ...
Using Numbers in Qualitative Research
Keywords. The use of numbers in qualitative research is controversial. Particularly since the "paradigm wars" of the 1970s and 1980s, many qualitative researchers have rejected the use of numeri-cal data in their studies and reports for philosophical reasons. Primarily, this is because they have believed that numerical data are incompatible ...
Measurement Issues in Quantitative Research
Abstract. Measurement is central to empirical research whether observational or experimental. Common to all measurements is the systematic application of numerical value (scale) to a variable or a factor we wish to quantify. Measurement can be applied to physical, biological, or chemical attribute or to more complex factors such as human ...
How measurement science can improve confidence in research results
Go to: Abstract. The current push for rigor and reproducibility is driven by a desire for confidence in research results. Here, we suggest a framework for a systematic process, based on consensus principles of measurement science, to guide researchers and reviewers in assessing, documenting, and mitigating the sources of uncertainty in a study.
Conducting and Writing Quantitative and Qualitative Research
In quantitative research, the hypothesis is stated before testing. In qualitative research, the hypothesis is developed through inductive reasoning based on the data collected.27,28 For types of data and their analysis, qualitative research usually includes data in the form of words instead of numbers more commonly used in quantitative research.29
Types of Data
Types of data # In empirical research, we collect and interpret data in order to answer questions about the world. "Data" in this context usually results from some form of "measurement". The notion of measurement here is very broad - it could include familiar acts like using a ruler to measure the length of an object, but it could also include asking a human research subject a ...
Measurement: The Basic Building Block of Research
Measurement in science begins with the activity of distinguishing groups or phenomena from one another. This process, which is generally termed classification, implies that we can place units of scientific study—such as victims, offenders, crimes, or crime places—in clearly defined categories or along some continuum.
What is Qualitative Measurement? Definition and Examples
What is qualitative measurement? Qualitative measurement is a research method used to better understand a topic. It's most often used in projects or studies related to human thoughts and behavior. It involves non-numeric data and characteristics, so it can be observed or surveyed rather than counted or measured.
What Is Qualitative Research?
Qualitative research involves collecting and analyzing non-numerical data (e.g., text, video, or audio) to understand concepts, opinions, or experiences. It can be used to gather in-depth insights into a problem or generate new ideas for research. Qualitative research is the opposite of quantitative research, which involves collecting and ...
A narrative review on types of data and scales of measurement: An
Numerical data are usually summarized and presented by distribution, measures of central tendency and dispersion. For normally distributed data, arithmetic mean and standard deviation are used.
Improving Error Estimates for Evaluating Satellite-Based ...
Estimating the concentration of carbon dioxide (CO 2) in the atmosphere with a high degree of accuracy and precision is an important objective for identifying and quantifying its global sources and sinks as well as for monitoring international agreements aimed at limiting its emissions.Because of the important role played by the increase in atmospheric CO 2 in global change, in addition to in ...
Measurement in social research: some misunderstandings
The concept of numerical measurement based on the manipulation of objects has impoverished and distorted the meaning of magnitude and scale. This article aims to contribute to a concept of the most fruitful measurement for the development of the social sciences, with reference to specific aspects indicating the differences from the natural one and regarding, in particular, the non-numeric.
Quantitative Methods
Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques.Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon.
Resolving bedload flux variability
Bedload transport plays a vital role in shaping Earth's environment by promoting the formation and growth of geological features of various scales, including ripples and dunes, deltas and fans, and laminations and cross-bedding. A key problem hampering our understanding of bedload-induced landscape evolution is the notoriously large variability commonly associated with measurements of bedload ...
Medical Terms in Lay Language
Human Subjects Office / IRB Hardin Library, Suite 105A 600 Newton Rd Iowa City, IA 52242-1098. Voice: 319-335-6564 Fax: 319-335-7310
Possible contamination of Ukraine and neighboring countries by Cs-137
The objective of this research is to assess possible contamination of the territory of Ukraine and neighboring countries by Cs-137, emitted in a hypothetical accident at ZNPP, depending on weather patterns usually observed over the domain. ... depending on weather patterns usually observed over the domain. The assessment is based on numerical ...
Experimental and numerical characterization of a flexible ...
Abstract We demonstrated the feasibility of obtaining a low-cost, flexible strain sensor by spraying a conductive thin layer of MWCNT's over an S-pattern embedded within a PDMS matrix. The final composite conforms a dog bone-shaped tensile specimen intended to measure the strain associated with a human wrist extension movement. Our sensor works with a combination of different mechanisms ...
A three-species model of aeolian saltation incorporating cooperative
Most aeolian sand transport models incorporate a so-called splash function that describes the number and velocity of particles ejected by the splash of an impacting particle. It is usually obtained from experiments or simulations in which an incident grain is shot onto a static granular packing. However, it has recently been discovered that, during aeolian sand transport, the bed cannot be ...
Collect your own data
Quantitative methods emphasize objective measurements and the statistical, mathematical, or numerical analysis of data collected through polls, questionnaires, and surveys, or by manipulating pre-existing statistical data using computational techniques.Quantitative research focuses on gathering numerical data and generalizing it across groups of people or to explain a particular phenomenon.

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Quantitative Data – Types, Methods and Examples

Quantitative Data

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Quantitative Data Gathering Guide

Examples of Quantitative Data

Applications of Quantitative Data

Purpose of Quantitative Data

When to use Quantitative Data

Characteristics of Quantitative Data

Advantages of Quantitative Data

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Conducting and Writing Quantitative and Qualitative Research

Glafera Janet Matanguihan

Atsuko Furuta

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