outcome variable research

13 Predictor and Outcome Variable Examples

A predictor variable is used to predict the occurrence and/or level of another variable, called the outcome variable.

A researcher will measure both variables in a scientific study and then use statistical software to determine if the predictor variable is associated with the outcome variable. If there is a strong correlation, we say the predictor variable has high predictive validity .

This methodology is often used in epidemiological research. Researchers will measure both variables in a given population and then determine the degree of association between the predictor and outcome variable.

This allows scientists to examine the connection between many meaningful variables, such as exercise and health or personality type and depression, just to give a few examples.

Although this type of research can provide significant insights that help us understand a phenomenon, we cannot say that the predictor valuable causes the outcome variable.

In order to use the term ‘cause and effect’, the researcher must be able to control and manipulate the level of a variable and then observe the changes in the other variable.

Definition of Predictor and Outcome Variables

In reality, many variables usually affect the outcome variable. So, researchers will measure numerous predictor variables in the population under study and then determine the degree of association that each one has with the outcome variable.

It sounds a bit complicated, but fortunately, the use of a statistical technique called multiple regression analysis simplifies the process.

As long as the variables are measured accurately and the population size is large, the software will be able to determine which of the predictor variables are associated with the outcome variable and the degree of association.

Not all predictors will have an equal influence on the outcome variable. Some may have a very small impact, some may have a substantial impact, and others may have no impact at all.

Predictor and outcome are not to be confused with independent and dependent variables .

Examples of Predictor and Outcome Variables

1. diet and health.

Does the food you eat have any impact on your physical health? This is a question that a lot of people want to know the answer to.

Many of us have very poor diets, with lots of fast food and salty snacks. Other people, however, almost never make a run through the drive-thru, and consume mostly fruits and veggies.

Thankfully, epidemiological research can give us a relatively straightforward answer. First, researchers measure the quality of diet of each person in a large population.

So, they will track how much fast food and fruits and veggies people consume. There are a lot of different ways to measure this.

Secondly, researchers will measure some aspects of health. This could involve checking cholesterol levels, for example. There are a lot of different ways to measure health. The final step is to input all of the data into the statistical software program and perform the regression analysis to see the results.

Quality of diet is the predictor variable, and health is the outcome variable.

2. Noise Pollution and IQ

One scientist speculates that living in a noisy environment will affect a person’s ability to concentrate, which will then affect their mental acuity and subsequent cognitive development .

So, they decide to conduct a study examining the relationship between noise pollution and IQ.

First, they travel through lots of different neighborhoods and use a sound level meter to assess noise pollution. Some neighborhoods are in the suburbs, and some are near busy highways or construction sites.

Next, they collect data on SAT scores of the children living in those neighborhoods.

They then conduct a regression analysis to determine the connection between the sound level meter data and the SAT scores.

In this example, the predictor variable is the sound levels, and the outcome variable is the SAT scores.

Surprisingly, the results revealed an inverse relationship between noise and SAT scores. That is, the more noise in the environment the higher the SAT score. Any idea why?

3. Family Income and Achievement Test Scores

In this study, sociologists conducted a study examining the relationship between how much income a family has and the achievement test scores of their children.

The researchers collected data from schools on the achievement test scores of hundreds of students and then estimated the household income of the families based on the occupation of the parents.

The results revealed a strong relationship between family income and test scores, such that the higher the family income, the higher the test score of the child.

In this example, family income is the predictor variable, and test score is the outcome variable.

4. Parental Utterances and Children’s Vocabulary

A team of child psychologist is interested in the impact of how much parents talk to their child and that child’s verbal skills.

So, they design a study that involves observing families in the home environment. They randomly choose 50 families to study that live nearby.

A research assistant visits each family, records, and later counts the number of utterances spoken by the mother directed at their only child.

On a different occasion, a second research assistant administers a verbal skills test to every child. Yes, this type of study takes a lot of time.

The regression analysis reveals a direct relationship between the number of utterances from the mother and the child’s verbal skills test score. The more utterances, the higher the score.

In this example, the predictor variable is the number of utterances directed at the child, and the outcome variable is the child’s verbal skills test score.

5. Video Games and Aggressiveness

The debate about the effects of TV violence and video games has been raging for nearly 70 years. There have been hundreds, maybe even thousands of studies conducted on the issue.

One type of study involves assessing how frequently a group of people play certain video games and then tracking their level of aggressiveness over a period of time.

Of course, there are other factors involved in whether a person is aggressive or not, so the researchers might assess those variables as well.

In this type of study, the predictor variable is the frequency of playing video games, and the outcome variable is the level of aggressiveness.

6. Chemicals in Food Products and Puberty

In many countries, farmers may inject various antibiotics and growth hormones into their cattle to ward off infection and increase body mass and milk production.

Unfortunately, those chemicals do not disappear once the food hits the supermarket shelves. Some parents, educators, and food scientists began to notice an association between these agricultural practices and the onset of puberty in young children.

Numerous scientific studies were conducted examining the relationship between these practices and puberty.

So, the researchers studied the relationship between the predictor variable (chemicals in food) and the outcome variable (onset of puberty).

7. Full Moon and Craziness

Who hasn’t heard that a full moon brings out the crazies? A lot of people have theorized that when the moon is full, people get a little bit wild and uninhibited.

That can lead to people doing things they would not normally do.

To put this theory to the test, a group of criminologists decides to examine the police records of numerous large cities and compare that with the lunar cycle.

The researchers input all of the data into a stats program to examine the degree of association between police incidents and the moon.

In this study, the lunar cycle is the predictor variable, and contravention of the law is the outcome variable.  

8. Testosterone and Leadership Style

There are many types of leadership styles. Some leaders are very people-oriented and try to help their employees prosper and feel good about their jobs.

Other leaders are more task-driven and prefer to clearly define objectives, set deadlines, and push their staff to work hard.

To examine the relationship between leadership style and testosterone, a researcher first administers a questionnaire to hundreds of employees in several types of companies. The questionnaire asks the employees to describe the leadership style of their primary supervisor.

At the same time, the researcher also collects data on the testosterone levels of those supervisors and matches them with the questionnaire data.

By examining the association between the two, it will be possible to determine if there is a link between leadership style and testosterone.

The predictor variable is testosterone, and the outcome variable is leadership style.  

9. Personality Type and Driver Safety

A national bus company wants to hire the safest drivers possible. Fewer accidents mean passengers will be safe and their insurance rates will be lower. 

So, the HR staff begin collecting data on the safety records of their drivers over the last 3 years. At the same time, they administer a personality inventory that assesses Type A and Type B personalities.

The Type A personality is intense, impatient, and highly competitive. The Type B personality is easygoing and relaxed. People have varying levels of each type.

The HR department wants to know if there is a relationship between personality type (A or B) and accidents among their drivers.

The predictor variable is personality type, and the outcome variable is the number of accidents.

10. Vitamins and Health

Americans take a lot of vitamins. However, there is some debate about whether vitamins actually do anything to improve health.

There are so many factors that affect health, will taking a daily supplement really count?

So, a group of small vitamin companies pull their resources and hire an outside consulting firm to conduct a large-scale scientific study.

The firm randomly selects thousands of people from throughout the country to participate in the study. The people selected come from a wide range of SES backgrounds, ethnicities, and ages.

Each person is asked to go to a nearby hospital and have a basic health screening that includes cholesterol and blood pressure. They also respond to a questionnaire that asks if they take a multi-vitamin, how many and how often.

The consulting firm then compares the degree of association between multi-vitamins and health.

Multi-vitamin use is the predictor variable, and health is the outcome variable.

11. Automobiles and Climate Change

A group of climatologists has received funding from the EU to conduct a large-scale study on climate change.

The researchers collect data on a wide range of variables that are suspected of affecting the climate. Some of those variables include automobile production, industrial output, size of cattle herds, and deforestation, just to name a few.

The researchers proceed by gathering the data beginning with the 1970s all the way to the current year. They also collect data on yearly temperature fluctuations.

Once all the data is collected, it is put into a stats program, and a few minutes later, the results are revealed.

In this example, there are many predictor variables, such as automobile production, and one primary outcome variable (yearly temperature fluctuations).

12. Smartphone Use and Eye Strain

If you’ve ever noticed, people spend a lot of time looking at their smartphones.

When they are reading, when they are waiting in line, in bed at night, and even when walking from point A to point B.

Many optometrists are concerned that all of this screen time is doing harm to people’s eyesight. So, they decide to conduct a study.

Fortunately, they all work for a nationwide optometry company with offices located in Wal-Marts.

When patients come into their office, they give each one a standard eye exam. They also put a question on the in-take form asking each person to estimate how many hours a day they spend looking at their smartphone screen. 

Then they examine the relation between screen-time usage and the results of the eye exams.

In this study, the predictor variable is screen-time, and the outcome variable is the eye-exam results.

13. Soil Composition and Agricultural Yields

Although farming looks easy, it can be a very scientific enterprise. Agriculturalists study the composition of soil to help determine what type of food will grow best.

Today, they know a lot about which soil nutrients affect the growth of different plant varieties because there have been decades of studies.

The research involves collecting soil samples, measuring crop yields, and then examining the association between the two.

For example, scientists will measure the pH levels, mineral composition, as well as water and air content over many acres of land and relate that to the amount harvested of a particular crop (e.g., corn).

In this example, there are numerous predictor variables, all of which have some effect on crop growth, which is the outcome variable.

Even though there are so many variables to consider, the regression analysis will be able to tell us how important each one is in predicting the outcome variable.

There can be a lot of reasons why something happens. More often than not, nothing happens as a result of just one factor. Our physical health, climate change, and a person’s level of aggressiveness are all the result of numerous factors.

Fortunately for science, there is a brilliant way of determining which factors are connected to a phenomenon and how strong is each and every one of them.

By collecting data on a predictor variable (or variables) and then examining the association with the outcome variable, we can gain valuable insights into just about any subject matter we wish to study.

Ferguson, C. J., & Kilburn, J. (2010). Much ado about nothing: The misestimation and overinterpretation of violent video game effects in Eastern and Western nations: Comment on Anderson et al. (2010). Psychological Bulletin, 136 (2), 174–178. https://doi.org/10.1037/a0018566

Ferguson, C. J., San Miguel, C., Garza, A., & Jerabeck, J. M. (2012). A longitudinal test of video game violence influences on dating and aggression: A 3-year longitudinal study of adolescents, Journal of Psychiatric Research, 46 (2), 141-146. https://doi.org/10.1016/j.jpsychires.2011.10.014

Gordon, R. (2015). Regression Analysis for the Social Sciences (2 nd ed). New York: Routledge.

Hoff, E. (2003). The specificity of environmental influence: Socioeconomic status affects early vocabulary development via maternal speech. Child Development, 74 (5), 1368–1378.

Lopez-Rodriguez, D., Franssen, D., Heger, S., & Parent, AS. (2011). Endocrine-disrupting chemicals and their effects on puberty. Best Practice & Research Clinical Endocrinology & Metabolism, 35 (5), 101579. https://doi.org/10.1016/j.beem.2021.101579

Man, A., Li, H., & Xia, N. (2020). Impact of lifestyles (Diet and Exercise) on vascular health: Oxidative stress and endothelial function. Oxidative Medicine and Cellular Longevity , 1496462. https://doi.org/10.1155/2020/1496462

Thompson, R., Smith, R. B., Karim, Y. B., Shen, C., Drummond, K., Teng, C., & Toledano, M. B. (2022). Noise pollution and human cognition: An updated systematic review and meta-analysis of recent evidence. Environment International , 158 , 106905.

Dave Cornell (PhD)

Dr. Cornell has worked in education for more than 20 years. His work has involved designing teacher certification for Trinity College in London and in-service training for state governments in the United States. He has trained kindergarten teachers in 8 countries and helped businessmen and women open baby centers and kindergartens in 3 countries.

• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 25 Positive Punishment Examples
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 25 Dissociation Examples (Psychology)
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 15 Zone of Proximal Development Examples
• Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ Perception Checking: 15 Examples and Definition

Chris Drew (PhD)

This article was peer-reviewed and edited by Chris Drew (PhD). The review process on Helpful Professor involves having a PhD level expert fact check, edit, and contribute to articles. Reviewers ensure all content reflects expert academic consensus and is backed up with reference to academic studies. Dr. Drew has published over 20 academic articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education and holds a PhD in Education from ACU.

• Chris Drew (PhD) #molongui-disabled-link 25 Positive Punishment Examples
• Chris Drew (PhD) #molongui-disabled-link 25 Dissociation Examples (Psychology)
• Chris Drew (PhD) #molongui-disabled-link 15 Zone of Proximal Development Examples
• Chris Drew (PhD) #molongui-disabled-link Perception Checking: 15 Examples and Definition

1 thought on “13 Predictor and Outcome Variable Examples”

If I want to undertake an interventional study where I measure the Knowledge, attitudes and practices of adolescents in 3 key sexual and reproductive areas. And their parents’ acceptance of ASRH education for their children, and their misconceptions of ASRH. And then I introduce both children and parents to ASRH education. Then I do an end line to look for improvement in the adolescent’s KAP in those 3 areas, and an increased acceptance of ASRH education among parents, what is my predictor variable and outcome variable?

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Quantitative Outcome Variables

• First Online: 31 May 2019

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After a brief summary of Chaps.  1 – 7 , this eighth chapter delves into some important questions when dealing with quantitative outcome variables. Since an example with a quantitative outcome variable and no substantial departures from assumptions is already covered in Chap.  2 , this chapter focusses on three types of somewhat more difficult situations: considerable skewness in a time outcome variable, skewness inherent to the nature of a count outcome variable for perhaps not so frequent (or rare) events, and non-linearity. For each of these three types of situations, different ways of dealing with departure from ‘the typical’ (i.e., Normal and linear) are presented with their advantages and disadvantages.

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Leppink, J. (2019). Quantitative Outcome Variables. In: Statistical Methods for Experimental Research in Education and Psychology. Springer Texts in Education. Springer, Cham. https://doi.org/10.1007/978-3-030-21241-4_8

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COMMON MISTEAKS MISTAKES IN USING STATISTICS: Spotting and Avoiding Them

Glossary      blog, choosing an outcome 1 variable, example 1: how to measure "big", example 2: how to measure "unemployment rate".

• Do not assume you understand what a measure is just because the name makes sense to you. Be sure to find and read the definition carefully; it may not be what you think.
• Be especially careful when making comparisons. The same term might be used differently by different authors or in different places. For example, different countries have different definitions of unemployment rate. (See http://www.bls.gov/fls/flsfaqs.htm#laborforcedefinitions )

Example 3: What is a good outcome variable for deciding whether cancer treatment in a country has been improving?

Example 4: what is a good outcome variable for answering the question, "do males or females suffer more traffic fatalities", example 5: what is a good outcome variable for research on the effect of medication on bone fractures  , statistical considerations.

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Methodology

• Independent vs. Dependent Variables | Definition & Examples

Independent vs. Dependent Variables | Definition & Examples

Published on February 3, 2022 by Pritha Bhandari . Revised on June 22, 2023.

In research, variables are any characteristics that can take on different values, such as height, age, temperature, or test scores.

Researchers often manipulate or measure independent and dependent variables in studies to test cause-and-effect relationships.

• The independent variable is the cause. Its value is independent of other variables in your study.
• The dependent variable is the effect. Its value depends on changes in the independent variable.

Your independent variable is the temperature of the room. You vary the room temperature by making it cooler for half the participants, and warmer for the other half.

Table of contents

What is an independent variable, types of independent variables, what is a dependent variable, identifying independent vs. dependent variables, independent and dependent variables in research, visualizing independent and dependent variables, other interesting articles, frequently asked questions about independent and dependent variables.

An independent variable is the variable you manipulate or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.

Independent variables are also called:

• Explanatory variables (they explain an event or outcome)
• Predictor variables (they can be used to predict the value of a dependent variable)
• Right-hand-side variables (they appear on the right-hand side of a regression equation).

These terms are especially used in statistics , where you estimate the extent to which an independent variable change can explain or predict changes in the dependent variable.

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There are two main types of independent variables.

• Experimental independent variables can be directly manipulated by researchers.
• Subject variables cannot be manipulated by researchers, but they can be used to group research subjects categorically.

Experimental variables

In experiments, you manipulate independent variables directly to see how they affect your dependent variable. The independent variable is usually applied at different levels to see how the outcomes differ.

You can apply just two levels in order to find out if an independent variable has an effect at all.

You can also apply multiple levels to find out how the independent variable affects the dependent variable.

You have three independent variable levels, and each group gets a different level of treatment.

You randomly assign your patients to one of the three groups:

• A low-dose experimental group
• A high-dose experimental group
• A placebo group (to research a possible placebo effect )

A true experiment requires you to randomly assign different levels of an independent variable to your participants.

Random assignment helps you control participant characteristics, so that they don’t affect your experimental results. This helps you to have confidence that your dependent variable results come solely from the independent variable manipulation.

Subject variables

Subject variables are characteristics that vary across participants, and they can’t be manipulated by researchers. For example, gender identity, ethnicity, race, income, and education are all important subject variables that social researchers treat as independent variables.

It’s not possible to randomly assign these to participants, since these are characteristics of already existing groups. Instead, you can create a research design where you compare the outcomes of groups of participants with characteristics. This is a quasi-experimental design because there’s no random assignment. Note that any research methods that use non-random assignment are at risk for research biases like selection bias and sampling bias .

Your independent variable is a subject variable, namely the gender identity of the participants. You have three groups: men, women and other.

Your dependent variable is the brain activity response to hearing infant cries. You record brain activity with fMRI scans when participants hear infant cries without their awareness.

A dependent variable is the variable that changes as a result of the independent variable manipulation. It’s the outcome you’re interested in measuring, and it “depends” on your independent variable.

In statistics , dependent variables are also called:

• Response variables (they respond to a change in another variable)
• Outcome variables (they represent the outcome you want to measure)
• Left-hand-side variables (they appear on the left-hand side of a regression equation)

The dependent variable is what you record after you’ve manipulated the independent variable. You use this measurement data to check whether and to what extent your independent variable influences the dependent variable by conducting statistical analyses.

Based on your findings, you can estimate the degree to which your independent variable variation drives changes in your dependent variable. You can also predict how much your dependent variable will change as a result of variation in the independent variable.

Distinguishing between independent and dependent variables can be tricky when designing a complex study or reading an academic research paper .

A dependent variable from one study can be the independent variable in another study, so it’s important to pay attention to research design .

Here are some tips for identifying each variable type.

Recognizing independent variables

Use this list of questions to check whether you’re dealing with an independent variable:

• Is the variable manipulated, controlled, or used as a subject grouping method by the researcher?
• Does this variable come before the other variable in time?
• Is the researcher trying to understand whether or how this variable affects another variable?

Recognizing dependent variables

Check whether you’re dealing with a dependent variable:

• Is this variable measured as an outcome of the study?
• Is this variable dependent on another variable in the study?
• Does this variable get measured only after other variables are altered?

Independent and dependent variables are generally used in experimental and quasi-experimental research.

Here are some examples of research questions and corresponding independent and dependent variables.

For experimental data, you analyze your results by generating descriptive statistics and visualizing your findings. Then, you select an appropriate statistical test to test your hypothesis .

The type of test is determined by:

• your variable types
• level of measurement
• number of independent variable levels.

You’ll often use t tests or ANOVAs to analyze your data and answer your research questions.

In quantitative research , it’s good practice to use charts or graphs to visualize the results of studies. Generally, the independent variable goes on the x -axis (horizontal) and the dependent variable on the y -axis (vertical).

The type of visualization you use depends on the variable types in your research questions:

• A bar chart is ideal when you have a categorical independent variable.
• A scatter plot or line graph is best when your independent and dependent variables are both quantitative.

To inspect your data, you place your independent variable of treatment level on the x -axis and the dependent variable of blood pressure on the y -axis.

You plot bars for each treatment group before and after the treatment to show the difference in blood pressure.

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.

• Normal distribution
• Degrees of freedom
• Null hypothesis
• Discourse analysis
• Control groups
• Mixed methods research
• Non-probability sampling
• Quantitative research
• Ecological validity

Research bias

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

An independent variable is the variable you manipulate, control, or vary in an experimental study to explore its effects. It’s called “independent” because it’s not influenced by any other variables in the study.

A dependent variable is what changes as a result of the independent variable manipulation in experiments . It’s what you’re interested in measuring, and it “depends” on your independent variable.

In statistics, dependent variables are also called:

Determining cause and effect is one of the most important parts of scientific research. It’s essential to know which is the cause – the independent variable – and which is the effect – the dependent variable.

You want to find out how blood sugar levels are affected by drinking diet soda and regular soda, so you conduct an experiment .

• The type of soda – diet or regular – is the independent variable .
• The level of blood sugar that you measure is the dependent variable – it changes depending on the type of soda.

No. The value of a dependent variable depends on an independent variable, so a variable cannot be both independent and dependent at the same time. It must be either the cause or the effect, not both!

Yes, but including more than one of either type requires multiple research questions .

For example, if you are interested in the effect of a diet on health, you can use multiple measures of health: blood sugar, blood pressure, weight, pulse, and many more. Each of these is its own dependent variable with its own research question.

You could also choose to look at the effect of exercise levels as well as diet, or even the additional effect of the two combined. Each of these is a separate independent variable .

To ensure the internal validity of an experiment , you should only change one independent variable at a time.

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• Published: 31 January 2022

The clinician’s guide to interpreting a regression analysis

• Sofia Bzovsky 1 ,
• Mark R. Phillips   ORCID: orcid.org/0000-0003-0923-261X 2 ,
• Robyn H. Guymer   ORCID: orcid.org/0000-0002-9441-4356 3 , 4 ,
• Charles C. Wykoff 5 , 6 ,
• Lehana Thabane   ORCID: orcid.org/0000-0003-0355-9734 2 , 7 ,
• Mohit Bhandari   ORCID: orcid.org/0000-0001-9608-4808 1 , 2 &
• Varun Chaudhary   ORCID: orcid.org/0000-0002-9988-4146 1 , 2

on behalf of the R.E.T.I.N.A. study group

Eye volume  36 ,  pages 1715–1717 ( 2022 ) Cite this article

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• Outcomes research

Introduction

When researchers are conducting clinical studies to investigate factors associated with, or treatments for disease and conditions to improve patient care and clinical practice, statistical evaluation of the data is often necessary. Regression analysis is an important statistical method that is commonly used to determine the relationship between several factors and disease outcomes or to identify relevant prognostic factors for diseases [ 1 ].

This editorial will acquaint readers with the basic principles of and an approach to interpreting results from two types of regression analyses widely used in ophthalmology: linear, and logistic regression.

Linear regression analysis

Linear regression is used to quantify a linear relationship or association between a continuous response/outcome variable or dependent variable with at least one independent or explanatory variable by fitting a linear equation to observed data [ 1 ]. The variable that the equation solves for, which is the outcome or response of interest, is called the dependent variable [ 1 ]. The variable that is used to explain the value of the dependent variable is called the predictor, explanatory, or independent variable [ 1 ].

In a linear regression model, the dependent variable must be continuous (e.g. intraocular pressure or visual acuity), whereas, the independent variable may be either continuous (e.g. age), binary (e.g. sex), categorical (e.g. age-related macular degeneration stage or diabetic retinopathy severity scale score), or a combination of these [ 1 ].

When investigating the effect or association of a single independent variable on a continuous dependent variable, this type of analysis is called a simple linear regression [ 2 ]. In many circumstances though, a single independent variable may not be enough to adequately explain the dependent variable. Often it is necessary to control for confounders and in these situations, one can perform a multivariable linear regression to study the effect or association with multiple independent variables on the dependent variable [ 1 , 2 ]. When incorporating numerous independent variables, the regression model estimates the effect or contribution of each independent variable while holding the values of all other independent variables constant [ 3 ].

When interpreting the results of a linear regression, there are a few key outputs for each independent variable included in the model:

Estimated regression coefficient—The estimated regression coefficient indicates the direction and strength of the relationship or association between the independent and dependent variables [ 4 ]. Specifically, the regression coefficient describes the change in the dependent variable for each one-unit change in the independent variable, if continuous [ 4 ]. For instance, if examining the relationship between a continuous predictor variable and intra-ocular pressure (dependent variable), a regression coefficient of 2 means that for every one-unit increase in the predictor, there is a two-unit increase in intra-ocular pressure. If the independent variable is binary or categorical, then the one-unit change represents switching from one category to the reference category [ 4 ]. For instance, if examining the relationship between a binary predictor variable, such as sex, where ‘female’ is set as the reference category, and intra-ocular pressure (dependent variable), a regression coefficient of 2 means that, on average, males have an intra-ocular pressure that is 2 mm Hg higher than females.

Confidence Interval (CI)—The CI, typically set at 95%, is a measure of the precision of the coefficient estimate of the independent variable [ 4 ]. A large CI indicates a low level of precision, whereas a small CI indicates a higher precision [ 5 ].

P value—The p value for the regression coefficient indicates whether the relationship between the independent and dependent variables is statistically significant [ 6 ].

Logistic regression analysis

As with linear regression, logistic regression is used to estimate the association between one or more independent variables with a dependent variable [ 7 ]. However, the distinguishing feature in logistic regression is that the dependent variable (outcome) must be binary (or dichotomous), meaning that the variable can only take two different values or levels, such as ‘1 versus 0’ or ‘yes versus no’ [ 2 , 7 ]. The effect size of predictor variables on the dependent variable is best explained using an odds ratio (OR) [ 2 ]. ORs are used to compare the relative odds of the occurrence of the outcome of interest, given exposure to the variable of interest [ 5 ]. An OR equal to 1 means that the odds of the event in one group are the same as the odds of the event in another group; there is no difference [ 8 ]. An OR > 1 implies that one group has a higher odds of having the event compared with the reference group, whereas an OR < 1 means that one group has a lower odds of having an event compared with the reference group [ 8 ]. When interpreting the results of a logistic regression, the key outputs include the OR, CI, and p-value for each independent variable included in the model.

Clinical example

Sen et al. investigated the association between several factors (independent variables) and visual acuity outcomes (dependent variable) in patients receiving anti-vascular endothelial growth factor therapy for macular oedema (DMO) by means of both linear and logistic regression [ 9 ]. Multivariable linear regression demonstrated that age (Estimate −0.33, 95% CI − 0.48 to −0.19, p  < 0.001) was significantly associated with best-corrected visual acuity (BCVA) at 100 weeks at alpha = 0.05 significance level [ 9 ]. The regression coefficient of −0.33 means that the BCVA at 100 weeks decreases by 0.33 with each additional year of older age.

Multivariable logistic regression also demonstrated that age and ellipsoid zone status were statistically significant associated with achieving a BCVA letter score >70 letters at 100 weeks at the alpha = 0.05 significance level. Patients ≥75 years of age were at a decreased odds of achieving a BCVA letter score >70 letters at 100 weeks compared to those <50 years of age, since the OR is less than 1 (OR 0.96, 95% CI 0.94 to 0.98, p  = 0.001) [ 9 ]. Similarly, patients between the ages of 50–74 years were also at a decreased odds of achieving a BCVA letter score >70 letters at 100 weeks compared to those <50 years of age, since the OR is less than 1 (OR 0.15, 95% CI 0.04 to 0.48, p  = 0.001) [ 9 ]. As well, those with a not intact ellipsoid zone were at a decreased odds of achieving a BCVA letter score >70 letters at 100 weeks compared to those with an intact ellipsoid zone (OR 0.20, 95% CI 0.07 to 0.56; p  = 0.002). On the other hand, patients with an ungradable/questionable ellipsoid zone were at an increased odds of achieving a BCVA letter score >70 letters at 100 weeks compared to those with an intact ellipsoid zone, since the OR is greater than 1 (OR 2.26, 95% CI 1.14 to 4.48; p  = 0.02) [ 9 ].

The narrower the CI, the more precise the estimate is; and the smaller the p value (relative to alpha = 0.05), the greater the evidence against the null hypothesis of no effect or association.

Simply put, linear and logistic regression are useful tools for appreciating the relationship between predictor/explanatory and outcome variables for continuous and dichotomous outcomes, respectively, that can be applied in clinical practice, such as to gain an understanding of risk factors associated with a disease of interest.

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Home » Variables in Research – Definition, Types and Examples

Variables in Research – Definition, Types and Examples

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Variables in Research

Definition:

In Research, Variables refer to characteristics or attributes that can be measured, manipulated, or controlled. They are the factors that researchers observe or manipulate to understand the relationship between them and the outcomes of interest.

Types of Variables in Research

Types of Variables in Research are as follows:

Independent Variable

This is the variable that is manipulated by the researcher. It is also known as the predictor variable, as it is used to predict changes in the dependent variable. Examples of independent variables include age, gender, dosage, and treatment type.

Dependent Variable

This is the variable that is measured or observed to determine the effects of the independent variable. It is also known as the outcome variable, as it is the variable that is affected by the independent variable. Examples of dependent variables include blood pressure, test scores, and reaction time.

Confounding Variable

This is a variable that can affect the relationship between the independent variable and the dependent variable. It is a variable that is not being studied but could impact the results of the study. For example, in a study on the effects of a new drug on a disease, a confounding variable could be the patient’s age, as older patients may have more severe symptoms.

Mediating Variable

This is a variable that explains the relationship between the independent variable and the dependent variable. It is a variable that comes in between the independent and dependent variables and is affected by the independent variable, which then affects the dependent variable. For example, in a study on the relationship between exercise and weight loss, the mediating variable could be metabolism, as exercise can increase metabolism, which can then lead to weight loss.

Moderator Variable

This is a variable that affects the strength or direction of the relationship between the independent variable and the dependent variable. It is a variable that influences the effect of the independent variable on the dependent variable. For example, in a study on the effects of caffeine on cognitive performance, the moderator variable could be age, as older adults may be more sensitive to the effects of caffeine than younger adults.

Control Variable

This is a variable that is held constant or controlled by the researcher to ensure that it does not affect the relationship between the independent variable and the dependent variable. Control variables are important to ensure that any observed effects are due to the independent variable and not to other factors. For example, in a study on the effects of a new teaching method on student performance, the control variables could include class size, teacher experience, and student demographics.

Continuous Variable

This is a variable that can take on any value within a certain range. Continuous variables can be measured on a scale and are often used in statistical analyses. Examples of continuous variables include height, weight, and temperature.

Categorical Variable

This is a variable that can take on a limited number of values or categories. Categorical variables can be nominal or ordinal. Nominal variables have no inherent order, while ordinal variables have a natural order. Examples of categorical variables include gender, race, and educational level.

Discrete Variable

This is a variable that can only take on specific values. Discrete variables are often used in counting or frequency analyses. Examples of discrete variables include the number of siblings a person has, the number of times a person exercises in a week, and the number of students in a classroom.

Dummy Variable

This is a variable that takes on only two values, typically 0 and 1, and is used to represent categorical variables in statistical analyses. Dummy variables are often used when a categorical variable cannot be used directly in an analysis. For example, in a study on the effects of gender on income, a dummy variable could be created, with 0 representing female and 1 representing male.

Extraneous Variable

This is a variable that has no relationship with the independent or dependent variable but can affect the outcome of the study. Extraneous variables can lead to erroneous conclusions and can be controlled through random assignment or statistical techniques.

Latent Variable

This is a variable that cannot be directly observed or measured, but is inferred from other variables. Latent variables are often used in psychological or social research to represent constructs such as personality traits, attitudes, or beliefs.

Moderator-mediator Variable

This is a variable that acts both as a moderator and a mediator. It can moderate the relationship between the independent and dependent variables and also mediate the relationship between the independent and dependent variables. Moderator-mediator variables are often used in complex statistical analyses.

Variables Analysis Methods

There are different methods to analyze variables in research, including:

• Descriptive statistics: This involves analyzing and summarizing data using measures such as mean, median, mode, range, standard deviation, and frequency distribution. Descriptive statistics are useful for understanding the basic characteristics of a data set.
• Inferential statistics : This involves making inferences about a population based on sample data. Inferential statistics use techniques such as hypothesis testing, confidence intervals, and regression analysis to draw conclusions from data.
• Correlation analysis: This involves examining the relationship between two or more variables. Correlation analysis can determine the strength and direction of the relationship between variables, and can be used to make predictions about future outcomes.
• Regression analysis: This involves examining the relationship between an independent variable and a dependent variable. Regression analysis can be used to predict the value of the dependent variable based on the value of the independent variable, and can also determine the significance of the relationship between the two variables.
• Factor analysis: This involves identifying patterns and relationships among a large number of variables. Factor analysis can be used to reduce the complexity of a data set and identify underlying factors or dimensions.
• Cluster analysis: This involves grouping data into clusters based on similarities between variables. Cluster analysis can be used to identify patterns or segments within a data set, and can be useful for market segmentation or customer profiling.
• Multivariate analysis : This involves analyzing multiple variables simultaneously. Multivariate analysis can be used to understand complex relationships between variables, and can be useful in fields such as social science, finance, and marketing.

Examples of Variables

• Age : This is a continuous variable that represents the age of an individual in years.
• Gender : This is a categorical variable that represents the biological sex of an individual and can take on values such as male and female.
• Education level: This is a categorical variable that represents the level of education completed by an individual and can take on values such as high school, college, and graduate school.
• Income : This is a continuous variable that represents the amount of money earned by an individual in a year.
• Weight : This is a continuous variable that represents the weight of an individual in kilograms or pounds.
• Ethnicity : This is a categorical variable that represents the ethnic background of an individual and can take on values such as Hispanic, African American, and Asian.
• Time spent on social media : This is a continuous variable that represents the amount of time an individual spends on social media in minutes or hours per day.
• Marital status: This is a categorical variable that represents the marital status of an individual and can take on values such as married, divorced, and single.
• Blood pressure : This is a continuous variable that represents the force of blood against the walls of arteries in millimeters of mercury.
• Job satisfaction : This is a continuous variable that represents an individual’s level of satisfaction with their job and can be measured using a Likert scale.

Applications of Variables

Variables are used in many different applications across various fields. Here are some examples:

• Scientific research: Variables are used in scientific research to understand the relationships between different factors and to make predictions about future outcomes. For example, scientists may study the effects of different variables on plant growth or the impact of environmental factors on animal behavior.
• Business and marketing: Variables are used in business and marketing to understand customer behavior and to make decisions about product development and marketing strategies. For example, businesses may study variables such as consumer preferences, spending habits, and market trends to identify opportunities for growth.
• Healthcare : Variables are used in healthcare to monitor patient health and to make treatment decisions. For example, doctors may use variables such as blood pressure, heart rate, and cholesterol levels to diagnose and treat cardiovascular disease.
• Education : Variables are used in education to measure student performance and to evaluate the effectiveness of teaching strategies. For example, teachers may use variables such as test scores, attendance, and class participation to assess student learning.
• Social sciences : Variables are used in social sciences to study human behavior and to understand the factors that influence social interactions. For example, sociologists may study variables such as income, education level, and family structure to examine patterns of social inequality.

Purpose of Variables

Variables serve several purposes in research, including:

• To provide a way of measuring and quantifying concepts: Variables help researchers measure and quantify abstract concepts such as attitudes, behaviors, and perceptions. By assigning numerical values to these concepts, researchers can analyze and compare data to draw meaningful conclusions.
• To help explain relationships between different factors: Variables help researchers identify and explain relationships between different factors. By analyzing how changes in one variable affect another variable, researchers can gain insight into the complex interplay between different factors.
• To make predictions about future outcomes : Variables help researchers make predictions about future outcomes based on past observations. By analyzing patterns and relationships between different variables, researchers can make informed predictions about how different factors may affect future outcomes.
• To test hypotheses: Variables help researchers test hypotheses and theories. By collecting and analyzing data on different variables, researchers can test whether their predictions are accurate and whether their hypotheses are supported by the evidence.

Characteristics of Variables

Characteristics of Variables are as follows:

• Measurement : Variables can be measured using different scales, such as nominal, ordinal, interval, or ratio scales. The scale used to measure a variable can affect the type of statistical analysis that can be applied.
• Range : Variables have a range of values that they can take on. The range can be finite, such as the number of students in a class, or infinite, such as the range of possible values for a continuous variable like temperature.
• Variability : Variables can have different levels of variability, which refers to the degree to which the values of the variable differ from each other. Highly variable variables have a wide range of values, while low variability variables have values that are more similar to each other.
• Validity and reliability : Variables should be both valid and reliable to ensure accurate and consistent measurement. Validity refers to the extent to which a variable measures what it is intended to measure, while reliability refers to the consistency of the measurement over time.
• Directionality: Some variables have directionality, meaning that the relationship between the variables is not symmetrical. For example, in a study of the relationship between smoking and lung cancer, smoking is the independent variable and lung cancer is the dependent variable.

Advantages of Variables

Here are some of the advantages of using variables in research:

• Control : Variables allow researchers to control the effects of external factors that could influence the outcome of the study. By manipulating and controlling variables, researchers can isolate the effects of specific factors and measure their impact on the outcome.
• Replicability : Variables make it possible for other researchers to replicate the study and test its findings. By defining and measuring variables consistently, other researchers can conduct similar studies to validate the original findings.
• Accuracy : Variables make it possible to measure phenomena accurately and objectively. By defining and measuring variables precisely, researchers can reduce bias and increase the accuracy of their findings.
• Generalizability : Variables allow researchers to generalize their findings to larger populations. By selecting variables that are representative of the population, researchers can draw conclusions that are applicable to a broader range of individuals.
• Clarity : Variables help researchers to communicate their findings more clearly and effectively. By defining and categorizing variables, researchers can organize and present their findings in a way that is easily understandable to others.

Disadvantages of Variables

Here are some of the main disadvantages of using variables in research:

• Simplification : Variables may oversimplify the complexity of real-world phenomena. By breaking down a phenomenon into variables, researchers may lose important information and context, which can affect the accuracy and generalizability of their findings.
• Measurement error : Variables rely on accurate and precise measurement, and measurement error can affect the reliability and validity of research findings. The use of subjective or poorly defined variables can also introduce measurement error into the study.
• Confounding variables : Confounding variables are factors that are not measured but that affect the relationship between the variables of interest. If confounding variables are not accounted for, they can distort or obscure the relationship between the variables of interest.
• Limited scope: Variables are defined by the researcher, and the scope of the study is therefore limited by the researcher’s choice of variables. This can lead to a narrow focus that overlooks important aspects of the phenomenon being studied.
• Ethical concerns: The selection and measurement of variables may raise ethical concerns, especially in studies involving human subjects. For example, using variables that are related to sensitive topics, such as race or sexuality, may raise concerns about privacy and discrimination.

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Types of Variable

All experiments examine some kind of variable(s). A variable is not only something that we measure, but also something that we can manipulate and something we can control for. To understand the characteristics of variables and how we use them in research, this guide is divided into three main sections. First, we illustrate the role of dependent and independent variables. Second, we discuss the difference between experimental and non-experimental research. Finally, we explain how variables can be characterised as either categorical or continuous.

Dependent and Independent Variables

An independent variable, sometimes called an experimental or predictor variable, is a variable that is being manipulated in an experiment in order to observe the effect on a dependent variable, sometimes called an outcome variable.

Imagine that a tutor asks 100 students to complete a maths test. The tutor wants to know why some students perform better than others. Whilst the tutor does not know the answer to this, she thinks that it might be because of two reasons: (1) some students spend more time revising for their test; and (2) some students are naturally more intelligent than others. As such, the tutor decides to investigate the effect of revision time and intelligence on the test performance of the 100 students. The dependent and independent variables for the study are:

Dependent Variable: Test Mark (measured from 0 to 100)

Independent Variables: Revision time (measured in hours) Intelligence (measured using IQ score)

The dependent variable is simply that, a variable that is dependent on an independent variable(s). For example, in our case the test mark that a student achieves is dependent on revision time and intelligence. Whilst revision time and intelligence (the independent variables) may (or may not) cause a change in the test mark (the dependent variable), the reverse is implausible; in other words, whilst the number of hours a student spends revising and the higher a student's IQ score may (or may not) change the test mark that a student achieves, a change in a student's test mark has no bearing on whether a student revises more or is more intelligent (this simply doesn't make sense).

Therefore, the aim of the tutor's investigation is to examine whether these independent variables - revision time and IQ - result in a change in the dependent variable, the students' test scores. However, it is also worth noting that whilst this is the main aim of the experiment, the tutor may also be interested to know if the independent variables - revision time and IQ - are also connected in some way.

In the section on experimental and non-experimental research that follows, we find out a little more about the nature of independent and dependent variables.

Experimental and Non-Experimental Research

• Experimental research : In experimental research, the aim is to manipulate an independent variable(s) and then examine the effect that this change has on a dependent variable(s). Since it is possible to manipulate the independent variable(s), experimental research has the advantage of enabling a researcher to identify a cause and effect between variables. For example, take our example of 100 students completing a maths exam where the dependent variable was the exam mark (measured from 0 to 100), and the independent variables were revision time (measured in hours) and intelligence (measured using IQ score). Here, it would be possible to use an experimental design and manipulate the revision time of the students. The tutor could divide the students into two groups, each made up of 50 students. In "group one", the tutor could ask the students not to do any revision. Alternately, "group two" could be asked to do 20 hours of revision in the two weeks prior to the test. The tutor could then compare the marks that the students achieved.
• Non-experimental research : In non-experimental research, the researcher does not manipulate the independent variable(s). This is not to say that it is impossible to do so, but it will either be impractical or unethical to do so. For example, a researcher may be interested in the effect of illegal, recreational drug use (the independent variable(s)) on certain types of behaviour (the dependent variable(s)). However, whilst possible, it would be unethical to ask individuals to take illegal drugs in order to study what effect this had on certain behaviours. As such, a researcher could ask both drug and non-drug users to complete a questionnaire that had been constructed to indicate the extent to which they exhibited certain behaviours. Whilst it is not possible to identify the cause and effect between the variables, we can still examine the association or relationship between them. In addition to understanding the difference between dependent and independent variables, and experimental and non-experimental research, it is also important to understand the different characteristics amongst variables. This is discussed next.

Categorical and Continuous Variables

Categorical variables are also known as discrete or qualitative variables. Categorical variables can be further categorized as either nominal , ordinal or dichotomous .

• Nominal variables are variables that have two or more categories, but which do not have an intrinsic order. For example, a real estate agent could classify their types of property into distinct categories such as houses, condos, co-ops or bungalows. So "type of property" is a nominal variable with 4 categories called houses, condos, co-ops and bungalows. Of note, the different categories of a nominal variable can also be referred to as groups or levels of the nominal variable. Another example of a nominal variable would be classifying where people live in the USA by state. In this case there will be many more levels of the nominal variable (50 in fact).
• Dichotomous variables are nominal variables which have only two categories or levels. For example, if we were looking at gender, we would most probably categorize somebody as either "male" or "female". This is an example of a dichotomous variable (and also a nominal variable). Another example might be if we asked a person if they owned a mobile phone. Here, we may categorise mobile phone ownership as either "Yes" or "No". In the real estate agent example, if type of property had been classified as either residential or commercial then "type of property" would be a dichotomous variable.
• Ordinal variables are variables that have two or more categories just like nominal variables only the categories can also be ordered or ranked. So if you asked someone if they liked the policies of the Democratic Party and they could answer either "Not very much", "They are OK" or "Yes, a lot" then you have an ordinal variable. Why? Because you have 3 categories, namely "Not very much", "They are OK" and "Yes, a lot" and you can rank them from the most positive (Yes, a lot), to the middle response (They are OK), to the least positive (Not very much). However, whilst we can rank the levels, we cannot place a "value" to them; we cannot say that "They are OK" is twice as positive as "Not very much" for example.

Continuous variables are also known as quantitative variables. Continuous variables can be further categorized as either interval or ratio variables.

• Interval variables are variables for which their central characteristic is that they can be measured along a continuum and they have a numerical value (for example, temperature measured in degrees Celsius or Fahrenheit). So the difference between 20°C and 30°C is the same as 30°C to 40°C. However, temperature measured in degrees Celsius or Fahrenheit is NOT a ratio variable.
• Ratio variables are interval variables, but with the added condition that 0 (zero) of the measurement indicates that there is none of that variable. So, temperature measured in degrees Celsius or Fahrenheit is not a ratio variable because 0°C does not mean there is no temperature. However, temperature measured in Kelvin is a ratio variable as 0 Kelvin (often called absolute zero) indicates that there is no temperature whatsoever. Other examples of ratio variables include height, mass, distance and many more. The name "ratio" reflects the fact that you can use the ratio of measurements. So, for example, a distance of ten metres is twice the distance of 5 metres.

Ambiguities in classifying a type of variable

In some cases, the measurement scale for data is ordinal, but the variable is treated as continuous. For example, a Likert scale that contains five values - strongly agree, agree, neither agree nor disagree, disagree, and strongly disagree - is ordinal. However, where a Likert scale contains seven or more value - strongly agree, moderately agree, agree, neither agree nor disagree, disagree, moderately disagree, and strongly disagree - the underlying scale is sometimes treated as continuous (although where you should do this is a cause of great dispute).

It is worth noting that how we categorise variables is somewhat of a choice. Whilst we categorised gender as a dichotomous variable (you are either male or female), social scientists may disagree with this, arguing that gender is a more complex variable involving more than two distinctions, but also including measurement levels like genderqueer, intersex and transgender. At the same time, some researchers would argue that a Likert scale, even with seven values, should never be treated as a continuous variable.

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The Independent Variable vs. Dependent Variable in Research

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In any scientific research, there are typically two variables of interest: independent variables and dependent variables. In forming the backbone of scientific experiments , they help scientists understand relationships, predict outcomes and, in general, make sense of the factors that they're investigating.

Understanding the independent variable vs. dependent variable is so fundamental to scientific research that you need to have a good handle on both if you want to design your own research study or interpret others' findings.

To grasp the distinction between the two, let's delve into their definitions and roles.

What Is an Independent Variable?

What is a dependent variable, research study example, predictor variables vs. outcome variables, other variables, the relationship between independent and dependent variables.

The independent variable, often denoted as X, is the variable that is manipulated or controlled by the researcher intentionally. It's the factor that researchers believe may have a causal effect on the dependent variable.

In simpler terms, the independent variable is the variable you change or vary in an experiment so you can observe its impact on the dependent variable.

The dependent variable, often represented as Y, is the variable that is observed and measured to determine the outcome of the experiment.

In other words, the dependent variable is the variable that is affected by the changes in the independent variable. The values of the dependent variable always depend on the independent variable.

Let's consider an example to illustrate these concepts. Imagine you're conducting a research study aiming to investigate the effect of studying techniques on test scores among students.

In this scenario, the independent variable manipulated would be the studying technique, which you could vary by employing different methods, such as spaced repetition, summarization or practice testing.

The dependent variable, in this case, would be the test scores of the students. As the researcher following the scientific method , you would manipulate the independent variable (the studying technique) and then measure its impact on the dependent variable (the test scores).

You can also categorize variables as predictor variables or outcome variables. Sometimes a researcher will refer to the independent variable as the predictor variable since they use it to predict or explain changes in the dependent variable, which is also known as the outcome variable.

When conducting an experiment or study, it's crucial to acknowledge the presence of other variables, or extraneous variables, which may influence the outcome of the experiment but are not the focus of study.

These variables can potentially confound the results if they aren't controlled. In the example from above, other variables might include the students' prior knowledge, level of motivation, time spent studying and preferred learning style.

As a researcher, it would be your goal to control these extraneous variables to ensure you can attribute any observed differences in the dependent variable to changes in the independent variable. In practice, however, it's not always possible to control every variable.

The distinction between independent and dependent variables is essential for designing and conducting research studies and experiments effectively.

By manipulating the independent variable and measuring its impact on the dependent variable while controlling for other factors, researchers can gain insights into the factors that influence outcomes in their respective fields.

Whether investigating the effects of a new drug on blood pressure or studying the relationship between socioeconomic factors and academic performance, understanding the role of independent and dependent variables is essential for advancing knowledge and making informed decisions.

Correlation vs. Causation

Understanding the relationship between independent and dependent variables is essential for making sense of research findings. Depending on the nature of this relationship, researchers may identify correlations or infer causation between the variables.

Correlation implies that changes in one variable are associated with changes in another variable, while causation suggests that changes in the independent variable directly cause changes in the dependent variable.

Control and Intervention

In experimental research, the researcher has control over the independent variable, allowing them to manipulate it to observe its effects on the dependent variable. This controlled manipulation distinguishes experiments from other types of research designs.

For example, in observational studies, researchers merely observe variables without intervention, meaning they don't control or manipulate any variables.

Context and Analysis

Whether it's intentional or unintentional, independent, dependent and other variables can vary in different contexts, and their effects may differ based on various factors, such as age, characteristics of the participants, environmental influences and so on.

Researchers employ statistical analysis techniques to measure and analyze the relationships between these variables, helping them to draw meaningful conclusions from their data.

We created this article in conjunction with AI technology, then made sure it was fact-checked and edited by a HowStuffWorks editor.

Please copy/paste the following text to properly cite this HowStuffWorks.com article:

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Outcome variables - Definition & Meaning

What is outcome variables.

Outcome variables are usually the dependent variables which are observed and measured by changing independent variables. These variables determine the effect of the cause (independent) variables when changed for different values. The dependent variables are the outcomes of the experiments determining what was caused or what changed as a result of the study.

For a simple example, the marks a student obtains in an exam is a result of the hard word measured in the number of hours put behind studying and the intelligence measured in IQ are the independent variables. The marks obtained thus represents the dependent or outcome variable. When the values of the independent variables are changed, the marks may or may not change and hence dependent variables are dependent on the independent variables while the opposite is implausible i.e., when the marks are changed, it doesn’t change the number of hours of study or the IQ of the student.

The response variable is also called as the dependent variable because it depends on the causal factor, the independent variable. Depending on the various input values of the experimental variables, the responses are recorded.

This article has been researched & authored by the Business Concepts Team . It has been reviewed & published by the MBA Skool Team. The content on MBA Skool has been created for educational & academic purpose only.

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• Published: 06 April 2024

Statistical analyses of ordinal outcomes in randomised controlled trials: a scoping review

• Chris J. Selman   ORCID: orcid.org/0000-0002-1277-5538 1 , 2 ,
• Katherine J. Lee 1 , 2 ,
• Kristin N. Ferguson 4 ,
• Clare L. Whitehead 4 , 5 ,
• Brett J. Manley 4 , 6 , 7 &
• Robert K. Mahar 1 , 3  

Trials volume  25 , Article number:  241 ( 2024 ) Cite this article

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Randomised controlled trials (RCTs) aim to estimate the causal effect of one or more interventions relative to a control. One type of outcome that can be of interest in an RCT is an ordinal outcome, which is useful to answer clinical questions regarding complex and evolving patient states. The target parameter of interest for an ordinal outcome depends on the research question and the assumptions the analyst is willing to make. This review aimed to provide an overview of how ordinal outcomes have been used and analysed in RCTs.

The review included RCTs with an ordinal primary or secondary outcome published between 2017 and 2022 in four highly ranked medical journals (the British Medical Journal , New England Journal of Medicine , The Lancet , and the Journal of the American Medical Association ) identified through PubMed. Details regarding the study setting, design, the target parameter, and statistical methods used to analyse the ordinal outcome were extracted.

The search identified 309 studies, of which 144 were eligible for inclusion. The most used target parameter was an odds ratio, reported in 78 (54%) studies. The ordinal outcome was dichotomised for analysis in 47 ( \(33\%\) ) studies, and the most common statistical model used to analyse the ordinal outcome on the full ordinal scale was the proportional odds model (64 [ \(44\%\) ] studies). Notably, 86 (60%) studies did not explicitly check or describe the robustness of the assumptions for the statistical method(s) used.

Conclusions

The results of this review indicate that in RCTs that use an ordinal outcome, there is variation in the target parameter and the analytical approaches used, with many dichotomising the ordinal outcome. Few studies provided assurance regarding the appropriateness of the assumptions and methods used to analyse the ordinal outcome. More guidance is needed to improve the transparent reporting of the analysis of ordinal outcomes in future trials.

Peer Review reports

Randomised controlled trials (RCTs) aim to estimate the causal effect of one or more interventions relative to a control or reference intervention. Ordinal outcomes are useful in RCTs because the categories can represent multiple patient states within a single endpoint. The definition of an ordinal outcome is one that comprises monotonically ranked categories that are ordered hierarchically such that the distance between any two categories is not necessarily equal (or even meaningfully quantifiable) [ 1 ]. Ordinal outcomes should have categories that are mutually exclusive and unambiguously defined and can be used to capture improvement and deterioration relative to a baseline value where relevant [ 2 ]. If an ordinal scale is being used to capture change in patient status, then the ordinal outcome should also be symmetric to avoid favouring a better or worse health outcome [ 2 ]. Commonly used ordinal outcomes in RCTs include the modified-Rankin scale, a 7-category measure of disability following stroke or neurological insult [ 3 , 4 , 5 , 6 ], the Glasgow Outcome Scale-Extended (GOS-E), an 8-category measure of functional impairment post traumatic brain injury [ 7 ], and the World Health Organization (WHO) COVID-19 Clinical Progression Scale [ 8 ], an 11-point measure of disease severity among patients with COVID-19. The WHO Clinical Progression Scale, developed specifically for COVID-19 in 2020 [ 8 ], has been used in many RCTs evaluating COVID-19 disease severity and progression [ 9 , 10 ] and has helped to increase the familiarity of ordinal data and modelling approaches for ordinal outcomes for clinicians and statisticians alike [ 11 ].

Randomised controlled trials that use ordinal outcomes need to be designed and analysed with care. This includes the need to explicitly define the target parameter to compare the intervention groups (i.e. the target of estimation, for example, a proportional odds ratio (OR)), the analysis approach, and whether assumptions used in the analysis are valid. Although this is true for all RCTs, these issues are more complex when using an ordinal outcome compared to a binary or continuous outcome. For example, the choice of target parameter for an ordinal outcome depends on both the research question [ 12 , 13 ] and the assumptions that the analyst is willing to make about the data.

One option is to preserve the ordinal nature of the outcome, which can give rise to a number of different target parameters. Principled analysis of ordinal data often relies on less familiar statistical methods and underlying assumptions. Many statistical methods have been proposed to analyse ordinal outcomes. One approach to estimate the effect of treatment on the distribution of ordinal endpoints is to use a cumulative logistic model [ 14 , 15 ]. This model uses the distribution of the cumulative log-odds of the ordinal outcome to estimate a set of ORs [ 16 ], which, for an increase in the value of a covariate, represents the odds of being in the same or higher category at each level of the ordinal scale [ 15 ]. Modelling is vastly simplified by assuming that each covariate in the model exerts the same effect on the cumulative log odds for each binary split of the ordinal outcome, regardless of the threshold. This is known as the proportional odds (PO) assumption, with the model referred to as ordered logistic regression or the PO model (we refer to the latter term herein). The PO model has desirable properties of palindromic invariance (where the estimates of the parameters are not equivalent when the order of the categories are reversed) and invariance under collapsibility (where the estimated target parameter is changed when categories of the response are combined or removed) [ 17 ]. Studies have shown that an ordinal analysis of the outcome using a PO model increases the statistical power relative to an analysis of the dichotomised scale [ 18 , 19 ]. The target parameter from this model, the proportional or common OR, also has a relatively intuitive interpretation [ 20 , 21 ], representing a shift in the distribution of ordinal scale scores toward a better outcome in an intervention group compared to a reference group.

The PO model approach makes the assumption that the odds are proportional for each binary split of the ordinal outcome. If this assumption is violated then the proportional OR may be misleading in certain circumstances. Specifically, violation to PO can affect type I or II errors and/or may distort the magnitude of the treatment effect. For example, violation of proportional odds can increase the likelihood of making a type I error since the model may incorrectly identify evidence of a relationship between the treatment and outcome. Violation of the proportional odds assumption may also increase the likelihood of a type II error as the model may fail to identify a relationship between the treatment and the ordinal outcome because the model may fail to capture the true complexity of the relationship. In addition, a treatment may exert a harmful effect for some categories of the ordinal outcome but exert a beneficial effect for the remaining categories, which can ‘average’ out to no treatment effect when assuming a constant OR across the levels of the ordinal scale. The violation of PO may be harmful if the interest is also to estimate predicted probabilities for the categories of the ordinal scale, which will be too low or high for some outcomes when PO is assumed. Although the PO assumption will ‘average’ the treatment effect across the categories of the ordinal outcome, this may not be a problem if all of the treatment effects for each cut-point are in the same direction and the research aim is to simply show whether the treatment is effective even in the presence of non-PO. If the PO assumption is meaningfully violated and the interest is either in the treatment effect on a specific range of the outcome or to obtain predicted probabilities for each category of the scale, the PO model can be extended to a partial proportional odds (PPO) model which allows the PO assumption to be relaxed for a specific set or for all covariates in the model [ 22 ]. There are two types of PPO models: the unconstrained PPO model, in which the cumulative log-ORs across each cut-point vary freely across some or all of the cut-points [ 23 ], and the constrained PPO model, which assumes some functional relationship between the cumulative log-ORs [ 21 ]. However, such an approach may be more inefficient than using a PO model [ 24 , 25 ].

Alternative statistical methods that can be used to analyse the ordinal outcome include multinomial regression, which estimates an OR for each category of the ordinal outcome relative to the baseline category. The disadvantage of multinomial regression is that the number of ORs requiring estimation increases with the number of categories in the ordinal outcome. A larger sample size may therefore be required to ensure accurate precision of the many target parameters. Other methods are the continuation ratio model or adjacent-category logistic model, though these models lack two desirable properties: palindromic invariance and invariance under collapsibility [ 15 , 17 , 26 ].

Another option is to use alternative methods, such as the Mann-Whitney U  test or Wilcoxon rank-sum test [ 27 ] (referred to as the Wilcoxon test herein). The Wilcoxon test is equivalent to the PO model with a single binary exposure variable [ 15 , 28 ]. The treatment effect from a Wilcoxon test is the concordance probability that represents the probability that a randomly chosen observation from a treatment group is greater than a randomly chosen observation from a control group [ 29 , 30 ]. This parameter closely mirrors the OR derived from the PO model. Importantly, the direction of the OR from the PO model always agrees with the direction of the concordance probability. The disadvantages of the Wilcoxon test are that the concordance probability may be unfamiliar to clinicians, and the Wilcoxon test cannot be adjusted for covariates.

Another option is to dichotomise the ordinal outcome and use an OR or risk difference as the target parameter, estimated using logistic or binomial regression. This produces an effect estimate with clear clinical interpretations that may be suitable for specific clinical settings. The disadvantage of dichotomising an ordinal outcome is that it means discarding potentially useful information within the levels of the scale. This means that the trial may require a larger sample size to maintain the same level of statistical power to detect a clinically important treatment effect [ 19 ], which may not be feasible in all RCTs depending on cost constraints or the rate of recruitment. The decision to dichotomise may also depend on when the outcome is being measured. This was highlighted in a study that showed that an ordinal analysis of the modified-Rankin scale captured differences in long-term outcomes in survivors of stroke better than an analysis that dichotomised the ordinal outcome [ 3 , 31 ].

An alternative to dichotomisation is to treat the ordinal outcome as continuous and focus on the mean difference as the target parameter. This choice to treat the outcome as continuous may be based on the number of categories, where the more categories, the more the outcome resembles a continuum if proximate categories measure similar states or if the scale reflects a latent continuous variable. This has the advantage that modelling is straightforward and familiar, but it can lead to ill-defined clinical interpretations of the treatment effect since the difference between proximate categories is unequal nor quantifiable. Such an analysis also wrongly assumes that the outcome has an unbounded range.

There has been commentary [ 32 ] and research conducted on the methodology of using ordinal outcomes in certain RCT settings that have mainly focused on the benefit of an ordinal analysis using a PO model [ 19 , 33 , 34 , 35 ], including investigations into the use of a PPO model when the PO assumption is violated [ 36 ]. However, these studies have primarily focused on a limited number of statistical methods and in mostly specific medical areas such as neurology and may not be applicable more generally. Given the growing use of ordinal outcomes in RCTs, it is crucial to gain a deeper understanding of how ordinal outcomes are utilised in practice. This understanding will help identify any issues in the use of ordinal outcomes in RCTs and facilitate discussions on improving the reporting and analysis of such outcomes. To address this, we conducted a scoping review to systematically examine the use and analysis of ordinal outcomes in the current literature. Specifically, we aimed to:

Identify which target parameters are of interest in RCTs that use an ordinal outcome and whether these are explicitly defined.

Describe how ordinal outcomes are analysed in RCTs to estimate a treatment effect.

Describe whether RCTs that use an ordinal outcome adequately report key methodological aspects specific to the analysis of the ordinal outcome.

A pre-specified protocol was developed for this scoping review [ 37 ]. Deviations from the protocol are outlined in Additional file 1 . Here, we provide an overview of the protocol and present the findings from the review which have been reported using the Preferred Reporting Items for Systematic Reviews and Meta-Analyses extension for Scoping Reviews (PRISMA-ScR) checklist [ 38 ].

Eligibility criteria

Studies were included in the review if they were published in one of four highly ranked medical journals ( British Medical Journal (BMJ), New England Journal of Medical (NEJM), Journal of the American Medical Association (JAMA), or The Lancet) between 1 January 2017 and 31 July 2022 and reported the results of at least one RCT (e.g. if reporting results from multiple trials) with either a primary or secondary outcome that was measured on an ordinal scale. These journals were chosen because they are leading medical journals that publish original and peer-reviewed research with primarily clinical aims and have been used in other reviews of trial methodology [ 39 , 40 ]. RCTs were defined using the Cochrane definition of an RCT, which is a study that prospectively assigns individuals to one of two (or more) interventions using some random or quasi-random method of allocation [ 41 ].

Studies were excluded from this review if they were written in a language other than English, since we did not have sufficient resources to translate studies written in another language. We also excluded studies which were purely methodological, where the abstract or full-text was not available, which reported data from non-human subjects, and those that provided a commentary, review opinion, or were description only. Manuscripts that reported only a trial protocol or statistical analysis plan were also excluded, since one of the main objectives of this review was to determine which statistical methods are being used to analyse trial data. Studies that used ordinal outcomes that were measured on a numerical rating or visual analogue scale were also excluded. Although these scales are often considered ordinal, they imply equidistance between contiguous categories, and can conceivably be analysed as continuous data.

Information sources

Studies were identified and included in the review by searching the online bibliographic database, PubMed, executed on 3 August, 2022.

Search strategy

The search strategy for this review was developed by CJS in consultation with KJL and RKM. The search strategy employed terms that have been developed to identify RCTs [ 41 ] and terms that have been used to describe an ordinal outcome in published manuscripts for RCTs. The complete search strategy that was used in this review is described in Table 1 .

Selection of sources of evidence

There was no pre-specified sample size for this review. All eligible studies that were identified via the search strategy were included in the review.

Piloting of the eligibility criteria was conducted by CJS and RKM who independently assessed the titles and abstracts of 20 studies to ensure consistency between reviewers. CJS then performed the search on the PubMed database. All titles and abstracts identified were extracted into Covidence, a web-based tool for managing systematic reviews [ 42 ]. A two-phase screening process was employed, where all abstracts and titles were screened by CJS in the first phase. Those studies that were not excluded were then moved to the second phase of the screening process, where the full text was evaluated against the eligibility criteria by CJS. A random sample of 40 studies were also assessed for eligibility by a second reviewer (one of KJL, RKM, BJM, or CLW). All studies that were deemed eligible were included in the data extraction.

Data extraction

A data extraction questionnaire was developed in Covidence [ 42 ] and piloted by CJS and RKM using a sample of 10 studies, which was further refined. The final version of the questionnaire is shown in Additional file 2 , and a full list of the data extraction items is provided in Table 2 . Data was extracted from both the main manuscript and any supplementary material, including statistical analysis plans. CJS extracted data from all eligible studies in the review. Double data extraction was performed by KJL and RKM on a random sample of 20 studies. Any uncertainties in the screening and data extraction process were discussed and resolved by consensus among all reviewers. Simplifications and assumptions that were made for eligibility and data extraction are outlined in Additional file 1 .

Synthesis of results

The data extracted from Covidence were cleaned and analysed using Stata [ 43 ]. Descriptive statistics were used to summarise the data. Frequencies and percentages and medians and interquartile ranges (IQRs) were reported for categorical and continuous variables respectively. Qualitative data were synthesised in a narrative format.

Results of the search

The initial search identified 309 studies, of which 46 were excluded for not being an RCT. There were 263 studies that underwent full text review. Of these, 119 were excluded: 110 because they did not have an ordinal outcome, and nine because they were not an RCT. In total, 144 studies were eligible for data extraction [ 44 , 45 , 46 , 47 , 48 , 49 , 50 , 51 , 52 , 53 , 54 , 55 , 56 , 57 , 58 , 59 , 60 , 61 , 62 , 63 , 64 , 65 , 66 , 67 , 68 , 69 , 70 , 71 , 72 , 73 , 74 , 75 , 76 , 77 , 78 , 79 , 80 , 81 , 82 , 83 , 84 , 85 , 86 , 87 , 88 , 89 , 90 , 91 , 92 , 93 , 94 , 95 , 96 , 97 , 98 , 99 , 100 , 101 , 102 , 103 , 104 , 105 , 106 , 107 , 108 , 109 , 110 , 111 , 112 , 113 , 114 , 115 , 116 , 117 , 118 , 119 , 120 , 121 , 122 , 123 , 124 , 125 , 126 , 127 , 128 , 129 , 130 , 131 , 132 , 133 , 134 , 135 , 136 , 137 , 138 , 139 , 140 , 141 , 142 , 143 , 144 , 145 , 146 , 147 , 148 , 149 , 150 , 151 , 152 , 153 , 154 , 155 , 156 , 157 , 158 , 159 , 160 , 161 , 162 , 163 , 164 , 165 , 166 , 167 , 168 , 169 , 170 , 171 , 172 , 173 , 174 , 175 , 176 , 177 , 178 , 179 , 180 , 181 , 182 , 183 , 184 , 185 , 186 , 187 ]. A flow diagram of the study selection is shown in Fig. 1 . The questionnaire that was used to extract the data from each study is provided in Additional file 2 .

Flow diagram of the study

Study characteristics

A summary of the study characteristics is presented in Table 3 . The highest proportion of studies were published in the NEJM (61 studies, \(42\%\) ), followed by JAMA (40, 28%) and The Lancet (34, 24%), with only nine studies published in the BMJ ( \(6\%\) ). The number of studies that used an ordinal outcome were higher in 2020 and 2021 ( \(30, 21\%\) in each year) compared to earlier years ( \(21, 15\%\) in 2019, \(24, 17\%\) in 2018 and \(23, 16\%\) in 2017). Nearly all studies were conducted in a clinical setting ( \(141, 98\%\) ). The most common medical condition being studied was stroke ( \(39, 28\%\) ), followed by COVID-19 ( \(22, 16\%\) ) and atopic dermatitis ( \(6, 4\%\) ). The most common medical field was neurology ( \(54, 38\%\) ) followed by infectious diseases ( \(22, 16\%\) , all of which were COVID-19 studies), dermatology ( \(13, 9\%\) ), and psychiatry ( \(12, 9\%\) ). Studies were mostly funded by public sources ( \(104, 72\%\) ). The median number of participants in the primary analysis of the ordinal outcome was 380 (interquartile range (IQR): 202–803).

Of the 144 included studies, 58 (40%) used some form of adaptive design, with 47 ( \(33\%\) ) having explicitly defined early stopping rules for efficacy or futility, 18 ( \(13\%\) ) used sample size re-estimation, three ( \(2\%\) ) used response adaptive randomisation, three ( \(2\%\) ) used covariate adaptive randomisation, three ( \(2\%\) ) were platform trials, and three ( \(2\%\) ) used adaptive enrichment that focused on specific subgroups of patients.

Ordinal outcomes and target parameters

A summary of the properties of the ordinal outcomes used in the studies is shown in Table 4 . An ordinal scale was used as a primary outcome in 59 ( \(41\%\) ) of studies. Most studies used an ordinal scale to describe an outcome at a single point in time ( \(128, 89\%\) ), with 16 studies using an ordinal outcome to capture changes over time ( \(11\%\) ). One study used a Likert scale where the categories were ambiguously defined in the manuscript. Another study used an ordinal outcome to measure change over time, but it was asymmetric and biased towards a favourable outcome. The median number of categories in the ordinal outcome was 7 (IQR: 6–7) and ranged from 3 to 23 categories.

There were 32 studies that determined the sample size in advance based on the ordinal outcome, of which 26 out of 32 studies ( \(81\%\) ) used an analytical approach and 6 out of 32 studies ( \(19\%\) ) used simulation to estimate the sample size. Among those studies that used an analytical approach, five studies reported to have used the Whitehead method and three studies reported to have used a t -test. Among the remaining studies that used an analytical approach, it was unclear which specific method was used to compute the sample size.

The ordinal outcome was dichotomised for analysis in 47 ( \(33\%\) ) studies. Some justifications for the dichotomisation of the ordinal outcome included that it represented a clinically meaningful effect and/or that it was common in the analysis of the outcome in similar studies (reported in 24 studies), that the dichotomised outcome represented an agreeable endpoint based on feedback between clinicians and/or patients and families (two studies), or that the assumptions of the statistical model for the categorical outcome were violated (reported in three studies).

There were a variety of target parameters used for the ordinal outcomes. In 130 studies, the target parameter could be determined; however, 59 of these studies ( \(45\%\) ) did not clearly or explicitly define the target parameter of interest. Of those where the target parameter could be determined based on the information provided in the manuscript (e.g. since it was not reported), an OR was the most common target parameter ( \(78, 54\%\) ), followed by a risk difference ( \(31, 22\%\) ). A difference in mean or median was the target parameter in 11 (8%) and 8 (6%) studies respectively. There were 14 ( \(10\%\) ) studies that did not estimate a target parameter. This was either because the study was descriptive in nature, the analysis used a non-parametric procedure, or the target parameter could not be determined (or some combination thereof).

Statistical methods and assumptions

There was a variety of descriptive measures used to summarise the distribution of the ordinal outcome by intervention groups (Table 5 ). The most common descriptive statistics were frequencies and/or percentages in each category of the ordinal outcome ( \(116, 81\%\) ), followed by the median score across all categories ( \(33, 23\%\) ) and IQRs ( \(31, 22\%\) ). The mean and standard deviation across the categories of the ordinal outcome were only summarised in 16 (11%) and 10 (7%) studies respectively.

Many different statistical methods were used to analyse the ordinal outcome (Table 5 ). The PO model was the most common statistical method used to analyse the ordinal outcome (64, \(44\%\) ) that was used to estimate a proportional OR in 62 studies. In studies that used a PO model for the analysis, the interpretation of the target parameter varied between studies (see Additional file 3 ). The most frequent definition used was that the proportional OR represented an ordinal shift in the distribution of ordinal scale scores toward a better outcome in the intervention relative to the control group ( \(12, 19\%\) ). When the outcome was dichotomised, logistic regression was used in 16 studies ( \(11\%\) of all studies) that usually estimated an OR or a risk difference using g-computation. Seven studies estimated a risk difference or risk ratio using binomial regression. Studies also calculated and reported a risk difference with corresponding \(95\%\) confidence intervals estimated using methods such as the Wald method or bootstrapping ( \(31, 22\%\) ). There were 19 (13%) studies that used a non-parametric method to analyse the ordinal outcome (either dichotomised or not), including the Cochran-Mantel-Haenszel test ( \(15, 10\%\) ) to estimate an odds ratio, the Wilcoxon test ( \(14, 10\%\) ), of which no study reported a concordance probability as the target parameter, or the Fisher’s exact or Chi-Square test (12, \(8\%\) ). Other statistical methods that were used were the Hodges-Lehmann estimator, used to estimate a median difference ( \(3, 2\%\) ) and the Van Elteren test ( \(2, 1\%\) ), an extension of the Wilcoxon test for comparing treatments in a stratified experiment. Linear regression was used in 16 ( \(11\%\) ) studies that tended to estimate a mean or risk difference (despite the model having an unbounded support).

The majority of studies ( \(86, 60\%\) ) did not explicitly check the validity of the assumptions for the statistical method(s) used. For example, no study that analysed the ordinal outcome using linear regression commented on the appropriateness of assigning specific numbers of the outcome categories. Among the 64 studies that used a PO model, 20 (31%) did not report whether the assumption of PO was satisfied. Overall, there were 46 studies that reported checking key modelling assumptions; however, the method that was used to check these assumptions were not reported in 6 ( \(13\%)\) of these studies. The most common way to verify model assumptions was to use statistical methods ( \(31, 67\%\) ), followed by graphical methods ( \(2, 4\%\) ).

Among the 44 studies that assessed the validity of the PO assumption for a PO model, 13 studies ( \(30\%\) ) used a likelihood ratio test, 10 studies ( \(23\%\) ) used the Brant test, and 10 studies ( \(23\%\) ) also used the Score test. Six ( \(14\%\) ) studies assessed the robustness of the PO assumption by fitting a logistic regression model to every level of the ordinal outcome across the scale, in which the OR for each dichotomous break was presented. Two studies assessed the PO assumption using graphical methods, which plotted either the inverse cumulative log odds or the empirical cumulative log odds. It was unclear which method was used to assess the PO assumption in ten studies that reported to have checked the assumption.

There were 12 studies ( \(8\%\) ) that reported using a different statistical method than originally planned. Ten of these studies had originally planned to use a PO model, but the PO assumption was determined to have been violated and an alternative method was chosen. One study removed the covariate that was reported to have violated the PO assumption and still used a PO model to analyse the outcome. Two studies used an unconstrained PPO model that reported an adjusted OR for each binary split of the ordinal outcome. Three studies used a Wilcoxon test, with one study stratifying by a baseline covariate that violated the PO assumption. Another study dichotomised the ordinal outcome for the analysis. One study used a Van Elteren test that estimated a median difference (which inappropriately assumes that there is an equal distance between proximate categories), another used a Poisson model with robust standard errors, and one study retained the analysis despite the violation in PO. Notably, a PPO model was not reported to have been used in studies that reported that a covariate other than the treatment violated the PO assumption. Seven studies also did not report which covariate(s) violated the PO assumption.

Frequentist inference was the most common framework for conducting the analysis (133, 92%), with Bayesian methods being used in eight (6%) studies (where two studies used both), of which all eight studies used an adaptive design. Of those using Bayesian methods, seven studies used a Bayesian PO model for analysis. Of these studies, four used a Dirichlet prior distribution to model the baseline probabilities, and three used a normally distributed prior on the proportional log-OR scale. Two of these studies reported to use the median proportional OR with corresponding \(95\%\) credible interval, while one study reported the mean proportional OR. Three studies reported that the models were fitted with the use of a Markov-chain Monte Carlo algorithm with either 10, 000 (one study) or 100, 000 (two studies) samples from the joint posterior distribution. No study reported how the goodness-of-fit of the model was assessed.

For the 38 studies that collected repeated measurements on the ordinal outcome, 18 adjusted for the baseline measurement ( \(47\%\) ), 14 used mixed effects models ( \(37\%\) ), and four used generalised estimated equations ( \(11\%\) ) to capture the correlation among the repeated measures for an individual.

A range of statistical packages were used for the analysis of the ordinal outcome, with SAS ( \(81, 56\%\) ) and R ( \(35, 24\%\) ) being most common. Twelve ( \(8\%\) ) studies did not report the software used.

This review has provided an overview of how ordinal outcomes are used and analysed in contemporary RCTs. We describe the insight this review has provided on the study design, statistical analyses and reporting of trials using ordinal outcomes.

Target parameter

The target parameter of interest is an important consideration when planning any trial and should be aligned with the research question [ 12 , 13 ]. The most common target parameter in this review was an OR, either for a dichotomised version of the ordinal outcome or in an analysis that used the ordinal scale. When an ordinal analysis was used, it was common that the target parameter was a proportional OR, although there was variation in the interpretation of this parameter between studies. We found that it was most common to interpret the proportional OR as an average shift in the distribution of the ordinal scale scores toward a better outcome in the intervention, relative to the comparator(s) [ 19 , 35 , 188 , 189 ]. In the studies that dichotomised the ordinal outcome, many lacked justification for doing so and, in one case, dichotomisation was used only due to the violation of PO, despite the fact that this changed the target parameter.

Some studies in our review treated the ordinal outcome as if it were continuous, and used a difference in means or medians as the target parameter. These quantities do not represent a clinically meaningful effect when the outcome is ordinal, since proximate categories in the scale are not necessarily separated by a quantifiable or equal distance, which can affect the translation of the trial results into practice. If a study is to use a mean difference then the researchers should justify the appropriateness of assigning specific numbers used to the ordinal outcome categories.

The target parameter and statistical method used to estimate it could not be determined in some studies. Notably, the definition of the target parameter was not explicitly defined in almost half of the studies, despite the current recommendations on the importance of clearly defining the estimand of interest, one component of which is the target parameter [ 12 , 13 ]. Furthermore, there is a lack of clarity in defining the target parameter when a PO model was used, despite the interpretation being analogous to the OR for a binary outcome, but applying to an interval of the ordinal scale instead of a single value. Consistency in the definition of a target parameter in RCTs can allow easy interpretation for clinicians and applied researchers. Explicit definition of the target parameter of interest is essential for readers to understand the interpretation of a clinically meaningful treatment effect, and also reflects the present push within clinical research with regards to estimands [ 12 , 13 ].

Statistical methods

It is important to summarise the distribution of the outcome by intervention group in any RCT. When the outcome is ordinal, frequencies and percentages in each category can provide a useful summary of this distribution. Most studies in this review reported frequencies and percentages in each category, although some studies that dichotomised the outcome only reported these summaries for the dichotomised scale. Some studies reported means and standard deviations across the categories which, as mentioned previously, may not have a valid interpretation.

Although there are a range of statistical methods that can be used to analyse an ordinal outcome, we found that the PO model was the most commonly used. This is likely because the PO model is relatively well-known among statisticians and is quite straightforward to fit in most statistical packages, and it possesses the desirable properties of palindromic invariance and invariance under collapsibility. However, when using this approach to estimate a specific treatment effect across all levels of the outcome, it is important to assess and report whether the PO assumption has been met when the aim is to estimate the treatment effect across the different categories or to estimate predicted probabilities in each category. The validity of the PO assumption is less important when the objective is to understand whether one treatment is ‘better’ on average compared to a comparator. In this review, it was common for studies that used a PO model to define the target parameter that related to a treatment benefiting patients with regard to every level of the outcome scale. However, only 44 out of 64 studies reported to have checked the PO assumption, which highlights the deficiency in this practice. Statistical methods were commonly used to assess the PO assumption, although it may be preferable to avoid hypothesis testing when assessing the PO assumption, particularly with small sample sizes, as these statistical tests can have poor statistical power [ 22 , 190 ]. Also, researchers should keep in mind that when the PO assumption is tested, the type I error of the analysis may change and that p -values and confidence intervals based on the updated model ignore the model-fitting uncertainty [ 191 ].

When the PO assumption was violated, a PPO model was rarely used, and instead baseline covariates were removed from the model to address the departure to PO. The fact that the PPO model is underused could be due to a lack of knowledge that such models exist and can be used to address violations in PO. Such a model could have been particularly useful in these studies that had only covariates other than the treatment variable that violated the PO assumption, as the PPO model could have been used to estimate a single proportional OR for the treatment effect. Of note, however, is that an unconstrained PPO model does not necessarily require ordinality as the categories can be arranged and the model fit would be hardly affected [ 192 ], and that estimated probabilities can be negative [ 193 ].

There are other methods that can be used to assess the validity of the PO assumption, such as plotting the differences in predicted log-odds between different categories of the ordinal outcome that should be parallel [ 16 ]. Another option is to fit a logistic regression model to every level of the ordinal outcome across the scale and compare the estimated ORs and corresponding confidence interval for each binary split of the ordinal outcome or simulating predictive distributions. However, estimating separate ORs in this way can be inefficient, particularly when the ordinal outcome has a high number of categories. Arguably, more important than assessing the validity of the PO assumption is to assess the impact of making compared to not making the assumption. If the treatment effect goes in the same direction across each category of the ordinal scale and the objective is to simply understand whether one treatment is better overall, then departures from PO may not be important. If, however, the interest is in estimating a treatment effect for every level of the ordinal outcome and/or the treatment has a detrimental effect for one end of the ordinal scale but a beneficial effect for the remaining categories, there should be careful consideration as to the validity to the type I and II error and the treatment effect if the PO model is used.

Finally, a handful of studies also used the Wilcoxon, Chi-Square, or Fisher’s exact test (the latter being too conservative [ 194 ] and potentially providing misleading results), where commonly only a p -value, not a target parameter, was reported when these methods were used. The lack of a target parameter for the treatment effect can make it difficult for clinicians to translate the results to practice.

Strengths and limitations

The strengths of this study are that we present a review of a large number of RCTs that used ordinal outcomes published in four highly ranked medical journals to highlight the current state of practice for analysing ordinal outcomes. The screening and data extraction process was conducted systematically, and pilot tests and double data extraction ensured the consistency and reliability of the extracted data. The PRISMA-ScR checklist was used to ensure that reporting has been conducted to the highest standard.

This review does, however, have limitations. The restriction to the PubMed database and four highly ranked medical journals may affect the generalisability of this review. We made this decision given the scoping nature of the review, to ensure reproducibility and to ensure that the total number of studies included in the review was manageable. We also aimed to include studies that are likely to reflect best practice of how research using ordinal outcomes is being conducted and reported upon at present. Given the selected journals represent highly ranked medical journals, these findings are likely to reflect the best-case scenario given these journals' reputation for rigour. In addition, our search strategy may have missed certain phrases or variants (particularly related to an ordinal outcome); however, we attempted to mitigate this through our piloting phase. Finally, we also did not review the protocol papers of the trials that may have included additional information related to the statistical methodology. This includes methods that were planned to be used to assess the PO assumption, and any alternative methods that were to be used instead.

Implications of this research

This review has implications for researchers designing RCTs that use an ordinal outcome. Although the majority of studies included in this review were in the fields of neurology and infectious diseases, the results of this review would apply to RCTs in all medical fields that use an ordinal outcome. We have shown that there is substantial variation in the analysis and reporting of ordinal outcomes in practice. Our results suggest that researchers should carefully consider the target parameter of interest and explicitly report what the target parameter represents; this is particularly important for an ordinal outcome which can be unfamiliar to readers. Defining the target parameter upfront will help to ensure that appropriate analytical methods are used to analyse the ordinal outcome and make transparent the assumptions the researchers are willing to make.

Our review also highlights the need for careful assessment and reporting of the validity of the model assumptions made during the analysis of an ordinal outcome. Doing so will ensure that robust statistical methods that align with the research question and categorical nature of the ordinal outcome are used to estimate a valid, clinically relevant target parameter that can be translated to practice.

Availability of data and materials

The datasets and code generated and/or analysed during the current study are available on GitHub [ 195 ].

Abbreviations

Randomised controlled trial

Proportional odds

Partial proportional odds

Statistical analysis plan

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Acknowledgements

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This work forms part of Chris Selman’s PhD, which is supported by the Research Training Program Scholarship, administered by the Australian Commonwealth Government and The University of Melbourne, Australia. Chris Selman’s PhD was also supported by a Centre of Research Excellence grant from the National Health and Medical Research Council of Australia ID 1171422, to the Australian Trials Methodology (AusTriM) Research Network. Research at the Murdoch Children’s Research Institute is supported by the Victorian Government’s Operational Infrastructure Support Program. This work was supported by the Australian National Health and Medical Research Council (NHMRC) Centre for Research Excellence grants to the Victorian Centre for Biostatistics (ID1035261) and the Australian Trials Methodology Research Network (ID1171422), including through seed funding awarded to Robert Mahar. Katherine Lee is funded by an NHMRC Career Development Fellowship (ID1127984). Brett Manley is funded by the NHMRC Investigator Grant (Leadership 1). The funding bodies played no role in the study conception, design, data collection, data analysis, data interpretation, or writing of the report.

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CJS, RKM, KJL, CLW, and BJM conceived the study and CJS wrote the first draft of the manuscript. All authors contributed to the design of the study, revision of the manuscript, and take responsibility for its content.

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Additional file 1..

Deviations from the protocol. This presents a summary of the deviations from the protocol, with reasons. We also provide an explanation of any simplifications and assumptions that were made for eligibility criteria and data extraction.

Additional file 2.

Data extraction questionnaire. This is a copy of the data extraction questionnaire that will be used for this review in PDF format.

Additional file 3.

Interpretation of the proportional odds ratio in proportional odds models. This presents a summary of the ways that the proportional odds ratio was interpreted across the studies.

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Selman, C.J., Lee, K.J., Ferguson, K.N. et al. Statistical analyses of ordinal outcomes in randomised controlled trials: a scoping review. Trials 25 , 241 (2024). https://doi.org/10.1186/s13063-024-08072-2

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Received : 02 July 2023

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DOI : https://doi.org/10.1186/s13063-024-08072-2

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ORIGINAL RESEARCH article

This article is part of the research topic.

Mendelian Randomization and Cardiovascular Diseases

No causal association between the volume of strenuous exercise and coronary atherosclerosis: A two-sample Mendelian randomization study Provisionally Accepted

• 1 Nanfang Hospital, Southern Medical University, China
• 2 School of Traditional Chinese Medicine, Southern Medical University, China
• 3 Second Clinical Medical College, Guangzhou University of Traditional Chinese Medicine, China

The final, formatted version of the article will be published soon.

Objective: Several observational studies have shown that high-volume and high-intensity exercise training increases the prevalence and severity of coronary atherosclerosis, but the causal effect still remains uncertain. This study aims to explore the causal relationship between the volume of strenuous exercise (SE) and coronary atherosclerosis (CA) using the Mendelian randomization (MR) method.The exposure factors were two basic parameters of the volume of strenuous exercise (duration and frequency of strenuous exercise), the outcome factor was coronary atherosclerosis, and the relevant genetic loci were extracted from the summary data of the genome-wide association study (GWAS) as the instrumental variables, and MR analyses were performed using the inverse variance weighting (IVW) method, the weighted median method, and the MR-egger method. Sensitivity analyses were performed using heterogeneity analysis, pleiotropy analysis, and the "leave-one-out" method. The original results were tested using other coronary atherosclerosis data sets.Result: IVW results showed no causal association between duration of strenuous exercise (DOSE) [OR=0.9937, 95% CI (0.9847, 1.0028), P=0.1757] and frequency of strenuous exercise (FOSE) in the last 4 weeks [OR=0.9930, 95% CI (0.9808, 1.0054), P=0.2660] and coronary atherosclerosis. All of the above results were validated with other coronary atherosclerosis data sets.The present study supports that the causal association of duration and frequency of SE with CA was not found, and provides valuable insights into the choice of scientific and correct volume of SE to cardiac rehabilitation (CR).

Keywords: Mendelian randomization, the volume of strenuous exercise, Coronary atherosclerosis, Cardiac Rehabilitation, Genome-Wide Association Study, High-intensity interval training

Received: 26 Nov 2023; Accepted: 11 Apr 2024.

Copyright: © 2024 Xiao, Huang, Li, Wang, Zheng, Li, Gong, Lv and Li. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY) . The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

* Correspondence: Mx. Jingjun Li, Nanfang Hospital, Southern Medical University, Guangzhou, 510515, Guangdong Province, China

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A Student’s Guide to the Classification and Operationalization of Variables in the Conceptualization and Design of a Clinical Study: Part 1

Chittaranjan andrade.

1 Dept. of Clinical Psychopharmacology and Neurotoxicology, National Institute of Mental Health and Neurosciences, Bengaluru, Karnataka, India.

Students without prior research experience may not know how to conceptualize and design a study. This article explains how an understanding of the classification and operationalization of variables is the key to the process. Variables describe aspects of the sample that is under study; they are so called because they vary in value from subject to subject in the sample. Variables may be independent or dependent. Independent variables influence the value of other variables; dependent variables are influenced in value by other variables. A hypothesis states an expected relationship between variables. A significant relationship between an independent and dependent variable does not prove cause and effect; the relationship may partly or wholly be explained by one or more confounding variables. Variables need to be operationalized; that is, defined in a way that permits their accurate measurement. These and other concepts are explained with the help of clinically relevant examples.

Key Message:

This article explains the following concepts: Independent variables, dependent variables, confounding variables, operationalization of variables, and construction of hypotheses.

In any body of research, the subject of study requires to be described and understood. For example, if we wish to study predictors of response to antidepressant drugs (ADs) in patients with major depressive disorder (MDD), we might select patient age, sex, age at onset of MDD, number of previous episodes of depression, duration of current depressive episode, presence of psychotic symptoms, past history of response to ADs, and other patient and illness characteristics as potential predictors. These characteristics or descriptors are called variables. Whether or not the patient responds to AD treatment is also a variable. A solid understanding of variables is the cornerstone in the conceptualization and preparation of a research protocol, and in the framing of study hypotheses. This subject is presented in two parts. This article, Part 1, explains what independent and dependent variables are, how an understanding of these is important in framing hypotheses, and what operationalization of a variable entails.

Variables are defined as characteristics of the sample that are examined, measured, described, and interpreted. Variables are so called because they vary in value from subject to subject in the study. As an example, if we wish to examine the relationship between age and height in a sample of children, age and height are the variables of interest; their values vary from child to child. In the earlier example, patients vary in age, sex, duration of current depressive episode, and response to ADs. Variables are classified as dependent and independent variables and are usually analyzed as categorical or continuous variables.

Independent and Dependent Variables

Independent variables are defined as those the values of which influence other variables. For example, age, sex, current smoking, LDL cholesterol level, and blood pressure are independent variables because their values (e.g., greater age, positive for current smoking, and higher LDL cholesterol level) influence the risk of myocardial infarction. Dependent variables are defined as those the values of which are influenced by other variables. For example, the risk of myocardial infarction is a dependent variable the value of which is influenced by variables such as age, sex, current smoking, LDL cholesterol level, and blood pressure. The risk is higher in older persons, in men, in current smokers, and so on.

There may be a cause–effect relationship between independent and dependent variables. For example, consider a clinical trial with treatment (iron supplement vs placebo) as the independent variable and hemoglobin level as the dependent variable. In children with anemia, an iron supplement will raise the hemoglobin level to a greater extent than will placebo; this is a cause–effect relationship because iron is necessary for the synthesis of hemoglobin. However, consider the variables teeth and weight . An alien from outer space who has no knowledge of human physiology may study human children below the age of 5 years and find that, as the number of teeth increases, weight increases. Should the alien conclude that there is a cause–effect relationship here, and that growing teeth causes weight gain? No, because a third variable, age, is a confounding variable 1 – 3 that is responsible for both increase in the number of teeth and increase in weight. In general, therefore, it is more proper to state that independent variables are associated with variations in the values of the dependent variables rather than state that independent variables cause variations in the values of the dependent variables. For causality to be asserted, other criteria must be fulfilled; this is out of the scope of the present article, and interested readers may refer to Schunemann et al. 4

As a side note, here, whether a particular variable is independent or dependent will depend on the question that is being asked. For example, in a study of factors influencing patient satisfaction with outpatient department (OPD) services, patient satisfaction is the dependent variable. But, in a study of factors influencing OPD attendance at a hospital, OPD attendance is the dependent variable, and patient satisfaction is merely one of many possible independent variables that can influence OPD attendance.

Importance of Variables in Stating the Research Objectives

Students must have a clear idea about what they want to study in order to conceptualize and frame a research protocol. The first matters that they need to address are “What are my research questions?” and “What are my hypotheses?” Both questions can be answered only after choosing the dependent variables and then the independent variables for study.

In the case of a student who is interested in studying predictors of AD outcomes in patients with MDD, treatment response is the dependent variable and patient and clinical characteristics are possible independent variables. So, the selection of dependent and independent variables helps defines the objectives of the study:

• To determine whether sociodemographic variables, such as age and sex, predict the outcome of an episode of depression in MDD patients who are treated with an AD.
• To determine whether clinical variables, such as age at onset of depression, number of previous depressive episodes, duration of current depressive episode, and the presence of soft neurological signs, predict the outcome of an episode of depression in MDD patients who are treated with an AD.

Note that in a formal research protocol, the student will need to state all the independent variables and not merely list examples. The student may also choose to include additional independent variables, such as baseline biochemical, psychophysiological, and neuroradiological measures.

Importance of Variables in Framing Hypotheses

A hypothesis is a clear statement of what the researcher expects to find in the study. As an example, a researcher may hypothesize that longer duration of current depression is associated with poorer response to ADs. In this hypothesis, the duration of the current episode of depression is the independent variable and treatment response is the dependent variable. It should be obvious, now, that a hypothesis can also be defined as the statement of an expected relationship between an independent and a dependent variable . Or, expressed visually, (independent variable) (arrow) (dependent variable) = hypothesis.

It would be a waste of time and energy to do a study to examine only one question: whether duration of current depression predicts treatment response. So, it is usual for research protocols to include many independent variables and many dependent variables in the generation of many hypotheses, as shown in Table 1 . Pairing each variable in the “independent variable” column with each variable in the “dependent variable” column would result in the generation of these hypotheses. Table 2 shows how this is done for age. Sets of hypotheses can likewise be constructed for the remaining independent and dependent variables in Table 1 . Importantly, the student must select one of these hypotheses as the primary hypothesis; the remaining hypotheses, no matter how many they are, would be secondary hypotheses. It is necessary to have only one hypothesis as the primary hypothesis in order to calculate the sample size necessary for an adequately powered study and to reduce the risk of false positive findings in the analysis. 5 In rare situations, two hypotheses may be considered equally important and may be stated as coprimary hypotheses.

Independent Variables and Dependent Variables in a Study on Sociodemographic and Clinical Prediction of Response of Major Depressive Disorder to Antidepressant Drug Treatment

Combinations of Age with Dependent Variables in the Generation of Hypotheses

Operationalization of Variables

In Table 1 , suicidality is listed as an independent variable and severity of depression, as a dependent variable. These variables need to be operationalized; that is, stated in a way that explains how they will be measured. Table 3 presents three ways in which suicidality can be measured and four ways in which (reduction in) the severity of depression can be measured. Now, each way of measurement in the “independent variable” column can be paired with a way of measurement in the “dependent variable” column, making a total of 12 possible hypotheses. In like manner, the many variables listed in Table 1 can each be operationalized in several different ways, resulting in the generation of a very large number of hypotheses. As already stated, the student must select only one hypothesis as the primary hypothesis.

Possible Ways of Operationalization of Suicidality and Depression

HAM-D: Hamilton Depression Rating Scale, MADRS: Montgomery–Asberg Depression Rating Scale.

Much thought should be given to the operationalization of variables because variables that are carelessly operationalized will be poorly measured; the data collected will then be of poor quality, and the study will yield unreliable results. For example, socioeconomic status may be operationalized as lower, middle, or upper class, depending on the patient’s monthly income, on the total monthly income of the family, or using a validated socioeconomic status assessment scale that takes into consideration income, education, occupation, and place of residence. The student must choose the method that would best suit the needs of the study, and the method that has the greatest scientific acceptability. However, it is also permissible to operationalize the same variable in many different ways and to include all these different operationalizations in the study, as shown in Table 3 . This is because conceptualizing variables in different ways can help understand the subject of the study in different ways.

Operationalization of variables requires a consideration of the reliability and validity of the method of operationalization; discussions on reliability and validity are out of the scope of this article. Operationalization of variables also requires specification of the scale of measurement: nominal, ordinal, interval, or ratio; this is also out of the scope of the present article. Finally, operationalization of variables can also specify details of the measurement procedure. As an example, in a study on the use of metformin to reduce olanzapine-associated weight gain, we may state that we will obtain the weight of the patient but fail to explain how we will do it. Better would be to state that the same weighing scale will be used. Still better would be to state that we will use a weighing instrument that works on the principle of moving weights on a levered arm, and that the same instrument will be used for all patients. And best would be to add that we will weigh patients, dressed in standard hospital gowns, after they have voided their bladder but before they have eaten breakfast. When the way in which a variable will be measured is defined, measurement of that variable becomes more objective and uniform

Concluding Notes

The next article, Part 2, will address what categorical and continuous variables are, why continuous variables should not be converted into categorical variables and when this rule can be broken, and what confounding variables are.

Declaration of Conflicting Interests: The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding: The author received no financial support for the research, authorship, and/or publication of this article.