research outcome variables

13 Predictor and Outcome Variable Examples

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.

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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.

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) https://helpfulprofessor.com/author/dave-cornell-phd/ 23 Achieved Status Examples
Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 25 Defense Mechanisms Examples
Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 15 Theory of Planned Behavior Examples
Dave Cornell (PhD) https://helpfulprofessor.com/author/dave-cornell-phd/ 18 Adaptive Behavior Examples

Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 23 Achieved Status Examples
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 15 Ableism Examples
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 25 Defense Mechanisms Examples
Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 15 Theory of Planned Behavior Examples

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?

Variables in Research – Definition, Types and Examples

Table of Contents

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.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

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By: Derek Jansen (MBA) | Expert Reviewed By: Kerryn Warren (PhD) | January 2023

If you’re new to the world of research, especially scientific research, you’re bound to run into the concept of variables , sooner or later. If you’re feeling a little confused, don’t worry – you’re not the only one! Independent variables, dependent variables, confounding variables – it’s a lot of jargon. In this post, we’ll unpack the terminology surrounding research variables using straightforward language and loads of examples .

Overview: Variables In Research

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What (exactly) is a variable?

The simplest way to understand a variable is as any characteristic or attribute that can experience change or vary over time or context – hence the name “variable”. For example, the dosage of a particular medicine could be classified as a variable, as the amount can vary (i.e., a higher dose or a lower dose). Similarly, gender, age or ethnicity could be considered demographic variables, because each person varies in these respects.

Within research, especially scientific research, variables form the foundation of studies, as researchers are often interested in how one variable impacts another, and the relationships between different variables. For example:

How someone’s age impacts their sleep quality
How different teaching methods impact learning outcomes
How diet impacts weight (gain or loss)

As you can see, variables are often used to explain relationships between different elements and phenomena. In scientific studies, especially experimental studies, the objective is often to understand the causal relationships between variables. In other words, the role of cause and effect between variables. This is achieved by manipulating certain variables while controlling others – and then observing the outcome. But, we’ll get into that a little later…

The “Big 3” Variables

Variables can be a little intimidating for new researchers because there are a wide variety of variables, and oftentimes, there are multiple labels for the same thing. To lay a firm foundation, we’ll first look at the three main types of variables, namely:

Independent variables (IV)
Dependant variables (DV)
Control variables

What is an independent variable?

Simply put, the independent variable is the “ cause ” in the relationship between two (or more) variables. In other words, when the independent variable changes, it has an impact on another variable.

For example:

Increasing the dosage of a medication (Variable A) could result in better (or worse) health outcomes for a patient (Variable B)
Changing a teaching method (Variable A) could impact the test scores that students earn in a standardised test (Variable B)
Varying one’s diet (Variable A) could result in weight loss or gain (Variable B).

It’s useful to know that independent variables can go by a few different names, including, explanatory variables (because they explain an event or outcome) and predictor variables (because they predict the value of another variable). Terminology aside though, the most important takeaway is that independent variables are assumed to be the “cause” in any cause-effect relationship. As you can imagine, these types of variables are of major interest to researchers, as many studies seek to understand the causal factors behind a phenomenon.

Need a helping hand?

What is a dependent variable?

While the independent variable is the “ cause ”, the dependent variable is the “ effect ” – or rather, the affected variable . In other words, the dependent variable is the variable that is assumed to change as a result of a change in the independent variable.

Keeping with the previous example, let’s look at some dependent variables in action:

Health outcomes (DV) could be impacted by dosage changes of a medication (IV)
Students’ scores (DV) could be impacted by teaching methods (IV)
Weight gain or loss (DV) could be impacted by diet (IV)

In scientific studies, researchers will typically pay very close attention to the dependent variable (or variables), carefully measuring any changes in response to hypothesised independent variables. This can be tricky in practice, as it’s not always easy to reliably measure specific phenomena or outcomes – or to be certain that the actual cause of the change is in fact the independent variable.

As the adage goes, correlation is not causation . In other words, just because two variables have a relationship doesn’t mean that it’s a causal relationship – they may just happen to vary together. For example, you could find a correlation between the number of people who own a certain brand of car and the number of people who have a certain type of job. Just because the number of people who own that brand of car and the number of people who have that type of job is correlated, it doesn’t mean that owning that brand of car causes someone to have that type of job or vice versa. The correlation could, for example, be caused by another factor such as income level or age group, which would affect both car ownership and job type.

To confidently establish a causal relationship between an independent variable and a dependent variable (i.e., X causes Y), you’ll typically need an experimental design , where you have complete control over the environmen t and the variables of interest. But even so, this doesn’t always translate into the “real world”. Simply put, what happens in the lab sometimes stays in the lab!

As an alternative to pure experimental research, correlational or “ quasi-experimental ” research (where the researcher cannot manipulate or change variables) can be done on a much larger scale more easily, allowing one to understand specific relationships in the real world. These types of studies also assume some causality between independent and dependent variables, but it’s not always clear. So, if you go this route, you need to be cautious in terms of how you describe the impact and causality between variables and be sure to acknowledge any limitations in your own research.

What is a control variable?

In an experimental design, a control variable (or controlled variable) is a variable that is intentionally held constant to ensure it doesn’t have an influence on any other variables. As a result, this variable remains unchanged throughout the course of the study. In other words, it’s a variable that’s not allowed to vary – tough life 🙂

As we mentioned earlier, one of the major challenges in identifying and measuring causal relationships is that it’s difficult to isolate the impact of variables other than the independent variable. Simply put, there’s always a risk that there are factors beyond the ones you’re specifically looking at that might be impacting the results of your study. So, to minimise the risk of this, researchers will attempt (as best possible) to hold other variables constant . These factors are then considered control variables.

Some examples of variables that you may need to control include:

Temperature
Time of day
Noise or distractions

Which specific variables need to be controlled for will vary tremendously depending on the research project at hand, so there’s no generic list of control variables to consult. As a researcher, you’ll need to think carefully about all the factors that could vary within your research context and then consider how you’ll go about controlling them. A good starting point is to look at previous studies similar to yours and pay close attention to which variables they controlled for.

Of course, you won’t always be able to control every possible variable, and so, in many cases, you’ll just have to acknowledge their potential impact and account for them in the conclusions you draw. Every study has its limitations , so don’t get fixated or discouraged by troublesome variables. Nevertheless, always think carefully about the factors beyond what you’re focusing on – don’t make assumptions!

A control variable is intentionally held constant (it doesn't vary) to ensure it doesn’t have an influence on any other variables.

Other types of variables

As we mentioned, independent, dependent and control variables are the most common variables you’ll come across in your research, but they’re certainly not the only ones you need to be aware of. Next, we’ll look at a few “secondary” variables that you need to keep in mind as you design your research.

Moderating variables
Mediating variables
Confounding variables
Latent variables

Let’s jump into it…

What is a moderating variable?

A moderating variable is a variable that influences the strength or direction of the relationship between an independent variable and a dependent variable. In other words, moderating variables affect how much (or how little) the IV affects the DV, or whether the IV has a positive or negative relationship with the DV (i.e., moves in the same or opposite direction).

For example, in a study about the effects of sleep deprivation on academic performance, gender could be used as a moderating variable to see if there are any differences in how men and women respond to a lack of sleep. In such a case, one may find that gender has an influence on how much students’ scores suffer when they’re deprived of sleep.

It’s important to note that while moderators can have an influence on outcomes , they don’t necessarily cause them ; rather they modify or “moderate” existing relationships between other variables. This means that it’s possible for two different groups with similar characteristics, but different levels of moderation, to experience very different results from the same experiment or study design.

What is a mediating variable?

Mediating variables are often used to explain the relationship between the independent and dependent variable (s). For example, if you were researching the effects of age on job satisfaction, then education level could be considered a mediating variable, as it may explain why older people have higher job satisfaction than younger people – they may have more experience or better qualifications, which lead to greater job satisfaction.

Mediating variables also help researchers understand how different factors interact with each other to influence outcomes. For instance, if you wanted to study the effect of stress on academic performance, then coping strategies might act as a mediating factor by influencing both stress levels and academic performance simultaneously. For example, students who use effective coping strategies might be less stressed but also perform better academically due to their improved mental state.

In addition, mediating variables can provide insight into causal relationships between two variables by helping researchers determine whether changes in one factor directly cause changes in another – or whether there is an indirect relationship between them mediated by some third factor(s). For instance, if you wanted to investigate the impact of parental involvement on student achievement, you would need to consider family dynamics as a potential mediator, since it could influence both parental involvement and student achievement simultaneously.

Mediating variables can explain the relationship between the independent and dependent variable, including whether it's causal or not.

What is a confounding variable?

A confounding variable (also known as a third variable or lurking variable ) is an extraneous factor that can influence the relationship between two variables being studied. Specifically, for a variable to be considered a confounding variable, it needs to meet two criteria:

It must be correlated with the independent variable (this can be causal or not)
It must have a causal impact on the dependent variable (i.e., influence the DV)

Some common examples of confounding variables include demographic factors such as gender, ethnicity, socioeconomic status, age, education level, and health status. In addition to these, there are also environmental factors to consider. For example, air pollution could confound the impact of the variables of interest in a study investigating health outcomes.

Naturally, it’s important to identify as many confounding variables as possible when conducting your research, as they can heavily distort the results and lead you to draw incorrect conclusions . So, always think carefully about what factors may have a confounding effect on your variables of interest and try to manage these as best you can.

What is a latent variable?

Latent variables are unobservable factors that can influence the behaviour of individuals and explain certain outcomes within a study. They’re also known as hidden or underlying variables , and what makes them rather tricky is that they can’t be directly observed or measured . Instead, latent variables must be inferred from other observable data points such as responses to surveys or experiments.

For example, in a study of mental health, the variable “resilience” could be considered a latent variable. It can’t be directly measured , but it can be inferred from measures of mental health symptoms, stress, and coping mechanisms. The same applies to a lot of concepts we encounter every day – for example:

Emotional intelligence
Quality of life
Business confidence
Ease of use

One way in which we overcome the challenge of measuring the immeasurable is latent variable models (LVMs). An LVM is a type of statistical model that describes a relationship between observed variables and one or more unobserved (latent) variables. These models allow researchers to uncover patterns in their data which may not have been visible before, thanks to their complexity and interrelatedness with other variables. Those patterns can then inform hypotheses about cause-and-effect relationships among those same variables which were previously unknown prior to running the LVM. Powerful stuff, we say!

Latent variables are unobservable factors that can influence the behaviour of individuals and explain certain outcomes within a study.

Let’s recap

In the world of scientific research, there’s no shortage of variable types, some of which have multiple names and some of which overlap with each other. In this post, we’ve covered some of the popular ones, but remember that this is not an exhaustive list .

To recap, we’ve explored:

Independent variables (the “cause”)
Dependent variables (the “effect”)
Control variables (the variable that’s not allowed to vary)

If you’re still feeling a bit lost and need a helping hand with your research project, check out our 1-on-1 coaching service , where we guide you through each step of the research journey. Also, be sure to check out our free dissertation writing course and our collection of free, fully-editable chapter templates .

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Variables in Research | Types, Definiton & Examples

Introduction

What is a variable, what are the 5 types of variables in research, other variables in research.

Variables are fundamental components of research that allow for the measurement and analysis of data. They can be defined as characteristics or properties that can take on different values. In research design , understanding the types of variables and their roles is crucial for developing hypotheses , designing methods , and interpreting results .

This article outlines the the types of variables in research, including their definitions and examples, to provide a clear understanding of their use and significance in research studies. By categorizing variables into distinct groups based on their roles in research, their types of data, and their relationships with other variables, researchers can more effectively structure their studies and achieve more accurate conclusions.

A variable represents any characteristic, number, or quantity that can be measured or quantified. The term encompasses anything that can vary or change, ranging from simple concepts like age and height to more complex ones like satisfaction levels or economic status. Variables are essential in research as they are the foundational elements that researchers manipulate, measure, or control to gain insights into relationships, causes, and effects within their studies. They enable the framing of research questions, the formulation of hypotheses, and the interpretation of results.

Variables can be categorized based on their role in the study (such as independent and dependent variables ), the type of data they represent (quantitative or categorical), and their relationship to other variables (like confounding or control variables). Understanding what constitutes a variable and the various variable types available is a critical step in designing robust and meaningful research.

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Variables are crucial components in research, serving as the foundation for data collection , analysis , and interpretation . They are attributes or characteristics that can vary among subjects or over time, and understanding their types is essential for any study. Variables can be broadly classified into five main types, each with its distinct characteristics and roles within research.

This classification helps researchers in designing their studies, choosing appropriate measurement techniques, and analyzing their results accurately. The five types of variables include independent variables, dependent variables, categorical variables, continuous variables, and confounding variables. These categories not only facilitate a clearer understanding of the data but also guide the formulation of hypotheses and research methodologies.

Independent variables

Independent variables are foundational to the structure of research, serving as the factors or conditions that researchers manipulate or vary to observe their effects on dependent variables. These variables are considered "independent" because their variation does not depend on other variables within the study. Instead, they are the cause or stimulus that directly influences the outcomes being measured. For example, in an experiment to assess the effectiveness of a new teaching method on student performance, the teaching method applied (traditional vs. innovative) would be the independent variable.

The selection of an independent variable is a critical step in research design, as it directly correlates with the study's objective to determine causality or association. Researchers must clearly define and control these variables to ensure that observed changes in the dependent variable can be attributed to variations in the independent variable, thereby affirming the reliability of the results. In experimental research, the independent variable is what differentiates the control group from the experimental group, thereby setting the stage for meaningful comparison and analysis.

Dependent variables

Dependent variables are the outcomes or effects that researchers aim to explore and understand in their studies. These variables are called "dependent" because their values depend on the changes or variations of the independent variables.

Essentially, they are the responses or results that are measured to assess the impact of the independent variable's manipulation. For instance, in a study investigating the effect of exercise on weight loss, the amount of weight lost would be considered the dependent variable, as it depends on the exercise regimen (the independent variable).

The identification and measurement of the dependent variable are crucial for testing the hypothesis and drawing conclusions from the research. It allows researchers to quantify the effect of the independent variable , providing evidence for causal relationships or associations. In experimental settings, the dependent variable is what is being tested and measured across different groups or conditions, enabling researchers to assess the efficacy or impact of the independent variable's variation.

To ensure accuracy and reliability, the dependent variable must be defined clearly and measured consistently across all participants or observations. This consistency helps in reducing measurement errors and increases the validity of the research findings. By carefully analyzing the dependent variables, researchers can derive meaningful insights from their studies, contributing to the broader knowledge in their field.

Categorical variables

Categorical variables, also known as qualitative variables, represent types or categories that are used to group observations. These variables divide data into distinct groups or categories that lack a numerical value but hold significant meaning in research. Examples of categorical variables include gender (male, female, other), type of vehicle (car, truck, motorcycle), or marital status (single, married, divorced). These categories help researchers organize data into groups for comparison and analysis.

Categorical variables can be further classified into two subtypes: nominal and ordinal. Nominal variables are categories without any inherent order or ranking among them, such as blood type or ethnicity. Ordinal variables, on the other hand, imply a sort of ranking or order among the categories, like levels of satisfaction (high, medium, low) or education level (high school, bachelor's, master's, doctorate).

Understanding and identifying categorical variables is crucial in research as it influences the choice of statistical analysis methods. Since these variables represent categories without numerical significance, researchers employ specific statistical tests designed for a nominal or ordinal variable to draw meaningful conclusions. Properly classifying and analyzing categorical variables allow for the exploration of relationships between different groups within the study, shedding light on patterns and trends that might not be evident with numerical data alone.

Continuous variables

Continuous variables are quantitative variables that can take an infinite number of values within a given range. These variables are measured along a continuum and can represent very precise measurements. Examples of continuous variables include height, weight, temperature, and time. Because they can assume any value within a range, continuous variables allow for detailed analysis and a high degree of accuracy in research findings.

The ability to measure continuous variables at very fine scales makes them invaluable for many types of research, particularly in the natural and social sciences. For instance, in a study examining the effect of temperature on plant growth, temperature would be considered a continuous variable since it can vary across a wide spectrum and be measured to several decimal places.

When dealing with continuous variables, researchers often use methods incorporating a particular statistical test to accommodate a wide range of data points and the potential for infinite divisibility. This includes various forms of regression analysis, correlation, and other techniques suited for modeling and analyzing nuanced relationships between variables. The precision of continuous variables enhances the researcher's ability to detect patterns, trends, and causal relationships within the data, contributing to more robust and detailed conclusions.

Confounding variables

Confounding variables are those that can cause a false association between the independent and dependent variables, potentially leading to incorrect conclusions about the relationship being studied. These are extraneous variables that were not considered in the study design but can influence both the supposed cause and effect, creating a misleading correlation.

Identifying and controlling for a confounding variable is crucial in research to ensure the validity of the findings. This can be achieved through various methods, including randomization, stratification, and statistical control. Randomization helps to evenly distribute confounding variables across study groups, reducing their potential impact. Stratification involves analyzing the data within strata or layers that share common characteristics of the confounder. Statistical control allows researchers to adjust for the effects of confounders in the analysis phase.

Properly addressing confounding variables strengthens the credibility of research outcomes by clarifying the direct relationship between the dependent and independent variables, thus providing more accurate and reliable results.

Beyond the primary categories of variables commonly discussed in research methodology , there exists a diverse range of other variables that play significant roles in the design and analysis of studies. Below is an overview of some of these variables, highlighting their definitions and roles within research studies:

Discrete variables : A discrete variable is a quantitative variable that represents quantitative data , such as the number of children in a family or the number of cars in a parking lot. Discrete variables can only take on specific values.
Categorical variables : A categorical variable categorizes subjects or items into groups that do not have a natural numerical order. Categorical data includes nominal variables, like country of origin, and ordinal variables, such as education level.
Predictor variables : Often used in statistical models, a predictor variable is used to forecast or predict the outcomes of other variables, not necessarily with a causal implication.
Outcome variables : These variables represent the results or outcomes that researchers aim to explain or predict through their studies. An outcome variable is central to understanding the effects of predictor variables.
Latent variables : Not directly observable, latent variables are inferred from other, directly measured variables. Examples include psychological constructs like intelligence or socioeconomic status.
Composite variables : Created by combining multiple variables, composite variables can measure a concept more reliably or simplify the analysis. An example would be a composite happiness index derived from several survey questions .
Preceding variables : These variables come before other variables in time or sequence, potentially influencing subsequent outcomes. A preceding variable is crucial in longitudinal studies to determine causality or sequences of events.

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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.

Types of Variables and Distributions

First Online: 17 April 2018

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Gregory R. Pond Ph.D., P.Stat. 3 &
Samantha-Jo Caetano M.Sc. 3

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Investigators must have a thorough understanding of the types of variables they might encounter as part of their research. Variables can be described using distributions. Some common distributions are described, along with specific types of variables, including independent, dependent, and confounding variables, which are defined and described. Understanding variables and distributions is imperative for planning and interpreting research studies.

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Pond, G.R., Caetano, SJ. (2018). Types of Variables and Distributions. In: Araújo, R., Riechelmann, R. (eds) Methods and Biostatistics in Oncology. Springer, Cham. https://doi.org/10.1007/978-3-319-71324-3_3

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Outcomes research: what is it and why does it matter?

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1 Ludwig Institute for Cancer Research, Heidelberg, Victoria, Australia. [email protected]
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DOI: 10.1046/j.1445-5994.2003.00302.x

Outcomes research is a broad umbrella term without a consistent definition. However it tends to describe research that is concerned with the effectiveness of public-health interventions and health services; that is, the outcomes of these services. Attention is frequently focused on the affected individual - with measures such as quality of life and preferences - but outcomes research may also refer to effectiveness of health-care delivery, with measures such as cost-effectiveness, health status and disease burden. The present review details the historical background of outcomes research to reveal the origins of its diversity. The value and relevance of outcomes research, commonly employed research techniques and examples of recent publications in the area are also discussed.

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Explanatory and Response Variables | Definitions & Examples

Explanatory and Response Variables | Definitions & Examples

Published on April 19, 2021 by Pritha Bhandari . Revised on June 22, 2023.

In research, you often investigate causal relationships between variables using experiments or observations. For example, you might test whether caffeine improves speed by providing participants with different doses of caffeine and then comparing their reaction times.

An explanatory variable is what you manipulate or observe changes in (e.g., caffeine dose), while a response variable is what changes as a result (e.g., reaction times).

The words “explanatory variable” and “response variable” are often interchangeable with other terms used in research.

Cause (what changes)	Effect (what’s measured)

Predictor variable	Outcome/criterion variable
Explanatory variable	Response variable

Explanatory vs. response variables, explanatory vs independent variables, visualizing explanatory and response variables, other interesting articles, frequently asked questions about explanatory and response variables.

The difference between explanatory and response variables is simple:

An explanatory variable is the expected cause, and it explains the results.
A response variable is the expected effect, and it responds to explanatory variables.

You expect changes in the response variable to happen only after changes in an explanatory variable.

There’s a causal relationship between the variables that may be indirect or direct. In an indirect relationship, an explanatory variable may act on a response variable through a mediator .

If you’re dealing with a purely correlational relationship, there are no explanatory and response variables. Even if changes in one variable are associated with changes in another, both might be caused by a confounding variable .

Errors relating to your variables can lead to research biases like omitted variable bias and information bias .

Examples of explanatory and response variables

In some studies, you’ll have only one explanatory variable and one response variable, but in more complicated research, you may predict one or more response variable(s) using several explanatory variables in a model.

Research question	Explanatory variables	Response variable
Does academic motivation predict performance?
Can overconfidence and risk perception explain financial risk taking behaviors?
Does the weather affect the transmission of Covid-19?

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Explanatory variables and independent variables are very similar, but there are subtle differences between them.

In research contexts, independent variables supposedly aren’t affected by or dependent on any other variable—they’re manipulated or altered only by researchers. For example, if you run a controlled experiment where you can control exactly how much caffeine each participant receives, then caffeine dose is an independent variable.

But sometimes, the term “explanatory variable” is preferred over “independent variable”, because in real world contexts, independent variables are often influenced by other variables. That means they’re not truly independent.

You gather a sample of young adults and ask them to complete a survey in the lab. They report their risk perceptions of different threatening scenarios while you record their stress reactions physiologically.

In your analyses, you find that gender identity and risk perception are highly correlated with each other. Participants who identify as women are more likely to rate situations as riskier than those who identify as men.

You’ll often see the terms “explanatory variable” and “response variable” used in regression analyses , which focus on predicting or accounting for changes in response variables as a result of explanatory variables.

The easiest way to visualize the relationship between an explanatory variable and a response variable is with a graph.

On graphs, the explanatory variable is conventionally placed on the x-axis, while the response variable is placed on the y-axis.

If you have quantitative variables , use a scatterplot or a line graph.
If your response variable is categorical, use a scatterplot or a line graph.
If your explanatory variable is categorical, use a bar graph.

When you have only one explanatory variable and one response variable, you’ll collect paired data . This means every response variable measurement is linked to an explanatory variable value for each unit or participant.

Your explanatory variable is academic motivation at the start of the school year.
Your response variable is GPA at the end of the school year.

Academic motivation is assessed using an 8-point scale, while GPA can range from 0–4. To visualize your data, you plot academic motivation at the start of the year on the x-axis and GPA at the end of the year on the y-axis. Each data point reflects the paired data of one participant.

From the scatterplot, you can see a clear explanatory relationship between academic motivation at the start of the year and GPA at the end of the year.

A scatterplot visualizing the relationship between an explanatory and response variable

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

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A response variable is the expected effect, and it responds to other variables.

The term “ explanatory variable ” is sometimes preferred over “ independent variable ” because, in real world contexts, independent variables are often influenced by other variables. This means they aren’t totally independent.

Multiple independent variables may also be correlated with each other, so “explanatory variables” is a more appropriate term.

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Definitions

Dependent Variable The variable that depends on other factors that are measured. These variables are expected to change as a result of an experimental manipulation of the independent variable or variables. It is the presumed effect.

Independent Variable The variable that is stable and unaffected by the other variables you are trying to measure. It refers to the condition of an experiment that is systematically manipulated by the investigator. It is the presumed cause.

Cramer, Duncan and Dennis Howitt. The SAGE Dictionary of Statistics . London: SAGE, 2004; Penslar, Robin Levin and Joan P. Porter. Institutional Review Board Guidebook: Introduction . Washington, DC: United States Department of Health and Human Services, 2010; "What are Dependent and Independent Variables?" Graphic Tutorial.

Identifying Dependent and Independent Variables

Don't feel bad if you are confused about what is the dependent variable and what is the independent variable in social and behavioral sciences research . However, it's important that you learn the difference because framing a study using these variables is a common approach to organizing the elements of a social sciences research study in order to discover relevant and meaningful results. Specifically, it is important for these two reasons:

You need to understand and be able to evaluate their application in other people's research.
You need to apply them correctly in your own research.

A variable in research simply refers to a person, place, thing, or phenomenon that you are trying to measure in some way. The best way to understand the difference between a dependent and independent variable is that the meaning of each is implied by what the words tell us about the variable you are using. You can do this with a simple exercise from the website, Graphic Tutorial. Take the sentence, "The [independent variable] causes a change in [dependent variable] and it is not possible that [dependent variable] could cause a change in [independent variable]." Insert the names of variables you are using in the sentence in the way that makes the most sense. This will help you identify each type of variable. If you're still not sure, consult with your professor before you begin to write.

Fan, Shihe. "Independent Variable." In Encyclopedia of Research Design. Neil J. Salkind, editor. (Thousand Oaks, CA: SAGE, 2010), pp. 592-594; "What are Dependent and Independent Variables?" Graphic Tutorial; Salkind, Neil J. "Dependent Variable." In Encyclopedia of Research Design , Neil J. Salkind, editor. (Thousand Oaks, CA: SAGE, 2010), pp. 348-349;

Structure and Writing Style

The process of examining a research problem in the social and behavioral sciences is often framed around methods of analysis that compare, contrast, correlate, average, or integrate relationships between or among variables . Techniques include associations, sampling, random selection, and blind selection. Designation of the dependent and independent variable involves unpacking the research problem in a way that identifies a general cause and effect and classifying these variables as either independent or dependent.

The variables should be outlined in the introduction of your paper and explained in more detail in the methods section . There are no rules about the structure and style for writing about independent or dependent variables but, as with any academic writing, clarity and being succinct is most important.

After you have described the research problem and its significance in relation to prior research, explain why you have chosen to examine the problem using a method of analysis that investigates the relationships between or among independent and dependent variables . State what it is about the research problem that lends itself to this type of analysis. For example, if you are investigating the relationship between corporate environmental sustainability efforts [the independent variable] and dependent variables associated with measuring employee satisfaction at work using a survey instrument, you would first identify each variable and then provide background information about the variables. What is meant by "environmental sustainability"? Are you looking at a particular company [e.g., General Motors] or are you investigating an industry [e.g., the meat packing industry]? Why is employee satisfaction in the workplace important? How does a company make their employees aware of sustainability efforts and why would a company even care that its employees know about these efforts?

Identify each variable for the reader and define each . In the introduction, this information can be presented in a paragraph or two when you describe how you are going to study the research problem. In the methods section, you build on the literature review of prior studies about the research problem to describe in detail background about each variable, breaking each down for measurement and analysis. For example, what activities do you examine that reflect a company's commitment to environmental sustainability? Levels of employee satisfaction can be measured by a survey that asks about things like volunteerism or a desire to stay at the company for a long time.

The structure and writing style of describing the variables and their application to analyzing the research problem should be stated and unpacked in such a way that the reader obtains a clear understanding of the relationships between the variables and why they are important. This is also important so that the study can be replicated in the future using the same variables but applied in a different way.

Fan, Shihe. "Independent Variable." In Encyclopedia of Research Design. Neil J. Salkind, editor. (Thousand Oaks, CA: SAGE, 2010), pp. 592-594; "What are Dependent and Independent Variables?" Graphic Tutorial; “Case Example for Independent and Dependent Variables.” ORI Curriculum Examples. U.S. Department of Health and Human Services, Office of Research Integrity; Salkind, Neil J. "Dependent Variable." In Encyclopedia of Research Design , Neil J. Salkind, editor. (Thousand Oaks, CA: SAGE, 2010), pp. 348-349; “Independent Variables and Dependent Variables.” Karl L. Wuensch, Department of Psychology, East Carolina University [posted email exchange]; “Variables.” Elements of Research. Dr. Camille Nebeker, San Diego State University.

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Next: Glossary of Research Terms >>
Last Updated: Sep 4, 2024 9:40 AM
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Identifiability and estimation for potential-outcome means with misclassified outcomes.

1. Introduction

2. setup, assumptions, and nonparametric identification, 3. efficient and multiply-robust estimation based on the semiparametric theory.

M 1 t : The models a t ( X ; θ t ) , B W 0 ( X ; γ ) , and B W ( X ; η ) are correctly specified, meaning that there exist θ t 0 , γ 0 , and η 0 such that a t ( X ; θ t 0 ) , B W 0 ( X ; γ 0 ) , and B W ( X ; η 0 ) equal to their corresponding true models, respectively.
M 2 : The models B W ( X ; η ) , f ( T ∣ X ; α ) , and f ( Y ∣ X ; β ) are correctly specified, meaning that there exist η 0 , α 0 , and θ 0 such that B W ( X ; η 0 ) , f ( T ∣ X ; α 0 ) , and f ( Y ∣ X ; β 0 ) equal to their corresponding true models, respectively.
M 3 t : The models a t ( X ; θ t ) , f ( T ∣ X ; α ) , and f ( Y ∣ X ; β ) are correctly specified, meaning that there exist θ t 0 , α 0 , and β 0 such that a t ( X ; θ t 0 ) , f ( T ∣ X ; α 0 ) , and f ( Y ∣ X ; β 0 ) equal to their corresponding true models, respectively.

4. Simulation Studies

5. data analysis, 6. discussion, author contributions, data availability statement, conflicts of interest.

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✓	✓	✓		0.0068	0.0785	0.0782	0.0007	0.0462	0.0462
				−0.0040	0.0914	0.0913	0.0002	0.0528	0.0528
			RD	0.0108	0.1000	0.0984	0.0005	0.0602	0.0602
			RR	0.0541	0.2391	0.2335	0.0119	0.1211	0.1206
✓	✕	✕		0.0007	0.0771	0.0771	0.0003	0.0471	0.0471
				−0.0024	0.0892	0.0892	−0.0019	0.0533	0.0533
			RD	0.0031	0.0988	0.0988	0.0022	0.0604	0.0604
			RR	0.0369	0.2447	0.2420	0.0151	0.1353	0.1345
✕	✓	✕		−0.0086	0.0809	0.0805	−0.0101	0.0496	0.0486
				−0.0143	0.0929	0.0919	−0.0102	0.0564	0.0555
			RD	0.0058	0.0985	0.0984	0.0002	0.0622	0.0623
			RR	0.0520	0.2531	0.2479	0.0183	0.1448	0.1437
✕	✕	✓		−0.0246	0.0909	0.0876	−0.0252	0.0582	0.0525
				−0.0297	0.0996	0.0952	−0.0285	0.0667	0.0603
			RD	0.0051	0.1033	0.1033	0.0034	0.0643	0.0643
			RR	0.0660	0.2757	0.2678	0.0394	0.1627	0.1579



✓	✓	✓	NBR	−0.0171	0.1596	0.1588	0.0050	0.1296	0.1295
			ABR	−0.0077	0.1609	0.1608	0.0075	0.1219	0.1217
			TBR	−0.0094	0.1984	0.1983	−0.0125	0.1162	0.1158
✓	✕	✕	NBR	−0.0382	0.1860	0.1822	0.0456	0.1399	0.1301
			ABR	−0.0810	0.2547	0.2416	−0.0760	0.1577	0.1383
			TBR	0.0428	0.2658	0.2625	0.0304	0.1551	0.1521
✕	✓	✕	NBR	0.0252	0.1717	0.1699	−0.0243	0.1393	0.1389
			ABR	−0.0054	0.2165	0.2164	0.0044	0.1223	0.1223
			TBR	0.0306	0.2162	0.2141	0.0199	0.1221	0.1206
✕	✕	✓	NBR	0.0456	0.1728	0.1668	0.0466	0.1328	0.1328
			ABR	−0.0674	0.2103	0.1993	−0.0562	0.1321	0.1296
			TBR	0.0219	0.2183	0.2173	0.0096	0.1318	0.1315

Estimand	Point Estimate	SE	Confidence Interval
	0.7109	0.0082	(0.6954, 0.7267)
	0.8206	0.0069	(0.8076, 0.8350)
RD	−0.1097	0.0083	(−0.1261, −0.0935)
RR	0.8663	0.0096	(0.8470, 0.8856)

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Share and Cite

Wei, S.; Zhang, C.; Geng, Z.; Luo, S. Identifiability and Estimation for Potential-Outcome Means with Misclassified Outcomes. Mathematics 2024 , 12 , 2801. https://doi.org/10.3390/math12182801

Wei S, Zhang C, Geng Z, Luo S. Identifiability and Estimation for Potential-Outcome Means with Misclassified Outcomes. Mathematics . 2024; 12(18):2801. https://doi.org/10.3390/math12182801

Wei, Shaojie, Chao Zhang, Zhi Geng, and Shanshan Luo. 2024. "Identifiability and Estimation for Potential-Outcome Means with Misclassified Outcomes" Mathematics 12, no. 18: 2801. https://doi.org/10.3390/math12182801

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Open access
Published: 11 September 2024

Characterization of spatiotemporal and kinetic gait variables in dogs with hindlimb ataxia and bilateral hindlimb lameness

Clair Park 1 ,
Dominique M. Sawyere 2 ,
Theresa E. Pancotto 3 ,
Otto I. Lanz 1 &
Stephen R. Werre 4

BMC Veterinary Research volume 20 , Article number: 405 ( 2024 ) Cite this article

51 Accesses

Metrics details

Discriminating the underlying cause of gait abnormalities can be challenging in a clinical setting, especially in the presence of bilateral disease. Pressure-sensitive walkways (PSWs) have been utilized to characterize the gait of dogs with various neurologic or orthopaedic conditions. The potential use of the PSW includes the discrimination of conditions that can be similar in clinical presentation, such as bilateral hindlimb lameness and hindlimb ataxia. The primary aim of this study was to describe the spatial, temporal, and kinetic gait parameters of dogs with hindlimb ataxia or bilateral hindlimb lameness and compare them to those of normal dogs. Forty-six dogs were prospectively recruited. The normal group included 20 dogs with normal neurologic and orthopaedic exams. The orthopaedic group included 15 dogs with bilateral hindlimb orthopaedic diseases with weight-bearing hindlimb lameness and normal neurologic exams. The neurologic group included 11 dogs with ambulatory paraparesis and normal orthopaedic exams. Each dog was walked across the PSW, and at least 3 valid trials were collected. The stride time, stance time, swing time, stride length, gait velocity, peak vertical force (PVF), vertical impulse (VI), and limb symmetry were recorded. The mean values of all parameters from the valid trials were calculated and used for data analysis. The outcomes were compared among all groups.

Compared with the normal group, the orthopaedic group had a significantly greater percent body weight distribution (%BWD) and vertical impulse distribution (VID) in the forelimbs. When comparing the spatiotemporal parameters, the neurologic group showed an increase in forelimb stance time compared to that of the normal group. Compared with that in the normal group, the stride velocity in the forelimbs in the orthopaedic group was greater. There were no significant differences in the kinetic parameters between the neurologic group and the normal group, nor in stride time or stride length among the groups.

The gait parameters obtained by PSW demonstrated that the orthopaedic and neurologic groups may have different compensatory mechanisms for their gait deficiencies. These parameters can potentially be used to construct a predictive model to evaluate PSW as a diagnostic tool in future studies.

Peer Review reports

Gait abnormalities in veterinary patients can be caused by orthopaedic or neurologic diseases, for which a thorough gait assessment and additional diagnostics are often required to determine the underlying cause [ 1 , 2 ]. While visual assessment of veterinary patients is a critical part of the diagnostic process in these patients, it is a subjective evaluation by clinicians [ 3 , 4 ]. Subjective evaluation has the advantage of being performed without the need for any specialized equipment. However, the subjective orthopaedic gait assessment depends on the skill level of the observer and is subject to interobserver variability, especially when the abnormality is subtle or bilateral [ 5 , 6 , 7 ]. Previous studies have demonstrated a poor correlation between the subjective gait scoring system and force plate gait analysis in dogs with lameness, further limiting the role of subjective evaluation as a diagnostic tool [ 6 , 7 ].

Objective gait assessments can be provided by force plate analysis, pressure-sensitive walkways (PSW), and stance analysers [ 8 , 9 , 10 ]. The PSW is a relatively new technology developed to analyse gait symmetry and can provide an objective measure of spatiotemporal gait parameters. These parameters include stride time, stride length, stance time, swing time, velocity, and calculated kinetic parameters such as peak vertical force (PVF) and vertical impulse (VI). While force plate analysis is often considered the ‘gold standard’ for objective gait analysis, PSW has been shown to generate consistent and precise gait data and has been validated as a reliable alternative method for assessing kinetic gait parameters in dogs [ 8 , 11 , 12 , 13 ]. The advantages of the PSW over force plate analysis are that the PSW can characterize and evaluate spatiotemporal gait parameters and provide consecutive measurements from all limbs simultaneously over multiple gait cycles in normal dogs [ 14 , 15 ]. Gait parameters obtained by the PSW are frequently used to characterize the gait of humans and animals with various orthopaedic or neurologic conditions for diagnostic and monitoring purposes [ 16 , 17 , 18 , 19 ]. Another potential use of the additional gait parameters obtained from the PSW might be to serve as a diagnostic tool to discriminate conditions that can be similar in clinical presentation, such as hindlimb ataxia and bilateral hindlimb lameness, in dogs.

Several canine studies have investigated spatiotemporal and kinetic parameters in dogs with neurologic or orthopaedic conditions using the PSW [ 20 , 21 , 22 , 23 , 24 ]. However, to the best of the authors’ knowledge, there are no studies comparing both kinetic and spatiotemporal gait parameters among clinically normal dogs, dogs with bilateral hindlimb lameness, and dogs with hindlimb ataxia. Therefore, the aim of this study was to describe the spatial, temporal, and kinetic gait parameters of dogs with hindlimb ataxia or bilateral hindlimb lameness to determine whether there were any discriminating variables in each group compared to those of normal group. We hypothesized that the PSW can be used to characterize distinct changes in the gait parameters of dogs with hindlimb ataxia and bilateral hindlimb lameness compared to those of clinically normal dogs and potentially identify gait parameters that can be used to differentiate the two gait patterns from the normal gait.

This study was conducted with the approval of the Institutional Animal Care and Use Committee of Virginia Tech (IACUC protocol #19–146), and a signed owner consent form was obtained for each dog. Client-owned dogs were prospectively recruited at the Virginia-Maryland College of Veterinary Medicine Teaching Hospital from 2019 to 2022. Dogs over 1 year of age, weighing between 4.5 and 60 kg, were enrolled in the study. The lower weight limit was determined according to the manufacturer’s recommendation for ensuring reliable detection of individual foot strikes by the equipment. A power analysis using PASS 16 (Power Analysis and Sample Size Software (2018). NCSS, LLC. Kaysville, Utah, USA) showed that 15 dogs per group would be needed to detect a difference with a power of 80%. As a prospective pilot study, the maximum number of subjects enrolled within the study period were included in each group. Each dog enrolled in this study underwent an orthopaedic and neurologic examination, which was performed by a board-certified surgeon and neurologist or house officers under the supervision of a board-certified specialist who were blinded to the group assignment. Each dog was assigned a lameness score for each individual limb based on a subjective five-point grading scale, as shown in Table 1 [ 25 ]. A Modified Frankel Scale was used to assess the neurologic status of the dogs, as shown in Table 2 [ 26 ]. The group assignment and exam findings of each dog were recorded by one of the investigators (CP).

The inclusion criteria for the normal group were dogs with normal orthopaedic and neurologic examination results performed by board-certified surgeons and neurologists and no history of orthopaedic or neurologic disease or any other significant comorbidities. The inclusion criteria for the neurologic group were dogs with ambulatory paraparesis (Modified Frankel Scale grade 2) with pelvic limb proprioceptive ataxia and a normal orthopaedic examination. Dogs were included if they were diagnosed with neurologic diseases causing a thoracolumbar myelopathy, based on advanced imaging findings, diagnostic results, and neurologic examination. Dogs were excluded if they had neurologic abnormalities in the forelimbs or if they had a history of orthopaedic disease or orthopaedic surgery. The inclusion criteria for the orthopaedic group were dogs with orthopaedic examination findings consistent with bilateral hindlimb orthopaedic diseases that exhibited weight-bearing hindlimb lameness (grades 1–3) and a normal neurologic examination. Dogs were excluded if they had forelimb gait abnormalities, a history of neurologic disease or neurologic surgery.

Data collection

The data were collected using a 1.95 m × 0.45 m PSW (Walkway High-Resolution; Tekscan Inc., South Boston, Massachusetts, USA). The PSW was calibrated to the weight of the dogs as directed by the manufacturer’s guidance before each use. Designated software (Walkway 7.80x software; Tekscan Inc., South Boston, Massachusetts, USA) was used for data acquisition and analysis. Dogs were walked by one handler on a loose neck lead and were acclimated to the walkway first by walking the dog for 3 to 5 min across the mat. A trial was considered valid if the dog walked in a straight line along the entire length of the PSW, was not noticeably distracted, each foot strike remained within the pressure mat, the velocity was maintained between 0.8 m/s and 1.4 m/s, and the acceleration was between − 0.5 m/s 2 and 0.5 m/s 2 . After accommodation, at least 3 valid trials were recorded for each dog. A video was recorded for each trial for review. All data acquisition was monitored and recorded by the investigator (CP) who was not blinded to the group assignment.

Data processing

After data acquisition, the custom software automatically identified the foot strikes and assigned LF (left forelimb), RF (right forelimb), LH (left hindlimb), or RH (right hindlimb) accordingly (Fig. 1 ). All videos of the trials were reviewed to ensure that each foot strike was correctly identified and assigned manually when needed. The mean values of all parameters from the minimum of 3 valid trials were calculated and used for data analysis. The spatial and temporal gait variables included stride time (seconds, s), stance time (seconds, s), swing time (seconds, s), stride length (meters, m), and gait velocity (meters per second, m/s). The kinetic variables included PVF (Newtons, N) and VI (Newton seconds, Nˑs). The PVF and VI values were normalized to body weight and were represented as a percentage of body weight distribution (%BWD) and VI distribution (VID), respectively, as previously described [ 9 , 27 ]. Additionally, the limb symmetry between the forelimbs and hindlimbs was calculated using the following formula as previously described [ 28 ].

Representative data acquired from a subject in the normal group. A A footstrike recording of the subject. B Graph of percent body weight (%BW) over time generated from the data

RF = right forelimb, LF = left forelimb, RH = right hindlimb, LH = left hindlimb

An SI = 0 indicates complete symmetry, an SI > 0 indicates that the forelimbs have higher values, and an SI < 0 indicates that the hindlimbs have higher values.

Asymmetry between the right and left limbs was calculated using the following formula.

An SI = 0 indicates complete symmetry, an SI > 0 indicates that the right limbs had a higher value and SI < 0 indicates that the left limbs had a higher value. The same formula was used for SI of right and left hindlimbs.

Statistical analyses

The normality of the data was determined by generating and inspecting a normal probability plot. The normal probability plots showed that all numerical variables, including weight, age, and gait parameter outcomes, were skewed. Accordingly, kinetic and temporospatial values were expressed as median, minimum, and maximum. The outcomes of the gait analyses were compared between groups using the Kruskal‒Wallis test followed by Dunn’s test for multiple comparisons. The association between sex and group was assessed using Fisher’s exact test. Overall, p values were adjusted for multiple testing using the Benjamini–Hochberg false discovery rate method. Statistical significance was set to P < 0.05. All analyses were performed using SAS version 9.4 (Cary, North Carolina, USA).

Forty-six dogs were enrolled in the study. The normal group included 20 dogs, 12 neutered males, and 8 spayed females, with a median age of 6 years (range, 1–12 years) and a median weight of 22.3 kg (range, 7.6–40.5 kg). The dog breeds included mixed-breed ( n = 14), Walker Hound (2), and one each of the following breeds: Border Collie, Danish Swedish Farm dog, Labrador Retriever, and Staffordshire Terrier. The orthopaedic group included 15 dogs, 7 neutered males, and 8 spayed females with a median age of 6 years (range, 2–12 years) and a median weight of 30.0 kg (range, 17–59 kg). The dog breeds included mixed-breed dog ( n = 5), Labrador Retriever (2), Staffordshire Terrier (2), and one each of the following breeds: Mastiff, English Bulldog, German Shepherd, American Foxhound, Siberian Husky, and English Springer Spaniel. The most common diagnoses attributable to bilateral lameness in the group included cranial cruciate ligament disease ( n = 7), followed by hip dysplasia (5), grade III/IV medial patella luxation (2), and chronic iliopsoas pain (1). The neurologic group included 11 dogs, 5 neutered males, and 6 spayed females, with a median age of 8 years (range, 4–11 years) and a median weight of 16.5 kg (range, 4.8–52.0 kg). The dog breeds were mixed breed ( n = 4), Dachshund (3), and one each of the following breeds: Bull Mastiff, English Bulldog, Brittany Spaniel, Boxer, or Shih Tzu. The prevalent diagnoses included intervertebral disc extrusion or protrusion ( n = 9), acute non-compressive nucleus pulposus extrusion (1), and degenerative myelopathy (1). There was no significant difference in age or sex among the groups. Overall, the average weight of the orthopaedic group was greater than that of the normal group and the neurologic group ( p < 0.01). There was no significant difference between the average weight of the normal group and the neurologic group ( p = 0.57).

The normalized kinetic gait parameters are summarized in Table 3 . Compared with the normal group, the orthopaedic group had greater %BWD and VID in the forelimbs and lower values in the hindlimbs. The differences were statistically significant ( p < 0.001) for all the individual limbs except for the left hindlimb, which closely approached statistical significance ( p = 0.051). The SI of the maximum force between the right hindlimb and the left hind limb in the orthopaedic group was significantly lower than that in the normal group ( p = 0.005). There were no significant differences in the %BWD or VID between the normal group and the neurologic group or between the orthopaedic group and the neurologic group.

The SIs between the gait parameters of the forelimbs and the hindlimbs are reported in Table 4 . The orthopaedic group had a greater forelimb: hindlimb SI of the maximum force ( p = 0.0002) compared to those of the normal group. When comparing the SIs of the spatiotemporal gait parameters among the groups, the neurologic group had a greater forelimb: hindlimb stance time compared to the normal group ( p = 0.02). In contrast, there was no significant difference in the stance time between the orthopaedic group and the normal group ( p = 0.148). The neurologic group had the lowest SIs of stride time and stride length in the forelimbs; however, the differences in the values among the groups were not statistically significant ( p > 0.07). The orthopaedic group had a greater stride velocity in the forelimbs than in the hindlimbs, as demonstrated by the significantly greater SI value in the orthopaedic group than in the normal group ( p = 0.009). There was no significant difference in the SI of the stride velocity between the neurologic group and the normal group ( p = 0.36).

This study demonstrated that compared to the normal group, the orthopaedic group had increased body weight distribution and increased stride velocity in the forelimbs, while the neurologic group had increased stance time in the forelimbs without significant changes in body weight distribution or stride velocity. These results support our hypothesis that PSW could detect distinct changes in kinetic and spatiotemporal gait parameters in dogs with bilateral hindlimb lameness and in dogs with hindlimb ataxia when compared to the normal dogs. Additionally, the results also indicate that dogs with bilateral hindlimb lameness and hindlimb ataxia may compensate for their gait abnormalities through different mechanisms. While thorough neurologic and orthopaedic exams are pivotal for the differentiation of two presentations, PSW analysis may provide additional information for clinicians to help in the differentiation of neurologic and orthopaedic hind limb disease.

For the kinetic parameters, the orthopaedic group had significantly greater %BWD and VID in the forelimb, as well as greater forelimb: hindlimb SI maximum force, than did the normal group. This indicates that dogs with bilateral hindlimb orthopaedic disease compensate by shifting their weight to their forelimbs; dogs with hindlimb ataxia did not demonstrate this effect. A possible explanation for the difference in compensation is that orthopaedic diseases often accompany variable degrees of pain associated with osteoarthritis in the affected limb, which may be alleviated by a redistribution of the weight to the unaffected limbs. On the other hand, the gait abnormalities in dogs with paraparesis and ataxia do not always involve pain in the affected limbs. This “compensatory cranial weight shift” in dogs with bilateral hindlimb orthopaedic diseases is commonly described in the clinical setting, however, objective data based on comparisons with a control group are sparse [ 29 , 30 ]. In a healthy dog, weight is approximately distributed 60% to the forelimbs and 40% to the hindlimbs, regardless of the body weight or size [ 29 , 31 , 32 , 33 ]. The median body weight distributions of the normal group in the current study were 28.3% (range: 25.9–32.9%) and 29.00% (25.0-33.1%) for the forelimbs and 21.6% (17.4–24.1%) and 20.65% (17.2–24.8%) for the left and right hindlimbs, respectively, which are comparable to the previously reported normal values for dogs and confirmed that the normal group was valid as a control.

Multiple previous studies evaluating the weight distribution of dogs with various naturally occurring or experimentally induced lameness have shown that dogs with lameness tend to redistribute their weight to the non-affected limbs, mainly to the contralateral and diagonal limbs, thus exhibiting more side-to-side compensation rather than a caudal-to-cranial shift [ 23 , 32 , 33 , 34 , 35 ]. However, a recent study utilizing a stance analyser to evaluate weight-bearing compensation in police-working dogs with bilateral hip osteoarthritis revealed that affected dogs had weight shift to the thoracic limbs, corroborating the common clinical description of “cranial weight shift” in bilaterally affected dogs [ 36 ]. The results from the current study are not only in line with these findings but also demonstrate statistical differences in the kinetic parameters in comparison to those of a normal control group to provide further objective parameters in support of the commonly accepted cranial weight shift phenomenon in dogs with bilateral hindlimb lameness.

In contrast to the orthopaedic group, the neurologic group showed similar body weight distribution in all limbs compared to the normal group, indicating that compensatory mechanisms may be different in dogs with paraparesis and proprioceptive ataxia secondary to thoracolumbar myelopathy. Changes in kinetic parameters in dogs with various neurologic diseases have been investigated in previous studies [ 20 , 37 , 38 , 39 ]. One study evaluated kinetic gait parameters in Doberman Pinchers with cervical spondylomyelopathy and found that there was no significant difference in the %BWD of the forelimb or the hindlimb compared to clinically normal dogs [ 20 ]. Another study revealed no significant differences in the PVF between the hindlimbs of normal Dachshunds and Dachshunds that underwent hemilaminectomy for thoracolumbar intervertebral disc disease [ 40 ]. This study also showed that the post-hemilaminectomy group had greater PVF on the more affected limb, which was contrary to findings in dogs affected by orthopaedic disease where lower PVF is expected in the limb with impaired function [ 5 , 6 , 23 , 40 , 41 ]. Along with the results from the current study, these findings support that dogs with ataxia may not necessarily redistribute their body weight to compensate for their uncoordinated gait. An alternative explanation is that these dogs might be unable to control the force exerted by the limbs due to loss of input from the upper motor neuron, preventing them from consciously compensating for the instability in their hindlimbs.

Interestingly, in another study that evaluated gait parameters in dogs with ataxia due to thoracolumbar myelopathy, the affected dogs had greater PVFs in the forelimbs than did the normal dogs [ 21 ]. The authors of that study postulated that dogs with thoracolumbar neurologic disease tend to shift their weight to the forelimbs as a result of hindlimb ataxia and instability [ 21 ]. This finding is in contrast with our data. The disparity in the observations between the studies may be due to several factors. In the aforementioned study, Dachshunds were overrepresented, composing 70% of the neurologic group in that study, while the neurologic group in our study included a more diverse population of dogs of various sizes, breeds, and conformations, with only 3 of 11 dogs being chondrodystrophic. Although the influences of the variation in the body weight and sizes of dogs can be avoided by the use of kinetic values normalized to the body weight, one study has suggested that there can be significant differences in the fully normalized ground reaction force and impulse distribution in the forelimb versus hindlimb between various dog breeds [ 27 , 42 ]. Therefore, the overrepresentation of a certain breed or body conformation may have led to different results in the distribution of body weight [ 42 ]. Additionally, the difference in the velocity range of the subjects and the method of normalization of this value may have led to different outcomes. It is known that kinetic gait parameters can be dependent on the velocity and acceleration of patients [ 43 , 44 ]. To avoid this influence, previous investigators have suggested maintaining the variables within a range during gait analysis [ 43 , 44 ]. In our study, all dogs were walked at velocities between 0.8 m/s and 1.4 m/s, in accordance with protocols validated in previous studies [ 43 , 44 ]. In contrast, the neurologic group in that study first walked at their preferred pace, which initially led to a significantly lower velocity than that of the clinically normal group [ 21 ]. Although the difference was not significant after the velocities of the groups were adjusted for the heights of the subjects by regression analysis, these overall differences in the data collection protocol and processing method may have contributed to the discrepancies in the gait variables in different studies.

Some studies found that the dogs with spinal cord injuries exhibit cranial shifts in the centre of pressure and the weight distribution measured by digital scales, compared to the healthy controls [ 45 , 46 ]. While the results may appear to be contradictory to that of the current study, it is notable that the severity of the diseases of the study population was very different in these studies, as both studies only included non-ambulatory paraparetic dogs or paraplegic dogs with or without pain perception. In contrast, the current study limited the inclusion criteria to dogs with ambulatory paraparesis and excluded any non-ambulatory dog, as the aetiology for these patients should be apparent at the time of the diagnosis and the comparison would be less clinically relevant. These differences in the findings suggest that the severity of the disease might influences the compensation mechanism in dogs with neurologic disease.

One of the notable changes in the neurologic group was the increase in the stance time of the forelimbs. When compared within a group, all groups had positive forelimb: hindlimb SI of the stance time, indicating that dogs in our study had a longer stance phase in the forelimbs than in the hindlimbs, regardless of their group. This finding is in agreement with another study that demonstrated longer stance times on the forelimbs than on the hindlimbs in dogs at a walk [ 47 ]. When comparing between groups, the forelimb: hindlimb SI stance time of the neurologic group was significantly greater than that of the normal group, which was not observed in the orthopaedic group. Instead, the orthopaedic group had relatively greater stride velocity in the forelimbs than the hindlimbs compared to the normal dogs. These distinct changes in spatiotemporal gait parameters in the orthopaedic and neurologic groups are likely reflective of different compensatory mechanisms for hindlimb instability: dogs in the neurologic group may stabilize their unsteady gait in the hindlimbs by increasing the time that the forelimbs are in contact with the ground, while dogs in the orthopaedic group may take quicker strides in the forelimbs to afford the increased weight distribution.

In our study, we found no significant differences in forelimb: hindlimb SI of the stride time or stride length among the groups. The neurologic group was the only group with negative mean values, as well as the lowest median forelimb: hindlimb SI values for stride time and stride length, but the differences between the neurologic group and the other groups did not reach statistical significance. Although our study did not find statistically corroborating results, a published study reported decreased stride time and stride length in the forelimbs of dogs with thoracolumbar myelopathy and hindlimb ataxia [ 22 ]. It has been shown that dogs with neurologic disease have greater variances in the spatiotemporal gait parameters compared to clinically normal dogs [ 21 ]. A larger sample size with the variables normalized to the height of the subjects may be required to detect statistically significant differences. In addition, the onset, progression, and chronicity of diseases in the neurologic group were not specified in the current study. These factors may have affected the degree or pattern of gait compensation. Future studies focusing on a specific disease process with a similar chronicity, disease progression, or neurologic grading may lead to different results.

The overall changes observed in the neurologic group included an increase in forelimb stance time and a relatively lower stride time and length. These findings are similar to those of a previously reported gait analysis study in rats with experimentally induced spinal cord injuries, in which the rats had increased stance time and decreased stride length in the forelimbs [ 48 ]. On the other hand, the orthopaedic group had increased body weight distribution and stride velocity in the forelimbs compared to those on the hindlimbs, without any increase in stance time. Thus, this can be interpreted as dogs with bilateral hindlimb lameness compensate by shifting body weight cranially, which subsequently increases the stride velocity of the forelimb to support weight shift during each gait cycle. Based on these observations, gait parameters such as %BWD, VID, forelimb: hindlimb SI of stance time, and stride velocity are worthy of further investigation to evaluate their potential to discriminate between the two presentations. A further study that determines the cut-off value for each variable and receiver operating characteristic (ROC) curve may assess the accuracy of the subset of these parameters in discriminating dogs with bilateral hindlimb lameness and ataxia based on the data obtained by the PSW.

The main limitation of the study was the relatively small sample size, which may have led to a type II error. This was demonstrated by the apparent sidedness observed in the orthopaedic group, even though all dogs within the group were confirmed to have bilateral orthopaedic diseases and decreased weight-bearing in both hindlimbs, as confirmed by gait analysis. The small sample size may also have affected the gait parameters for the neurologic group, especially when they had the greatest variability within the dataset, with greater ranges in many of the analysed gait parameters. While all dogs included in the neurologic group were classified as grade 2 (ambulatory paraparesis) based on the Modified Frankel Scale, the clinical status of individuals varied greatly from mild to severe ataxia. This inherent variability of the data in subjects with neurologic disease has been noted in both humans and dogs, and the use of the coefficient of variation of variables, rather than individual mean values, has been advocated for these patients [ 22 , 49 , 50 ]. Because the current study focused on the characterization of the spatiotemporal and kinetic gait parameters obtained by the PSW for each group to provide a pilot data for further investigation in their diagnostic potentials, the coefficient of variation was not included in the variables. Further studies including larger sample sizes and three-way comparisons of the coefficient of variation of the neurologic group, the orthopaedic group, and the normal group may reveal further discriminating gait parameters and patterns among the groups. Larger sample sizes will also help to build reliable predictive models based on the discriminating gait parameters found in the current study, which can be used to evaluate the reliability of the PSW as a diagnostic tool.

Another limitation of the current study is that the dogs were assigned to pre-selected groups based on the clinician’s subjective evaluation. Although this study established baseline gait parameters for each group and demonstrated the potential use of the PSW, its effectiveness in distinguishing between the groups could not be evaluated with the current study design. Future research will be needed to further verify the feasibility and utility of the PSW as a diagnostic tool. Our study included a heterogeneous group of dogs of various breeds, weights, and body conformations. Although this is a more accurate and practical presentation of clinical settings, one study suggested that various breeds, body conformations, heights, and weights of dogs can affect spatiotemporal and kinetic gait parameters [ 42 ]. There were no significant differences in age or sex among the groups in the current study, but the mean weight of the orthopaedic group was greater than that of the other groups. This was reflective of the fact that many of the dogs within the group were large breeds that presented with bilateral cruciate ligament disease. While authors are aware of this potential source of bias, it also reflects patient demographics encountered in a clinical setting. Additionally, a recent study showed that the %BWD and most SI values have low variability in a heterogeneous dog group [ 27 ]. The SI value also has a benefit in that it eliminates interpatient variability, as the patient serves as its own control. Thus, we focused on the comparison of the normalized kinetic variables and SI values to minimize the potential influence from the breeds and confirmation by comparing the changes in variables within the patient.

In conclusion, the orthopaedic and neurologic groups exhibited distinct changes in spatiotemporal and kinetic gait parameters compared to those of normal dogs. The findings also suggest that dogs with hindlimb gait abnormalities may have different compensatory mechanisms for their gait deficiencies depending on whether their gait abnormalities are orthopaedic or neurologic in origin. Compared to those in the normal group, significant differences were found in gait parameters such as the %BWD and forelimb: hindlimb SI values of the stride velocity of the orthopaedic group and in the SI stance time of the neurologic group. In the future, a larger-scale study may help to determine the optimal cut-off value and build predictive models based on the discriminating gait parameters found in the current study. This may further support the utility of the PSW in differentiating between two presentations that are often difficult to determine clinically.

Availability of data and materials

All data on the gait parameters that support the findings of this study are included within the manuscript and its supplementary Information files.

Abbreviations

Peak vertical force

Vertical impulse

Pressure sensitive walkway

Percentage of body weight distribution

Vertical impulse distribution

Symmetry index

Right forelimb

Left forelimb

Right hindlimb

Left hindlimb

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Acknowledgements

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This study was chosen as the winner of the 2020 Purina-sponsored grant contest by the American Association of Rehabilitation Veterinarians. The grant was awarded for data collection and statistical analysis.

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Park, C., Sawyere, D.M., Pancotto, T.E. et al. Characterization of spatiotemporal and kinetic gait variables in dogs with hindlimb ataxia and bilateral hindlimb lameness. BMC Vet Res 20 , 405 (2024). https://doi.org/10.1186/s12917-024-04265-8

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Indian Dermatol Online J
v.10(1); Jan-Feb 2019

Types of Variables, Descriptive Statistics, and Sample Size

Feroze kaliyadan.

Department of Dermatology, King Faisal University, Al Hofuf, Saudi Arabia

Vinay Kulkarni

1 Department of Dermatology, Prayas Amrita Clinic, Pune, Maharashtra, India

This short “snippet” covers three important aspects related to statistics – the concept of variables , the importance, and practical aspects related to descriptive statistics and issues related to sampling – types of sampling and sample size estimation.

What is a variable?[ 1 , 2 ] To put it in very simple terms, a variable is an entity whose value varies. A variable is an essential component of any statistical data. It is a feature of a member of a given sample or population, which is unique, and can differ in quantity or quantity from another member of the same sample or population. Variables either are the primary quantities of interest or act as practical substitutes for the same. The importance of variables is that they help in operationalization of concepts for data collection. For example, if you want to do an experiment based on the severity of urticaria, one option would be to measure the severity using a scale to grade severity of itching. This becomes an operational variable. For a variable to be “good,” it needs to have some properties such as good reliability and validity, low bias, feasibility/practicality, low cost, objectivity, clarity, and acceptance. Variables can be classified into various ways as discussed below.

Quantitative vs qualitative

A variable can collect either qualitative or quantitative data. A variable differing in quantity is called a quantitative variable (e.g., weight of a group of patients), whereas a variable differing in quality is called a qualitative variable (e.g., the Fitzpatrick skin type)

A simple test which can be used to differentiate between qualitative and quantitative variables is the subtraction test. If you can subtract the value of one variable from the other to get a meaningful result, then you are dealing with a quantitative variable (this of course will not apply to rating scales/ranks).

Quantitative variables can be either discrete or continuous

Discrete variables are variables in which no values may be assumed between the two given values (e.g., number of lesions in each patient in a sample of patients with urticaria).

Continuous variables, on the other hand, can take any value in between the two given values (e.g., duration for which the weals last in the same sample of patients with urticaria). One way of differentiating between continuous and discrete variables is to use the “mid-way” test. If, for every pair of values of a variable, a value exactly mid-way between them is meaningful, the variable is continuous. For example, two values for the time taken for a weal to subside can be 10 and 13 min. The mid-way value would be 11.5 min which makes sense. However, for a number of weals, suppose you have a pair of values – 5 and 8 – the midway value would be 6.5 weals, which does not make sense.

Under the umbrella of qualitative variables, you can have nominal/categorical variables and ordinal variables

Nominal/categorical variables are, as the name suggests, variables which can be slotted into different categories (e.g., gender or type of psoriasis).

Ordinal variables or ranked variables are similar to categorical, but can be put into an order (e.g., a scale for severity of itching).

Dependent and independent variables

In the context of an experimental study, the dependent variable (also called outcome variable) is directly linked to the primary outcome of the study. For example, in a clinical trial on psoriasis, the PASI (psoriasis area severity index) would possibly be one dependent variable. The independent variable (sometime also called explanatory variable) is something which is not affected by the experiment itself but which can be manipulated to affect the dependent variable. Other terms sometimes used synonymously include blocking variable, covariate, or predictor variable. Confounding variables are extra variables, which can have an effect on the experiment. They are linked with dependent and independent variables and can cause spurious association. For example, in a clinical trial for a topical treatment in psoriasis, the concomitant use of moisturizers might be a confounding variable. A control variable is a variable that must be kept constant during the course of an experiment.

Descriptive Statistics

Statistics can be broadly divided into descriptive statistics and inferential statistics.[ 3 , 4 ] Descriptive statistics give a summary about the sample being studied without drawing any inferences based on probability theory. Even if the primary aim of a study involves inferential statistics, descriptive statistics are still used to give a general summary. When we describe the population using tools such as frequency distribution tables, percentages, and other measures of central tendency like the mean, for example, we are talking about descriptive statistics. When we use a specific statistical test (e.g., Mann–Whitney U-test) to compare the mean scores and express it in terms of statistical significance, we are talking about inferential statistics. Descriptive statistics can help in summarizing data in the form of simple quantitative measures such as percentages or means or in the form of visual summaries such as histograms and box plots.

Descriptive statistics can be used to describe a single variable (univariate analysis) or more than one variable (bivariate/multivariate analysis). In the case of more than one variable, descriptive statistics can help summarize relationships between variables using tools such as scatter plots.

Descriptive statistics can be broadly put under two categories:

Sorting/grouping and illustration/visual displays
Summary statistics.

Sorting and grouping

Sorting and grouping is most commonly done using frequency distribution tables. For continuous variables, it is generally better to use groups in the frequency table. Ideally, group sizes should be equal (except in extreme ends where open groups are used; e.g., age “greater than” or “less than”).

Another form of presenting frequency distributions is the “stem and leaf” diagram, which is considered to be a more accurate form of description.

Suppose the weight in kilograms of a group of 10 patients is as follows:

56, 34, 48, 43, 87, 78, 54, 62, 61, 59

The “stem” records the value of the “ten's” place (or higher) and the “leaf” records the value in the “one's” place [ Table 1 ].

Stem and leaf plot


0	-
1	-
2	-
3	4
4	3 8
5	4 6 9
6	1 2
7	8
8	7
9	-

Illustration/visual display of data

The most common tools used for visual display include frequency diagrams, bar charts (for noncontinuous variables) and histograms (for continuous variables). Composite bar charts can be used to compare variables. For example, the frequency distribution in a sample population of males and females can be illustrated as given in Figure 1 .

An external file that holds a picture, illustration, etc.
Object name is IDOJ-10-82-g001.jpg

Composite bar chart

A pie chart helps show how a total quantity is divided among its constituent variables. Scatter diagrams can be used to illustrate the relationship between two variables. For example, global scores given for improvement in a condition like acne by the patient and the doctor [ Figure 2 ].

An external file that holds a picture, illustration, etc.
Object name is IDOJ-10-82-g002.jpg

Scatter diagram

Summary statistics

The main tools used for summary statistics are broadly grouped into measures of central tendency (such as mean, median, and mode) and measures of dispersion or variation (such as range, standard deviation, and variance).

Imagine that the data below represent the weights of a sample of 15 pediatric patients arranged in ascending order:

30, 35, 37, 38, 38, 38, 42, 42, 44, 46, 47, 48, 51, 53, 86

Just having the raw data does not mean much to us, so we try to express it in terms of some values, which give a summary of the data.

The mean is basically the sum of all the values divided by the total number. In this case, we get a value of 45.

The problem is that some extreme values (outliers), like “'86,” in this case can skew the value of the mean. In this case, we consider other values like the median, which is the point that divides the distribution into two equal halves. It is also referred to as the 50 th percentile (50% of the values are above it and 50% are below it). In our previous example, since we have already arranged the values in ascending order we find that the point which divides it into two equal halves is the 8 th value – 42. In case of a total number of values being even, we choose the two middle points and take an average to reach the median.

The mode is the most common data point. In our example, this would be 38. The mode as in our case may not necessarily be in the center of the distribution.

The median is the best measure of central tendency from among the mean, median, and mode. In a “symmetric” distribution, all three are the same, whereas in skewed data the median and mean are not the same; lie more toward the skew, with the mean lying further to the skew compared with the median. For example, in Figure 3 , a right skewed distribution is seen (direction of skew is based on the tail); data values' distribution is longer on the right-hand (positive) side than on the left-hand side. The mean is typically greater than the median in such cases.

An external file that holds a picture, illustration, etc.
Object name is IDOJ-10-82-g003.jpg

Location of mode, median, and mean

Measures of dispersion

The range gives the spread between the lowest and highest values. In our previous example, this will be 86-30 = 56.

A more valuable measure is the interquartile range. A quartile is one of the values which break the distribution into four equal parts. The 25 th percentile is the data point which divides the group between the first one-fourth and the last three-fourth of the data. The first one-fourth will form the first quartile. The 75 th percentile is the data point which divides the distribution into a first three-fourth and last one-fourth (the last one-fourth being the fourth quartile). The range between the 25 th percentile and 75 th percentile is called the interquartile range.

Variance is also a measure of dispersion. The larger the variance, the further the individual units are from the mean. Let us consider the same example we used for calculating the mean. The mean was 45.

For the first value (30), the deviation from the mean will be 15; for the last value (86), the deviation will be 41. Similarly we can calculate the deviations for all values in a sample. Adding these deviations and averaging will give a clue to the total dispersion, but the problem is that since the deviations are a mix of negative and positive values, the final total becomes zero. To calculate the variance, this problem is overcome by adding squares of the deviations. So variance would be the sum of squares of the variation divided by the total number in the population (for a sample we use “n − 1”). To get a more realistic value of the average dispersion, we take the square root of the variance, which is called the “standard deviation.”

The box plot

The box plot is a composite representation that portrays the mean, median, range, and the outliers [ Figure 4 ].

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Object name is IDOJ-10-82-g004.jpg

The concept of skewness and kurtosis

Skewness is a measure of the symmetry of distribution. Basically if the distribution curve is symmetric, it looks the same on either side of the central point. When this is not the case, it is said to be skewed. Kurtosis is a representation of outliers. Distributions with high kurtosis tend to have “heavy tails” indicating a larger number of outliers, whereas distributions with low kurtosis have light tails, indicating lesser outliers. There are formulas to calculate both skewness and kurtosis [Figures [Figures5 5 – 8 ].

An external file that holds a picture, illustration, etc.
Object name is IDOJ-10-82-g005.jpg

Positive skew

An external file that holds a picture, illustration, etc.
Object name is IDOJ-10-82-g008.jpg

High kurtosis (positive kurtosis – also called leptokurtic)

An external file that holds a picture, illustration, etc.
Object name is IDOJ-10-82-g006.jpg

Negative skew

An external file that holds a picture, illustration, etc.
Object name is IDOJ-10-82-g007.jpg

Low kurtosis (negative kurtosis – also called “Platykurtic”)

Sample Size

In an ideal study, we should be able to include all units of a particular population under study, something that is referred to as a census.[ 5 , 6 ] This would remove the chances of sampling error (difference between the outcome characteristics in a random sample when compared with the true population values – something that is virtually unavoidable when you take a random sample). However, it is obvious that this would not be feasible in most situations. Hence, we have to study a subset of the population to reach to our conclusions. This representative subset is a sample and we need to have sufficient numbers in this sample to make meaningful and accurate conclusions and reduce the effect of sampling error.

We also need to know that broadly sampling can be divided into two types – probability sampling and nonprobability sampling. Examples of probability sampling include methods such as simple random sampling (each member in a population has an equal chance of being selected), stratified random sampling (in nonhomogeneous populations, the population is divided into subgroups – followed be random sampling in each subgroup), systematic (sampling is based on a systematic technique – e.g., every third person is selected for a survey), and cluster sampling (similar to stratified sampling except that the clusters here are preexisting clusters unlike stratified sampling where the researcher decides on the stratification criteria), whereas nonprobability sampling, where every unit in the population does not have an equal chance of inclusion into the sample, includes methods such as convenience sampling (e.g., sample selected based on ease of access) and purposive sampling (where only people who meet specific criteria are included in the sample).

An accurate calculation of sample size is an essential aspect of good study design. It is important to calculate the sample size much in advance, rather than have to go for post hoc analysis. A sample size that is too less may make the study underpowered, whereas a sample size which is more than necessary might lead to a wastage of resources.

We will first go through the sample size calculation for a hypothesis-based design (like a randomized control trial).

The important factors to consider for sample size calculation include study design, type of statistical test, level of significance, power and effect size, variance (standard deviation for quantitative data), and expected proportions in the case of qualitative data. This is based on previous data, either based on previous studies or based on the clinicians' experience. In case the study is something being conducted for the first time, a pilot study might be conducted which helps generate these data for further studies based on a larger sample size). It is also important to know whether the data follow a normal distribution or not.

Two essential aspects we must understand are the concept of Type I and Type II errors. In a study that compares two groups, a null hypothesis assumes that there is no significant difference between the two groups, and any observed difference being due to sampling or experimental error. When we reject a null hypothesis, when it is true, we label it as a Type I error (also denoted as “alpha,” correlating with significance levels). In a Type II error (also denoted as “beta”), we fail to reject a null hypothesis, when the alternate hypothesis is actually true. Type II errors are usually expressed as “1- β,” correlating with the power of the test. While there are no absolute rules, the minimal levels accepted are 0.05 for α (corresponding to a significance level of 5%) and 0.20 for β (corresponding to a minimum recommended power of “1 − 0.20,” or 80%).

Effect size and minimal clinically relevant difference

For a clinical trial, the investigator will have to decide in advance what clinically detectable change is significant (for numerical data, this is could be the anticipated outcome means in the two groups, whereas for categorical data, it could correlate with the proportions of successful outcomes in two groups.). While we will not go into details of the formula for sample size calculation, some important points are as follows:

In the context where effect size is involved, the sample size is inversely proportional to the square of the effect size. What this means in effect is that reducing the effect size will lead to an increase in the required sample size.

Reducing the level of significance (alpha) or increasing power (1-β) will lead to an increase in the calculated sample size.

An increase in variance of the outcome leads to an increase in the calculated sample size.

A note is that for estimation type of studies/surveys, sample size calculation needs to consider some other factors too. This includes an idea about total population size (this generally does not make a major difference when population size is above 20,000, so in situations where population size is not known we can assume a population of 20,000 or more). The other factor is the “margin of error” – the amount of deviation which the investigators find acceptable in terms of percentages. Regarding confidence levels, ideally, a 95% confidence level is the minimum recommended for surveys too. Finally, we need an idea of the expected/crude prevalence – either based on previous studies or based on estimates.

Sample size calculation also needs to add corrections for patient drop-outs/lost-to-follow-up patients and missing records. An important point is that in some studies dealing with rare diseases, it may be difficult to achieve desired sample size. In these cases, the investigators might have to rework outcomes or maybe pool data from multiple centers. Although post hoc power can be analyzed, a better approach suggested is to calculate 95% confidence intervals for the outcome and interpret the study results based on this.

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There are no conflicts of interest.

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