three types of variables in thesis

Have a language expert improve your writing

Run a free plagiarism check in 10 minutes, automatically generate references for free.

• Knowledge Base
• Methodology
• Types of Variables in Research | Definitions & Examples

Types of Variables in Research | Definitions & Examples

Published on 19 September 2022 by Rebecca Bevans . Revised on 28 November 2022.

In statistical research, a variable is defined as an attribute of an object of study. Choosing which variables to measure is central to good experimental design .

You need to know which types of variables you are working with in order to choose appropriate statistical tests and interpret the results of your study.

You can usually identify the type of variable by asking two questions:

• What type of data does the variable contain?
• What part of the experiment does the variable represent?

Table of contents

Types of data: quantitative vs categorical variables, parts of the experiment: independent vs dependent variables, other common types of variables, frequently asked questions about variables.

Data is a specific measurement of a variable – it is the value you record in your data sheet. Data is generally divided into two categories:

• Quantitative data represents amounts.
• Categorical data represents groupings.

A variable that contains quantitative data is a quantitative variable ; a variable that contains categorical data is a categorical variable . Each of these types of variable can be broken down into further types.

Quantitative variables

When you collect quantitative data, the numbers you record represent real amounts that can be added, subtracted, divided, etc. There are two types of quantitative variables: discrete and continuous .

Categorical variables

Categorical variables represent groupings of some kind. They are sometimes recorded as numbers, but the numbers represent categories rather than actual amounts of things.

There are three types of categorical variables: binary , nominal , and ordinal variables.

*Note that sometimes a variable can work as more than one type! An ordinal variable can also be used as a quantitative variable if the scale is numeric and doesn’t need to be kept as discrete integers. For example, star ratings on product reviews are ordinal (1 to 5 stars), but the average star rating is quantitative.

Example data sheet

To keep track of your salt-tolerance experiment, you make a data sheet where you record information about the variables in the experiment, like salt addition and plant health.

To gather information about plant responses over time, you can fill out the same data sheet every few days until the end of the experiment. This example sheet is colour-coded according to the type of variable: nominal , continuous , ordinal , and binary .

Prevent plagiarism, run a free check.

Experiments are usually designed to find out what effect one variable has on another – in our example, the effect of salt addition on plant growth.

You manipulate the independent variable (the one you think might be the cause ) and then measure the dependent variable (the one you think might be the effect ) to find out what this effect might be.

You will probably also have variables that you hold constant ( control variables ) in order to focus on your experimental treatment.

In this experiment, we have one independent and three dependent variables.

The other variables in the sheet can’t be classified as independent or dependent, but they do contain data that you will need in order to interpret your dependent and independent variables.

What about correlational research?

When you do correlational research , the terms ‘dependent’ and ‘independent’ don’t apply, because you are not trying to establish a cause-and-effect relationship.

However, there might be cases where one variable clearly precedes the other (for example, rainfall leads to mud, rather than the other way around). In these cases, you may call the preceding variable (i.e., the rainfall) the predictor variable and the following variable (i.e., the mud) the outcome variable .

Once you have defined your independent and dependent variables and determined whether they are categorical or quantitative, you will be able to choose the correct statistical test .

But there are many other ways of describing variables that help with interpreting your results. Some useful types of variable are listed below.

A confounding variable is closely related to both the independent and dependent variables in a study. An independent variable represents the supposed cause , while the dependent variable is the supposed effect . A confounding variable is a third variable that influences both the independent and dependent variables.

Failing to account for confounding variables can cause you to wrongly estimate the relationship between your independent and dependent variables.

Discrete and continuous variables are two types of quantitative variables :

• Discrete variables represent counts (e.g., the number of objects in a collection).
• Continuous variables represent measurable amounts (e.g., water volume or weight).

You can think of independent and dependent variables in terms of cause and effect: an independent variable is the variable you think is the cause , while a dependent variable is the effect .

In an experiment, you manipulate the independent variable and measure the outcome in the dependent variable. For example, in an experiment about the effect of nutrients on crop growth:

• The  independent variable  is the amount of nutrients added to the crop field.
• The  dependent variable is the biomass of the crops at harvest time.

Defining your variables, and deciding how you will manipulate and measure them, is an important part of experimental design .

Cite this Scribbr article

If you want to cite this source, you can copy and paste the citation or click the ‘Cite this Scribbr article’ button to automatically add the citation to our free Reference Generator.

Bevans, R. (2022, November 28). Types of Variables in Research | Definitions & Examples. Scribbr. Retrieved 14 May 2024, from https://www.scribbr.co.uk/research-methods/variables-types/

Is this article helpful?

Rebecca Bevans

Other students also liked, a quick guide to experimental design | 5 steps & examples, quasi-experimental design | definition, types & examples, construct validity | definition, types, & examples.

• How it works

Types of Variables – A Comprehensive Guide

Published by Carmen Troy at August 14th, 2021 , Revised On October 26, 2023

A variable is any qualitative or quantitative characteristic that can change and have more than one value, such as age, height, weight, gender, etc.

Before conducting research, it’s essential to know what needs to be measured or analysed and choose a suitable statistical test to present your study’s findings. 

In most cases, you can do it by identifying the key issues/variables related to your research’s main topic.

Example:  If you want to test whether the hybridisation of plants harms the health of people. You can use the key variables like agricultural techniques, type of soil, environmental factors, types of pesticides used, the process of hybridisation, type of yield obtained after hybridisation, type of yield without hybridisation, etc.

Variables are broadly categorised into:

• Independent variables
• Dependent variable
• Control variable

Independent Vs. Dependent Vs. Control Variable

The research includes finding ways:

• To change the independent variables.
• To prevent the controlled variables from changing.
• To measure the dependent variables.

Note:  The term dependent and independent is not applicable in  correlational research  as this is not a  controlled experiment.  A researcher doesn’t have control over the variables. The association and between two or more variables are measured. If one variable affects another one, then it’s called the predictor variable and outcome variable.

Example:  Correlation between investment (predictor variable) and profit (outcome variable)

What data collection best suits your research?

• Find out by hiring an expert from ResearchProspect today!
• Despite how challenging the subject may be, we are here to help you.

Types of Variables Based on the Types of Data

A data is referred to as the information and statistics gathered for analysis of a research topic. Data is broadly divided into two categories, such as:

Quantitative/Numerical data  is associated with the aspects of measurement, quantity, and extent. 

Categorial data  is associated with groupings.

A qualitative variable consists of qualitative data, and a quantitative variable consists of a quantitative variable.

Quantitative Variable

The quantitative variable is associated with measurement, quantity, and extent, like how many . It follows the statistical, mathematical, and computational techniques in numerical data such as percentages and statistics. The research is conducted on a large group of population.

Example:  Find out the weight of students of the fifth standard studying in government schools.

The quantitative variable can be further categorised into continuous and discrete.

Categorial Variable

The categorical variable includes measurements that vary in categories such as names but not in terms of rank or degree. It means one level of a categorical variable cannot be considered better or greater than another level. 

Example: Gender, brands, colors, zip codes

The categorical variable is further categorised into three types:

Note:  Sometimes, an ordinal variable also acts as a quantitative variable. Ordinal data has an order, but the intervals between scale points may be uneven.

Example: Numbers on a rating scale represent the reviews’ rank or range from below average to above average. However, it also represents a quantitative variable showing how many stars and how much rating is given.

Not sure which statistical tests to use for your data?

Let the experts at researchprospect do the daunting work for you..

Using our approach, we illustrate how to collect data, sample sizes, validity, reliability, credibility, and ethics, so you won’t have to do it all by yourself!

Other Types of Variables

It’s important to understand the difference between dependent and independent variables and know whether they are quantitative or categorical to choose the appropriate statistical test.

There are many other types of variables to help you differentiate and understand them.

Also, read a comprehensive guide written about inductive and deductive reasoning .

• Entertainment
• Online education
• Database management, storage, and retrieval

Frequently Asked Questions

What are the 10 types of variables in research.

The 10 types of variables in research are:

• Independent
• Confounding
• Categorical
• Extraneous.

What is an independent variable?

An independent variable, often termed the predictor or explanatory variable, is the variable manipulated or categorized in an experiment to observe its effect on another variable, called the dependent variable. It’s the presumed cause in a cause-and-effect relationship, determining if changes in it produce changes in the observed outcome.

What is a variable?

In research, a variable is any attribute, quantity, or characteristic that can be measured or counted. It can take on various values, making it “variable.” Variables can be classified as independent (manipulated), dependent (observed outcome), or control (kept constant). They form the foundation for hypotheses, observations, and data analysis in studies.

What is a dependent variable?

A dependent variable is the outcome or response being studied in an experiment or investigation. It’s what researchers measure to determine the effect of changes in the independent variable. In a cause-and-effect relationship, the dependent variable is presumed to be influenced or caused by the independent variable.

What is a variable in programming?

In programming, a variable is a symbolic name for a storage location that holds data or values. It allows data storage and retrieval for computational operations. Variables have types, like integer or string, determining the nature of data they can hold. They’re fundamental in manipulating and processing information in software.

What is a control variable?

A control variable in research is a factor that’s kept constant to ensure that it doesn’t influence the outcome. By controlling these variables, researchers can isolate the effects of the independent variable on the dependent variable, ensuring that other factors don’t skew the results or introduce bias into the experiment.

What is a controlled variable in science?

In science, a controlled variable is a factor that remains constant throughout an experiment. It ensures that any observed changes in the dependent variable are solely due to the independent variable, not other factors. By keeping controlled variables consistent, researchers can maintain experiment validity and accurately assess cause-and-effect relationships.

How many independent variables should an investigation have?

Ideally, an investigation should have one independent variable to clearly establish cause-and-effect relationships. Manipulating multiple independent variables simultaneously can complicate data interpretation.

However, in advanced research, experiments with multiple independent variables (factorial designs) are used, but they require careful planning to understand interactions between variables.

You May Also Like

Content analysis is used to identify specific words, patterns, concepts, themes, phrases, or sentences within the content in the recorded communication.

This post provides the key disadvantages of secondary research so you know the limitations of secondary research before making a decision.

A case study is a detailed analysis of a situation concerning organizations, industries, and markets. The case study generally aims at identifying the weak areas.

USEFUL LINKS

LEARNING RESOURCES

COMPANY DETAILS

• How It Works

Research Variables 101

Independent variables, dependent variables, control variables and more

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

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!

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.

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!

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 .

Psst... there’s more!

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

You Might Also Like:

Very informative, concise and helpful. Thank you

Helping information.Thanks

practical and well-demonstrated

Very helpful and insightful

Submit a Comment Cancel reply

Your email address will not be published. Required fields are marked *

Save my name, email, and website in this browser for the next time I comment.

• Print Friendly

• Cookies & Privacy
• GETTING STARTED
• Introduction
• FUNDAMENTALS
• Acknowledgements
• Research questions & hypotheses
• Concepts, constructs & variables
• Research limitations
• Getting started
• Sampling Strategy
• Research Quality
• Research Ethics
• Data Analysis

Types of variables

Understanding the types of variables you are investigating in your dissertation is necessary for all types of quantitative research design , whether you using an experimental , quasi-experimental , relationship-based or descriptive research design. When you carry out your dissertation, you may need to measure , manipulate and/or control the variables you are investigating. In the section on Research Designs , you can learn more about the various types of quantitative research design. In this article, we present and illustrate the different types of variables you may come across in your dissertation. First, we discuss the main groups of variables: categorical variables and continuous variables . Second, we explain what dependent and independent variables are. This will provide you with one of the foundations required to tackle a dissertation based on a quantitative research design.

Categorical and continuous variables

Dependent and independent variables, ambiguities in classifying variables.

There are two groups of variables that you need to know about: categorical variables and continuous variables . We use the word groups of variables because both categorical and continuous variables include additional types of variable. However, there can also be some ambiguities when deciding whether a variable is categorical or continuous. We discuss the two groups of variable, as well as these potential ambiguities, in the sections that follow:

Categorical variables

Categorical variables are also known as qualitative (or discrete ) variables . These categorical variables can be further classified as being nominal , dichotomous or ordinal variables. Each of these types of categorical variable (i.e., nominal , dichotomous and ordinal ) has what are known as categories or levels . These categories or levels are the descriptions that you give a variable that help to explain how variables should be measured, manipulated and/or controlled. Take the following example:

Career choices of university students You are interested in the career choices of university students . You could ask university students a number of closed questions related to their career choices. For example: What is your planned occupation? What is the most important factor influencing your career choice?

The first question highlights the use of categories and the second question levels . For example:

Question 1 : What is your planned occupation? Variables with categories

Architect Attorney Biochemist Engineer Dentist Doctor Entrepreneur Social Worker Teacher ETC...

Career prospects Nature of the work Physical working conditions Salary and benefits ETC...

What is important to note about the categories in question 1 and the levels in question 2 is that these will be created by you. Ideally, you will have included these categories or levels based on some primary or secondary research. Ultimately, you choose which categories or levels to include and how many categories or levels there should be.

Each of these types of categorical variable (i.e., nominal , dichotomous and ordinal ) are described below with associated examples:

Nominal variables

The following are examples of nominal variables. These nominal variables could address questions like:

These examples highlight two core characteristics of nominal variables:

Nominal variables have two or more categories.

Nominal variables do not have an intrinsic order.

When we talk about nominal variables not having an intrinsic order , we mean that they can only have categories (e.g., black, blond, brown and red hair); not levels (e.g., a Likert scale from 1 to 5).

Dichotomous variables

The following are examples of dichotomous variables. These dichotomous variables could address questions like:

Dichotomous variables are nominal variables that have just two categories. They have a number of characteristics:

Dichotomous variables are designed to give you an either/or response

For example, you are either male or female. You either like watching television (i.e., you answer YES ) or you don't (i.e., you answer NO ).

Dichotomous variables can either be fixed or designed

For example, some variables (e.g., your sex ) can only be dichotomous (i.e., you can only be male or female ). They are therefore fixed . In other cases, dichotomous variables are designed by the researcher. For example, take the question: Do you like watching television? We have determined that the respondent can only select YES (i.e., I like watching television) or NO (i.e., I don't like watching television). However, another researcher could provide the respondent with more than two categories to this question (e.g., most of the time, sometimes , hardly ever ). Where more than two categories are used, these variables become known as nominal variables rather than dichotomous ones.

Ordinal variables

Just like nominal variables, ordinal variables have two or more categories. However, unlike nominal variables, ordinal variables can also be ordered or ranked (i.e., they have levels ). For example, take the following example of an ordinal variable:

So if you asked someone if they liked the policies of the Democratic Party and you presented them with the following three categories: Not very much , They are OK , or Yes, a lot ; you have an ordinal variable. Why? Because you have 3 categories ? namely Not very much , They are OK , and Yes, a lot ? and you can rank them from the most positive (Yes, a lot), to the middle response (They are OK), to the least positive (Not very much). However, whilst we can rank the three categories , we cannot place a value to them. For example, we cannot say that the response, They are OK , is twice as positive as the response, Not very much .

Other examples of ordinal variables are:

When it comes to Likert scales, as highlighted in the previous example, there can be some disagreement over whether these should be considered ordinal variables or continuous variables [see the section: Ambiguities in classifying variables ].

Continuous variables

Continuous variables, which are also known as quantitative variables, can be further classified a being either interval or ratio variables. Each of these types of continuous variable (i.e., interval and ratio ) has numerical properties. These numerical properties are the values by which continuous variables can be measured, manipulated and/or controlled. We illustrate the two types of continuous variable (i.e., interval and ratio ) and some associated values in the sections that follow:

Interval variables

Interval variables have a numerical value and can be measured along a continuum . Some examples of interval variables are:

However, temperature measured in degrees Celsius or Fahrenheit is NOT a ratio variable. This is because temperature measured in degrees Celsius or Fahrenheit is not a ratio variable because 0C does not mean there is no temperature.

Ratio variables

Ratio variables are interval variables that meet an additional condition: a measurement value of 0 (zero) must mean that there is none of that variable. Some examples of ratio variables are:

Sometimes, the measurement scale for data is ordinal , but the variable is treated as though it were continuous . This is more often the case when using Likert scales. When a Likert scale has five values (e.g., strongly agree, agree, neither agree nor disagree, disagree, and strongly disagree), it is treated as an ordinal variable. However, when a Likert scale has seven or more values (e.g., strongly agree, moderately agree, agree, neither agree nor disagree, disagree, moderately disagree, and strongly disagree), the variable is sometimes treated as a continuous variable. Nonetheless, this is a matter of dispute. Some researchers would argue that a Likert scale should never be treated as a continuous variable, even with seven levels/values.

Since you are responsible for setting the measurement scale for a variable, you will need to think carefully about how you characterise a variable. For example, social scientists may be more likely to consider the variable gender to be a nominal variable. This is because they view gender as having a number of categories, including male, female, bisexual and transsexual. By contrast, other researchers may simply view gender as a dichotomous variable, having just two categories: male and female. In such cases, it may be better to refer to the variable gender as sex .

A variable is not only something that you measure , but also something that you can manipulate and control for. An independent variable (sometimes called an experimental or predictor variable) is a variable that is being manipulated in an experiment in order to observe the effect this has on a dependent variable (sometimes called an outcome variable). The dependent variable is simply that; a variable that is dependent on an independent variable(s). We discuss these concepts in the example below:

For example: Imagine that a tutor asks 100 students to complete a maths test. The tutor wants to know why some students perform better than others. Whilst the tutor does not know the answer to this, she thinks that it might be because of two reasons:

Some students spend more time revising for their test; and

Some students are naturally more intelligent than others.

Therefore, the tutor decides to investigate the effect of revision time and intelligence on the test performance of the 100 students. As such, the dependent and independent variables for the study are:

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

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

You can find out more about the different uses of variables, especially in quantitative research designs (i.e., descriptive , experimental , quasi-experimental and relationship-based research designs), in the section on Research Designs .

An official website of the United States government

The .gov means it's official. Federal government websites often end in .gov or .mil. Before sharing sensitive information, make sure you're on a federal government site.

The site is secure. The https:// ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

• Publications
• Account settings
• Browse Titles

NCBI Bookshelf. A service of the National Library of Medicine, National Institutes of Health.

StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-.

StatPearls [Internet].

Types of variables and commonly used statistical designs.

Jacob Shreffler ; Martin R. Huecker .

Affiliations

Last Update: March 6, 2023 .

• Definition/Introduction

Suitable statistical design represents a critical factor in permitting inferences from any research or scientific study. [1]  Numerous statistical designs are implementable due to the advancement of software available for extensive data analysis. [1]  Healthcare providers must possess some statistical knowledge to interpret new studies and provide up-to-date patient care. We present an overview of the types of variables and commonly used designs to facilitate this understanding. [2]

• Issues of Concern

Individuals who attempt to conduct research and choose an inappropriate design could select a faulty test and make flawed conclusions. This decision could lead to work being rejected for publication or (worse) lead to erroneous clinical decision-making, resulting in unsafe practice. [1]  By understanding the types of variables and choosing tests that are appropriate to the data, individuals can draw appropriate conclusions and promote their work for an application. [3]

To determine which statistical design is appropriate for the data and research plan, one must first examine the scales of each measurement. [4]  Multiple types of variables determine the appropriate design.

Ordinal data (also sometimes referred to as discrete) provide ranks and thus levels of degree between the measurement. [5]  Likert items can serve as ordinal variables, but the Likert scale, the result of adding all the times, can be treated as a continuous variable. [6]  For example, on a 20-item scale with each item ranging from 1 to 5, the item itself can be an ordinal variable, whereas if you add up all items, it could result in a range from 20 to 100. A general guideline for determining if a variable is ordinal vs. continuous: if the variable has more than ten options, it can be treated as a continuous variable. [7]  The following examples are ordinal variables:

• Likert items
• Cancer stages
• Residency Year

Nominal, Categorical, Dichotomous, Binary

Other types of variables have interchangeable terms. Nominal and categorical variables describe samples in groups based on counts that fall within each category, have no quantitative relationships, and cannot be ranked. [8]  Examples of these variables include:

• Service (i.e., emergency, internal medicine, psychiatry, etc.)
• Mode of Arrival (ambulance, helicopter, car)

A dichotomous or a binary variable is in the same family as nominal/categorical, but this type has only two options. Binary logistic regression, which will be discussed below, has two options for the outcome of interest/analysis. Often used as (yes/no), examples of dichotomous or binary variables would be:

• Alive (yes vs. no)
• Insurance (yes vs. no)
• Readmitted (yes vs. no)

With this overview of the types of variables provided, we will present commonly used statistical designs for different scales of measurement. Importantly, before deciding on a statistical test, individuals should perform exploratory data analysis to ensure there are no issues with the data and consider type I, type II errors, and power analysis. Furthermore, investigators should ensure appropriate statistical assumptions. [9] [10]  For example, parametric tests, including some discussed below (t-tests, analysis of variance (ANOVA), correlation, and regression), require the data to have a normal distribution and that the variances within each group are similar. [6] [11]  After eliminating any issues based on exploratory data analysis and reducing the likelihood of committing type I and type II errors, a statistical test can be chosen. Below is a brief introduction to each of the commonly used statistical designs with examples of each type. An example of one research focus, with each type of statistical design discussed, can be found in Table 1 to provide more examples of commonly used statistical designs. 

Commonly Used Statistical Designs

Independent Samples T-test

An independent samples t-test allows a comparison of two groups of subjects on one (continuous) variable. Examples in biomedical research include comparing results of treatment vs. control group and comparing differences based on gender (male vs. female).

Example: Does adherence to the ketogenic diet (yes/no; two groups) have a differential effect on total sleep time (minutes; continuous)?

Paired T-test

A paired t-test analyzes one sample population, measuring the same variable on two different occasions; this is often useful for intervention and educational research.

Example :  Does participating in a research curriculum (one group with intervention) improve resident performance on a test to measure research competence (continuous)?

One-Way Analysis of Variance (ANOVA)

Analysis of variance (ANOVA), as an extension of the t-test, determines differences amongst more than two groups, or independent variables based on a dependent variable. [11]  ANOVA is preferable to conducting multiple t-tests as it reduces the likelihood of committing a type I error.

Example: Are there differences in length of stay in the hospital (continuous) based on the mode of arrival (car, ambulance, helicopter, three groups)?

Repeated Measures ANOVA

Another procedure commonly used if the data for individuals are recurrent (repeatedly measured) is a repeated-measures ANOVA. [1]  In these studies, multiple measurements of the dependent variable are collected from the study participants. [11]  A within-subjects repeated measures ANOVA determines effects based on the treatment variable alone, whereas mixed ANOVAs allow both between-group effects and within-subjects to be considered.

Within-Subjects Example: How does ketamine effect mean arterial pressure (continuous variable) over time (repeated measurement)?

Mixed Example: Does mean arterial pressure (continuous) differ between males and females (two groups; mixed) on ketamine throughout a surgical procedure (over time; repeated measurement)?  

Nonparametric Tests

Nonparametric tests, such as the Mann-Whitney U test (two groups; nonparametric t-test), Kruskal Wallis test (multiple groups; nonparametric ANOVA), Spearman’s rho (nonparametric correlation coefficient) can be used when data are ordinal or lack normality. [3] [5]  Not requiring normality means that these tests allow skewed data to be analyzed; they require the meeting of fewer assumptions. [11]

Example: Is there a relationship between insurance status (two groups) and cancer stage (ordinal)?  

A Chi-square test determines the effect of relationships between categorical variables, which determines frequencies and proportions into which these variables fall. [11]  Similar to other tests discussed, variants and extensions of the chi-square test (e.g., Fisher’s exact test, McNemar’s test) may be suitable depending on the variables. [8]

Example: Is there a relationship between individuals with methamphetamine in their system (yes vs. no; dichotomous) and gender (male or female; dichotomous)?

Correlation

Correlations (used interchangeably with ‘associations’) signal patterns in data between variables. [1]  A positive association occurs if values in one variable increase as values in another also increase. A negative association occurs if variables in one decrease while others increase. A correlation coefficient, expressed as r,  describes the strength of the relationship: a value of 0 means no relationship, and the relationship strengthens as r approaches 1 (positive relationship) or -1 (negative association). [5]

Example: Is there a relationship between age (continuous) and satisfaction with life survey scores (continuous)?

Linear Regression

Regression allows researchers to determine the degrees of relationships between a dependent variable and independent variables and results in an equation for prediction. [11]  A large number of variables are usable in regression methods.

Example: Which admission to the hospital metrics (multiple continuous) best predict the total length of stay (minutes; continuous)?

Binary Logistic Regression

This type of regression, which aims to predict an outcome, is appropriate when the dependent variable or outcome of interest is binary or dichotomous (yes/no; cured/not cured). [12]

Example: Which panel results (multiple of continuous, ordinal, categorical, dichotomous) best predict whether or not an individual will have a positive blood culture (dichotomous/binary)?

An example of one research focus, with each type of statistical design discussed, can be found in Table 1 to provide more examples of commonly used statistical designs.

(See Types of Variables and Statistical Designs Table 1)

• Clinical Significance

Though numerous other statistical designs and extensions of methods covered in this article exist, the above information provides a starting point for healthcare providers to become acquainted with variables and commonly used designs. Researchers should study types of variables before determining statistical tests to obtain relevant measures and valid study results. [6]  There is a recommendation to consult a statistician to ensure appropriate usage of the statistical design based on the variables and that the assumptions are upheld. [1]  With the variety of statistical software available, investigators must a priori understand the type of statistical tests when designing a study. [13]  All providers must interpret and scrutinize journal publications to make evidence-based clinical decisions, and this becomes enhanced by a limited but sound understanding of variables and commonly used study designs. [14]

• Nursing, Allied Health, and Interprofessional Team Interventions

All interprofessional healthcare team members need to be familiar with study design and the variables used in studies to accurately evaluate new data and studies as they are published and apply the latest data to patient care and drive optimal outcomes.

• Review Questions
• Access free multiple choice questions on this topic.
• Comment on this article.

Types of Variables and Statistical Designs Table 1 Contributed by Martin Huecker, MD and Jacob Shreffler, PhD

Disclosure: Jacob Shreffler declares no relevant financial relationships with ineligible companies.

Disclosure: Martin Huecker declares no relevant financial relationships with ineligible companies.

This book is distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ), which permits others to distribute the work, provided that the article is not altered or used commercially. You are not required to obtain permission to distribute this article, provided that you credit the author and journal.

• Cite this Page Shreffler J, Huecker MR. Types of Variables and Commonly Used Statistical Designs. [Updated 2023 Mar 6]. In: StatPearls [Internet]. Treasure Island (FL): StatPearls Publishing; 2024 Jan-.

In this Page

Bulk download.

• Bulk download StatPearls data from FTP

Related information

• PMC PubMed Central citations
• PubMed Links to PubMed

Similar articles in PubMed

• Suicidal Ideation. [StatPearls. 2024] Suicidal Ideation. Harmer B, Lee S, Duong TVH, Saadabadi A. StatPearls. 2024 Jan
• Prescription of Controlled Substances: Benefits and Risks. [StatPearls. 2024] Prescription of Controlled Substances: Benefits and Risks. Preuss CV, Kalava A, King KC. StatPearls. 2024 Jan
• The future of Cochrane Neonatal. [Early Hum Dev. 2020] The future of Cochrane Neonatal. Soll RF, Ovelman C, McGuire W. Early Hum Dev. 2020 Nov; 150:105191. Epub 2020 Sep 12.
• Review How to study improvement interventions: a brief overview of possible study types. [BMJ Qual Saf. 2015] Review How to study improvement interventions: a brief overview of possible study types. Portela MC, Pronovost PJ, Woodcock T, Carter P, Dixon-Woods M. BMJ Qual Saf. 2015 May; 24(5):325-36. Epub 2015 Mar 25.
• Review How to study improvement interventions: a brief overview of possible study types. [Postgrad Med J. 2015] Review How to study improvement interventions: a brief overview of possible study types. Portela MC, Pronovost PJ, Woodcock T, Carter P, Dixon-Woods M. Postgrad Med J. 2015 Jun; 91(1076):343-54.

Recent Activity

• Types of Variables and Commonly Used Statistical Designs - StatPearls Types of Variables and Commonly Used Statistical Designs - StatPearls

Your browsing activity is empty.

Activity recording is turned off.

Turn recording back on

Connect with NLM

National Library of Medicine 8600 Rockville Pike Bethesda, MD 20894

Web Policies FOIA HHS Vulnerability Disclosure

Help Accessibility Careers

What are Examples of Variables in Research?

Table of contents, introduction.

In writing your thesis, one of the first terms that you encounter is the word variable. Failure to understand the meaning and the usefulness of variables in your study will prevent you from doing excellent research. What are variables, and how do you use variables in your research?

I explain this key research concept below with lots of examples of variables commonly used in a study.

You may find it challenging to understand just what variables are in research, especially those that deal with quantitative data analysis. This initial difficulty about variables becomes much more confusing when you encounter the phrases “dependent variable” and “independent variable” as you go deeper in studying this vital concept of research, as well as statistics.

Understanding what variables mean is crucial in writing your thesis proposal because you will need these in constructing your conceptual framework  and in analyzing the data that you have gathered.

Therefore, it is a must that you should be able to grasp thoroughly the meaning of variables and ways on how to measure them. Yes, the variables should be measurable so that you will use your data for statistical analysis.

I will strengthen your understanding by providing examples of phenomena and their corresponding variables below.

Definition of Variable

Variables are those simplified portions of the complex phenomena that you intend to study. The word variable is derived from the root word “vary,” meaning, changing in amount, volume, number, form, nature, or type. These variables should be measurable, i.e., they can be counted or subjected to a scale.

The next section provides examples of variables related to climate change , academic performance, crime, fish kill, crop growth, and how content goes viral. Note that the variables in these phenomena can be measured, except the last one, where a bit more work is required.

Examples of Variables in Research: 6 Phenomena

The following are examples of phenomena from a global to a local perspective. The corresponding list of variables is given to illustrate how complex phenomena can be broken down into manageable pieces for better understanding and to subject the phenomena to research.

Phenomenon 1: Climate change

Examples of variables related to climate change :

• temperature
• the amount of carbon emission
• the amount of rainfall

Phenomenon 2: Crime and violence in the streets

Examples of variables related to crime and violence :

• number of robberies
• number of attempted murders
• number of prisoners
• number of crime victims
• number of laws enforcers
• number of convictions
• number of carnapping incidents

Phenomenon 3: Poor performance of students in college entrance exams

Examples of variables related to poor academic performance :

• entrance exam score
• number of hours devoted to studying
• student-teacher ratio
• number of students in the class
• educational attainment of teachers
• teaching style
• the distance of school from home
• number of hours devoted by parents in providing tutorial support

Phenomenon 4: Fish kill

Examples of variables related to fish kill :

• dissolved oxygen
• water salinity
• age of fish
• presence or absence of parasites
• presence or absence of heavy metal
• stocking density

Phenomenon 5: Poor crop growth

Examples of variables related to poor crop growth :

• the amount of nitrogen in the soil
• the amount of phosphorous in the soil
• the amount of potassium in the ground
• frequency of weeding
• type of soil

Phenomenon 6:  How Content Goes Viral

• interesting,
• surprising, and
• causing physiological arousal.

Notice in the above variable examples that all the factors listed under the phenomena can be counted or measured using an ordinal, ratio, or interval scale, except for the last one. The factors that influence how content goes viral are essentially subjective.

But researchers devised ways to measure those variables by grouping the respondents’ answers on whether content is positive, interesting, prominent, among others (see the  full description here ).

Thus, the variables in the last phenomenon represent the  nominal scale of measuring variables .

The expected values derived from these variables will be in terms of numbers, amount, category, or type. Quantified variables allow statistical analysis . Variable descriptions, correlations, or differences are then determined.

Difference Between Independent and Dependent Variables

Which of the above examples of variables are the independent and the dependent variables?

Independent Variables

The independent variables are those variables that may influence or affect the other variable, i.e., the dependent variable.

For example, in the second phenomenon, i.e., crime and violence in the streets, the independent variables are the number of law enforcers. If there are more law enforcers, it is expected that it will reduce the following:

• number of robberies,
• number of attempted murders,
• number of prisoners, 
• number of crime victims, and
• the number of carnapping incidents.

The five variables listed under crime and violence in the streets as the theme of a study are all dependent variables.

Dependent Variables

The dependent variable, as previously mentioned, is the variable affected or influenced by the independent variable.

For example, in the first phenomenon on climate change, temperature as the independent variable influences sea level rise, the dependent variable. Increased temperature will cause the expansion of water in the sea. Thus, sea-level rise on a global scale will occur.

I will leave the classification of the other variables to you. Find out whether those are independent or dependent variables. Note, however, that some variables can be both independent or dependent variables, as the context of the study dictates.

Finding the relationship between variables

How will you know that one variable may cause the other to behave in a certain way?

Finding the relationship between variables requires a thorough  review of the literature . Through a review of the relevant and reliable literature, you will find out which variables influence the other variable. You do not just guess relationships between variables. The entire process is the essence of research.

At this point, I believe that the concept of the variable is now clear to you. Share this information with your peers, who may have difficulty in understanding what the variables are in research.

Related Posts

Regression Analysis: 5 Steps and 4 Applications

Data Analysis: Five Essential Steps to Ensure Data Integrity, Accuracy, and Reliability

How to write the conceptual framework in a research proposal, about the author, patrick regoniel.

Dr. Regoniel, a faculty member of the graduate school, served as consultant to various environmental research and development projects covering issues and concerns on climate change, coral reef resources and management, economic valuation of environmental and natural resources, mining, and waste management and pollution. He has extensive experience on applied statistics, systems modelling and analysis, an avid practitioner of LaTeX, and a multidisciplinary web developer. He leverages pioneering AI-powered content creation tools to produce unique and comprehensive articles in this website.

128 Comments

Your question is unclear to me Biyaminu. What do you mean? If you want to cite this, see the citation box after the article.

• Pingback: Quantitative Research Design: 4 Common Ways to Gather Your Data Efficiently October 15, 2020

Dear Calvin, when you state your research objectives that’s where you will know if you need to use variables or not.

Great work. I’d just like to know in which situations are variables not used in scientific research please. thank you.

• Pingback: Nonparametric Tests: 8 Important Considerations Before Using Them October 11, 2020

I salute your work, before I was have no enough knowledge about variable I think I was claimed from my lecturers, but the real meaning I was in the mid night. thanks

Thank you very much for your nice NOTE! I have a question: Can you please give me any examples of variables in students’ indiscipline?

A well articulated exposition! Pls, I need a simple guide on the variables of the following topic : IMPACT OF TAX REFORMS ON REVENUE GENERATION IN NIGERIA: A CASE STUDY OF KOGI STATE. THANKS A LOT.

thanks for the explanation a bout variables. keep on posting information a bout reseach on my email.

This was extremely helpful and easy to digest

Dear Hamse, That depends on what variables you are studying. Are you doing a study on cause and effect?

Dear Sophia and Hamse,

As I mentioned earlier, please read the last part of the above article on how to determine the dependent and independent variables.

CHALLENGES FACING DEVELOPMENT OF COOPERATIVE MOVEMENT IN TANA RIVER COUNTY

What is the IV and DV of this Research topic?

You can see in the last part of the above article an explanation about dependent and independent variables.

Dear Maur, what you just want to do is to describe the challenges. No need for a conceptual framework.

Hey, I really appreciate your explanation however I’m having a hard time figuring out the IV and DV on the topic about fish kill, can you help me?

I am requested to write 50 variables in my research as per my topic which is about street vending. I am really clueless.

Hi Regoniel…your articles are much more guiding….pls am writing my thesis on impact of insurgency on Baga Road fish market Maiduguri.

How will my conceptual framework looks like What do I need to talk on

Dear Alhaji, just be clear about what you want to do. Your research question must be clearly stated before you build your conceptual framework.

• Pingback: How to Analyze Frequency Data | SimplyEducate.Me December 4, 2018

Thanks so much ! This article is so much simple to my understanding. A friend of my referred me to this site and I am so greatful. Please Sir, when writing the dependent and independent variables should it be in a table form ?

Dear Grace, Good day. I don’t understand what you mean. But if your school requires that the independent and dependent variables be written in table form, I see no problem with that. It’s just a way for you to clearly show what variables you are analyzing. And you need to justify that.

Can you please give me what are the possible variables in terms of installation of street lights along barangay roads of calauan, laguna: an assessment?

Hello sir, sorry to bother you but what are the guidelines for writing a good report

Guidelines for writing a good research report?

SimplyEducate.Me Privacy Policy

Conceptual and Theoretical Frameworks for Thesis Studies: What you must know

A theoretical framework is a conceptual model that provides a systematic and structured way of thinking about a research problem or question. It helps to identify key variables and the relationships between them and to guide the selection and interpretation of data. Theoretical frameworks draw on existing theories and research and can be used to develop new hypotheses or test existing ones. They provide a foundation for research design, data collection, and analysis and can help to ensure that research is relevant, rigorous, and coherent. Theoretical frameworks are common in many disciplines, including social sciences, natural sciences, and humanities, and are essential for building knowledge and advancing understanding in a field.

This article explains the importance of frameworks in a thesis study and the differences between conceptual frameworks and theoretical frameworks. It provides guidelines on how to write a thesis framework, definitions of variable types, and examples of framework types.

What is a research framework and why do I need one?

When planning your thesis study, you need to justify your research and explain its design to your readers. This is called the research framework.

When planning your thesis study, you need to justify your research and explain its design to your readers. This is called the research framework. Think of it as the foundation of a building. A good building needs a strong foundation. Similarly, your research needs to be supported by reviewing and explaining the existing knowledge in the field, describing how your research study will fit within or contribute to the existing literature (e.g., it could challenge or test an existing theory or address a knowledge gap), and informing the reader how your study design aligns with your thesis question or hypothesis.

Important components of the framework are a literature review of recent studies associated with your thesis topic as well as theories/models used in your field of research. The literature review acts as a filtering tool to select appropriate thesis questions and guide data collection, analysis, and interpretation of your findings. Think broadly! Apart from reviewing relevant published papers in your field of research, also explore theories that you have come across in your undergraduate courses, other published thesis studies, encyclopedias, and handbooks.

There are two types of research frameworks: theoretical and conceptual .

What is a conceptual framework?

A conceptual framework is a written or visual representation that explains the study variables and their relationships with each other. The starting point is a literature review of existing studies and theories about your topic.

Steps to develop a conceptual framework

• Clarify your study topic by identifying and defining key concepts in your thesis problem statement and thesis question. Essentially, your thesis should address a knowledge gap.
• Perform a literature review to provide a background to interpret and explain the study findings. Also, draw on empirical knowledge that you have gained from personal experience.
• Identify crucial variables from the literature review and your empirical knowledge, classify them as dependent or independent variables, and define them.
• Brainstorm all the possible factors that could affect each dependent variable.
• Propose relationships among the variables and determine any associations that exist between all variables.
• Use a flowchart or tree diagram to present your conceptual framework.

Types of variables

When developing a conceptual framework, you will need to identify the following:

• Independent variables
• Dependent variables
• Moderating variables
• Mediating variables
• Control variables

First, identify the independent (cause) and dependent (effect) variables in your study. Then, identify variables that influence this relationship, such as moderating variables, mediating variables, and control variables. A moderating variable changes the relationship between independent and dependent variables when its value increases or decreases. A mediating variable links independent and dependent variables to better explain the relationship between them. A control variable could potentially impact the cause-and-effect relationship but is kept constant throughout the study so that its effects on the findings/outcomes can be ruled out.

Example of a conceptual framework

You want to investigate the hours spent exercising (cause) on childhood obesity (effect).

Now, you need to consider moderating variables that affect the cause-and-effect relationship. In our example, the amount of junk food eaten would affect the level of obesity.

Next, you need to consider mediating variables. In our example, the maximum heart rate during exercise would affect the child’s weight.

Finally, you need to consider control variables. In this example, because we do not want to investigate the role of age in obesity, we can use this as a control variable. Thus, the study subjects would be children of a specific age (e.g., aged 6–10 years).

What is a theoretical framework?

A theoretical framework provides a general framework for data analysis. It defines the concepts used and explains existing theories and models in your field of research.

A theoretical framework provides a general framework for data analysis. It defines the concepts used and explains existing theories and models in your field of research. It also explains any assumptions that were used to inform your approach and your choice of specific rationales. Theoretical frameworks are often used in the fields of social sciences.

Purpose of a theoretical framework

• Test and challenge existing theories
• Establish orderly connections between observations and facts
• Predict and control situations
• Develop hypotheses

Steps to develop a theoretical framework

• Identify and define key concepts in your thesis problem statement and thesis question.
• Explain and evaluate existing theories by writing a literature review that describes the concepts, models, and theories that support your study.
• Choose the theory that best explains the relationships between the key variables in your study.
• Explain how your research study fills a knowledge gap or fits into existing studies (e.g., testing if an established theory applies to your thesis context).
• Discuss the relevance of any theoretical assumptions and limitations.

A thesis topic can be approached from a variety of angles, depending on the theories used.

• In psychology, a behavioral approach would use different methods and assumptions compared with a cognitive approach when treating anxiety.
• In literature, a book could be analyzed using different literary theories, such as Marxism or poststructuralism.

Structuring a theoretical framework

The structure of a theoretical framework is fluid, and there are no specific rules that need to be followed, as long as it is clearly and logically presented.

The theoretical framework is a natural extension of your literature review. The literature review should identify gaps in the field of your research, and reviewing existing theories will help to determine how these can be addressed. The structure of a theoretical framework is fluid, and there are no specific rules that need to be followed, as long as it is clearly and logically presented. The theoretical framework is sometimes integrated into the literature review chapter of a thesis, but it can also be included as a separate chapter, depending on the complexity of the theories.

Example of a theoretical framework

The sales staff at Company X are unmotivated and struggling to meet their monthly targets. Some members of the management team believe that this could be achieved by implementing a comprehensive product-training program, but others believe that introducing a sales commission structure will help.

Company X is not achieving their monthly sales targets

To increase monthly sales.

Research question:

How can Company X motivate their sales team to achieve its monthly sales targets?

Sub-questions:

• Why do the sales staff feel unmotivated?
• What is the relationship between motivation and monetary rewards?
• Do the sales staff feel that they have sufficient product knowledge?

Theoretical framework:

A literature search will need to be performed to understand the background of the many different theories of motivation in psychology. For example, Maslow’s Hierarchy of Needs (basic human needs—physiological, safety, love/belonging, esteem, and self-actualization—have to be fulfilled before one can live up to their true potential), Vroom’s Theory of Expectancy (people decide upon their actions based on the outcomes they expect), and Locke’s Goal-Setting Theory (goals are a key driver of one’s behavior). These theories would need to be investigated to determine which would be the best approach to increase the motivation of the sales staff in Company X so that the monthly sales targets are met.

A robust conceptual or theoretical framework is crucial when writing a thesis/dissertation. It defines your research gap, identifies your approach, and guides the interpretation of your results.

A thesis is the most important document you will write during your academic studies. For professional thesis editing and thesis proofreading services, check out Enago's Thesis Editing service s for more information.

Editor’s pick

Get free updates.

Subscribe to our newsletter for regular insights from the research and publishing industry!

What type of framework is used in the Humanities and Social Sciences (HSS) domain? +

Theoretical frameworks are typically used in the HSS domain, while conceptual frameworks are used in the Sciences domain.

What is the difference between mediating versus moderating variables? +

The difference between mediators and moderators can be confusing. A moderating variable is unaffected by the independent variable and can increase or decrease the strength of the relationship between the independent and dependent variables. A mediating variable is affected by the independent variable and can explain the relationship between the independent and dependent variables. T he statistical correlation between the independent and dependent variables is higher when the mediating variable is excluded.

What software should I use to present my conceptual framework? +

The software program Creately provides some useful templates that can help you get started. Other recommended programs are SmartDraw , Inkscape , and diagrams.net .

What Is a Variable in Science?

Understanding Variables in a Science Experiment

• Chemical Laws
• Periodic Table
• Projects & Experiments
• Scientific Method
• Biochemistry
• Physical Chemistry
• Medical Chemistry
• Chemistry In Everyday Life
• Famous Chemists
• Activities for Kids
• Abbreviations & Acronyms
• Weather & Climate
• Ph.D., Biomedical Sciences, University of Tennessee at Knoxville
• B.A., Physics and Mathematics, Hastings College

Variables are an important part of science projects and experiments. What is a variable? Basically, a variable is any factor that can be controlled, changed, or measured in an experiment. Scientific experiments have several types of variables. The independent and dependent variables are the ones usually plotted on a chart or graph, but there are other types of variables you may encounter.

Types of Variables

• Independent Variable: The independent variable is the one condition that you change in an experiment. Example: In an experiment measuring the effect of temperature on solubility, the independent variable is temperature.
• Dependent Variable: The dependent variable is the variable that you measure or observe. The dependent variable gets its name because it is the factor that is dependent on the state of the independent variable . Example: In the experiment measuring the effect of temperature on solubility, solubility would be the dependent variable.
• Controlled Variable: A controlled variable or constant variable is a variable that does not change during an experiment. Example : In the experiment measuring the effect of temperature on solubility, controlled variable could include the source of water used in the experiment, the size and type of containers used to mix chemicals, and the amount of mixing time allowed for each solution.
• Extraneous Variables: Extraneous variables are "extra" variables that may influence the outcome of an experiment but aren't taken into account during measurement. Ideally, these variables won't impact the final conclusion drawn by the experiment, but they may introduce error into scientific results. If you are aware of any extraneous variables, you should enter them in your lab notebook . Examples of extraneous variables include accidents, factors you either can't control or can't measure, and factors you consider unimportant. Every experiment has extraneous variables. Example : You are conducting an experiment to see which paper airplane design flies longest. You may consider the color of the paper to be an extraneous variable. You note in your lab book that different colors of papers were used. Ideally, this variable does not affect your outcome.

Using Variables in Science Experiment

In a science experiment , only one variable is changed at a time (the independent variable) to test how this changes the dependent variable. The researcher may measure other factors that either remain constant or change during the course of the experiment but are not believed to affect its outcome. These are controlled variables. Any other factors that might be changed if someone else conducted the experiment but seemed unimportant should also be noted. Also, any accidents that occur should be recorded. These are extraneous variables.

Variables and Attributes

In science, when a variable is studied, its attribute is recorded. A variable is a characteristic, while an attribute is its state. For example, if eye color is the variable, its attribute might be green, brown, or blue. If height is the variable, its attribute might be 5 m, 2.5 cm, or 1.22 km.

• Earl R. Babbie. The Practice of Social Research , 12th edition. Wadsworth Publishing, 2009.
• Scientific Variable
• What Is an Experiment? Definition and Design
• What Is a Dependent Variable?
• Difference Between Independent and Dependent Variables
• Independent Variable Definition and Examples
• Examples of Independent and Dependent Variables
• Dependent Variable Definition and Examples
• Scientific Method Vocabulary Terms
• Six Steps of the Scientific Method
• The Role of a Controlled Variable in an Experiment
• What Is the Difference Between a Control Variable and Control Group?
• DRY MIX Experiment Variables Acronym
• How To Design a Science Fair Experiment
• Understanding Experimental Groups
• What Are the Elements of a Good Hypothesis?
• Understanding Simple vs Controlled Experiments

Identifying Variables

Three types of tomatoes (MOs810, Wikimedia Commons)

How does this align with my curriculum?

Share on: facebook x/twitter linkedin pinterest.

Learn how scientists define independent, dependent and controlled variables in experimental inquiry.

As was mentioned in the  Asking Testable Questions  backgrounder, testable questions define the variables. In other words, what is being changed and what is to be kept constant, in an experimental inquiry.

What are variables in an experimental inquiry?

Scientists often use experimental inquiries to observe cause and effect relationships. In order to do so, scientists aim to make one change (the cause or  independent variable ) in order to determine if the variable is causing what is observed (the effect or  dependent variable ).

An experimental inquiry typically has three main types of variables: an independent variable, a dependent variable and controlled variables. We will look at each of these three types of variables and how they are related to experimental inquiries involving plants.

Independent Variables

The independent variable, also known as the experimental treatment , is the difference or change in the experimental conditions that is chosen by the scientist (the cause). To ensure a  fair test , a good experimental inquiry only has  one  independent variable and that variable should be something that can be measured quantitatively. For example, experimental inquiries about plants may include such independent variables as:

• Volume of water given to plants
• Nitrogen or phosphorus concentration in soil
• Duration, intensity or wavelength of light plants are exposed to
• Concentration or type of fertilizer

Dependent Variables

When a scientist chooses an independent variable (the cause), that person anticipates a certain response (the effect). This response is known as the dependent variable. The dependent variable should be something that is observable and measurable. Like the independent variable, an experimental inquiry should only have one dependent variable. For example, experimental inquiries about plants may include such dependent variables as:

• Days to germination
• Surface area of leaves
• Days to flowering or fruiting
• Dry mass (amount of plant material after all water has been removed)

Testable Question

How does the volume of water affect the number of days it takes for a tomato plant to flower?

Shown is a colour illustration explaining the relationship between an independent and a dependent variable. 

On the left is a blue oval with the word "Cause" inside it. This is labelled "Independent Variable" at the top, and "E.g., volume of water" below. On the right is a green rectangle with the word "Effect" inside. This is labelled "Dependent Variable" at the top, and "E.g., days to flowering" below. A red arrow points from cause on the left to the effect on the right.

Controlled Variables

In order for a scientist to ensure that only the independent variable is affecting the dependent variable, all the other factors acting upon the test situation (or test subjects) must be kept constant. The factors that must be kept the same are called the  controlled variables , or constant variables. In a given inquiry, there may be one or more variables that will need to be kept constant. For example, for an experimental inquiry in which you are interested in how the volume of water (independent variable) affects the days to flowering (dependent variable), you would want to keep constant:

• The type of seeds
• The type of soil
• The light source
• The humidity in the room
• The type of container (e.g., plastic pots vs. clay pots)
• The Temperature

Shown is a colour photograph of tomato plants in a greenhouse. 

Rows of tomato plants on both sides of the photograph stretch into the distance. Light comes in through a translucent ceiling. The plants are thick with green leaves. Tomato fruit is visible at the bottom of each plant. Most of the fruit is red and some is green.

A failure to control variables other than the independent variable will mean that you will not know which factor is actually causing the effects you see. In the example above, if some of the plants were sitting closer to the window than others, the differential exposure to light could be affecting the number of days to flowering, rather than the volume of water.

For more about designing experiments, see:  Setting Up a Fair Test

What are the variables in Tomatosphere™?

In the Seed Investigation, students investigate the germination rates of tomato seeds that have been to space (or exposed to space-like conditions) with seeds that have remained on Earth.

The  testable question  in the Seed Investigation is:

HOW DOES EXPOSURE TO THE SPACE ENVIRONMENT OR SPACE-LIKE CONDITIONS AFFECT THE GERMINATION RATE OF TOMATO SEEDS?

Independent variable:  type of seeds used - Earth seeds versus space seeds (sometimes seeds are treated to space-like conditions in years when seeds do not go to space)

Dependent variable:  number of seeds that germinate

Guided Practice

Have students read the following questions and determine the independent, dependent and potential controlled variables.

• How does the duration of light exposure affect the surface area of tomato plant leaves?
• How does the concentration of nitrogen fertilizer affect the days to flowering of tomato plants?
• How does the volume of water (mL) affect the number of days to germination of tomato plants?

In their own words, have students define the terms “Independent variable,” “Dependent variable,” and “Controlled variable.”

Have students brainstorm the variables that should be controlled in the Seed Investigation (e.g., quantity of water, type of soil, type of planting container, temperature, etc.).

Have the students think about the Seed Investigation and brainstorm variables that may not be controllable (e.g., giving plants different amounts of water, some plants being closer to a heat vent than others, using different types of soil, etc.).

• Independent variable:   duration of light (hours) Dependent variable:   surface area of plant leaves (Overall? Largest leaf? All leaves?) Controlled variable(s):   quantity of water, type of soil, depth of seeds, source of light, concentration/type of fertilizer (if any); temperature of the room, etc.
• Independent variable:   Concentration of nitrogen fertilizer Dependent variable:   days to flowering (when first flower on plants open) Controlled variable(s):   Same type of seeds, same quantity of water, same type of soil, same source of light, same duration of light, etc.
• Independent variable:   Volume of water in ml (per day) Dependent variable:   days to germination (when first seed germinates) Controlled variable(s):   Single type of seeds, same type of soil, same volume of soil, same type of pots, same source of light, same duration of light, temperature of the room, same time of day for watering, etc.

What are variables? How to use them in your science projects This page from Science Buddies explains different sorts of variables and how to use them to answer sample questions.

Controlled Variables This article by Explorable covers variables, control groups, and the value of consistency.

What are Independent and Dependent Variables?  (2019) This article by ThoughtCo explains how to tell the difference between independent and dependent variables, and how to plot variables on a graph.

Identifying and Controlling Variables in Scientific Investigations  (2015) This video (3:16 min.) from SciExperiment Basics explains how to identify and control variables in a scientific inquiry.

Related Topics

Online Plagiarism Checker For Academic Writing

Start Plagiarism Check

Online Proofreading for Your Academic Writing

Get it proofread now

Online Printing & Binding Services for Students

Configure binding now

• Academic essay overview
• The writing process
• Structuring academic essays
• Types of academic essays
• Academic writing overview
• Sentence structure
• Academic writing process
• Improving your academic writing
• Titles and headings
• APA style overview
• APA citation & referencing
• APA structure & sections
• Citation & referencing
• Structure and sections
• APA examples overview
• Commonly used citations
• Other examples
• British English vs. American English
• Chicago style overview
• Chicago citation & referencing
• Chicago structure & sections
• Chicago style examples
• Citing sources overview
• Citation format
• Citation examples
• College essay overview
• Application
• How to write a college essay
• Types of college essays
• Commonly confused words
• Definitions
• Dissertation overview
• Dissertation structure & sections
• Dissertation writing process
• Graduate school overview
• Application & admission
• Study abroad
• Harvard referencing overview
• Language rules overview
• Grammatical rules & structures
• Parts of speech
• Punctuation
• Methodology overview
• Analyzing data
• Experiments
• Observations
• Inductive vs. Deductive
• Qualitative vs. Quantitative
• Types of validity
• Types of reliability
• Sampling methods
• Theories & Concepts
• Types of research studies
• Types of variables
• MLA style overview
• MLA examples
• MLA citation & referencing
• MLA structure & sections
• Plagiarism overview
• Plagiarism checker
• Types of plagiarism
• Printing production overview
• Research bias overview
• Types of research bias
• Research paper structure & sections
• Types of research papers
• Research process overview
• Problem statement
• Research proposal
• Research topic
• Statistics overview
• Levels of measurment
• Measures of central tendency
• Hypothesis testing
• Parameters & test statistics
• Types of distributions
• Correlation
• Effect size
• Hypothesis testing assumptions
• Types of ANOVAs
• Types of chi-square
• Statistical data
• Statistical models
• Measures of variability
• Spelling mistakes
• Tips overview
• Academic writing tips
• Dissertation tips
• Sources tips
• Working with sources overview
• Evaluating sources
• Finding sources
• Including sources
• Types of sources

Your Step to Success

Online Printing & Binding

Types of Variables in Research – Definition & Examples

How do you like this article cancel reply.

Save my name, email, and website in this browser for the next time I comment.

A fundamental component in statistical investigations is the methodology you employ in selecting your research variables. The careful selection of appropriate variable types can significantly enhance the robustness of your experimental design . This piece explores the diverse array of variable classifications within the field of statistical research. Additionally, understanding the different types of variables in research can greatly aid in shaping your experimental hypotheses and outcomes.

Inhaltsverzeichnis

• 1 Types of Variables in Research – In a Nutshell
• 2 Definition: Types of variables in research
• 3 Types of variables in research – Quantitative vs. Categorical
• 4 Types of variables in research – Independent vs. Dependent
• 5 Other useful types of variables in research

Types of Variables in Research – In a Nutshell

• A variable is an attribute of an item of analysis in research.
• The types of variables in research can be categorized into: independent vs. dependent , or categorical vs. quantitative .
• The types of variables in research (correlational) can be classified into predictor or outcome variables.
• Other types of variables in research are confounding variables , latent variables , and composite variables.

Definition: Types of variables in research

A variable is a trait of an item of analysis in research. Types of variables in research are imperative, as they describe and measure places, people, ideas , or other research objects . There are many types of variables in research. Therefore, you must choose the right types of variables in research for your study.

Note that the correct variable will help with your research design , test selection, and result interpretation.

In a study testing whether some genders are more stress-tolerant than others, variables you can include are the level of stressors in the study setting, male and female subjects, and productivity levels in the presence of stressors.

Also, before choosing which types of variables in research to use, you should know how the various types work and the ideal statistical tests and result interpretations you will use for your study. The key is to determine the type of data the variable contains and the part of the experiment the variable represents.

Types of variables in research – Quantitative vs. Categorical

Data is the precise extent of a variable in statistical research that you record in a data sheet. It is generally divided into quantitative and categorical classes.

Quantitative or numerical data represents amounts, while categorical data represents collections or groupings.

The type of data contained in your variable will determine the types of variables in research. For instance, variables consisting of quantitative data are called quantitative variables, while those containing categorical data are called categorical variables. The section below explains these two types of variables in research better.

Quantitative variables

The scores you record when collecting quantitative data usually represent real values you can add, divide , subtract , or multiply . There are two types of quantitative variables: discrete variables and continuous variables .

The table below explains the elements that set apart discrete and continuous types of variables in research:

Categorical variables

Categorical variables contain data representing groupings. Additionally, the data in categorical variables is sometimes recorded as numbers . However, the numbers represent categories instead of real amounts.

There are three categorical types of variables in research: nominal variables, ordinal variables , and binary variables . Here is a tabular summary.

It is worth mentioning that some categorical variables can function as multiple types. For example, in some studies, you can use ordinal variables as quantitative variables if the scales are numerical and not discrete.

Data sheet of quantitative and categorical variables

A data sheet is where you record the data on the variables in your experiment.

In a study of the salt-tolerance levels of various plant species, you can record the data on salt addition and how the plant responds in your datasheet.

The key is to gather the information and draw a conclusion over a specific period and filling out a data sheet along the process.

Below is an example of a data sheet containing binary, nominal, continuous , and ordinal types of variables in research.

Types of variables in research – Independent vs. Dependent

The purpose of experiments is to determine how the variables affect each other. As stated in our experiment above, the study aims to find out how the quantity of salt introduce in the water affects the plant’s growth and survival.

Therefore, the researcher manipulates the independent variables and measures the dependent variables . Additionally, you may have control variables that you hold constant.

The table below summarizes independent variables, dependent variables , and control variables .

Data sheet of independent and dependent variables

In salt-tolerance research, there is one independent variable (salt amount) and three independent variables. All other variables are neither dependent nor independent.

Below is a data sheet based on our experiment:

Types of variables in correlational research

The types of variables in research may differ depending on the study.

In correlational research , dependent and independent variables do not apply because the study objective is not to determine the cause-and-effect link between variables.

However, in correlational research, one variable may precede the other, as illness leads to death, and not vice versa. In such an instance, the preceding variable, like illness, is the predictor variable, while the other one is the outcome variable.

Other useful types of variables in research

The key to conducting effective research is to define your types of variables as independent and dependent. Next, you must determine if they are categorical or numerical types of variables in research so you can choose the proper statistical tests for your study.

Below are other types of variables in research worth understanding.

What is the definition for independent and dependent variables?

An autonomous or independent variable is the one you believe is the origin of the outcome, while the dependent variable is the one you believe affects the outcome of your study.

What are quantitative and categorical variables?

Knowing the types of variables in research that you can work with will help you choose the best statistical tests and result representation techniques. It will also help you with your study design.

Discrete and continuous variables: What is their difference?

Discrete variables are types of variables in research that represent counts, like the quantities of objects. In contrast, continuous variables are types of variables in research that represent measurable quantities like age, volume, and weight.

We use cookies on our website. Some of them are essential, while others help us to improve this website and your experience.

• External Media

Individual Privacy Preferences

Cookie Details Privacy Policy Imprint

Here you will find an overview of all cookies used. You can give your consent to whole categories or display further information and select certain cookies.

Accept all Save

Essential cookies enable basic functions and are necessary for the proper function of the website.

Show Cookie Information Hide Cookie Information

Statistics cookies collect information anonymously. This information helps us to understand how our visitors use our website.

Content from video platforms and social media platforms is blocked by default. If External Media cookies are accepted, access to those contents no longer requires manual consent.

Privacy Policy Imprint

• Privacy Policy

Home » ANOVA (Analysis of variance) – Formulas, Types, and Examples

ANOVA (Analysis of variance) – Formulas, Types, and Examples

Table of Contents

Analysis of Variance (ANOVA)

Analysis of Variance (ANOVA) is a statistical method used to test differences between two or more means. It is similar to the t-test, but the t-test is generally used for comparing two means, while ANOVA is used when you have more than two means to compare.

ANOVA is based on comparing the variance (or variation) between the data samples to the variation within each particular sample. If the between-group variance is high and the within-group variance is low, this provides evidence that the means of the groups are significantly different.

ANOVA Terminology

When discussing ANOVA, there are several key terms to understand:

• Factor : This is another term for the independent variable in your analysis. In a one-way ANOVA, there is one factor, while in a two-way ANOVA, there are two factors.
• Levels : These are the different groups or categories within a factor. For example, if the factor is ‘diet’ the levels might be ‘low fat’, ‘medium fat’, and ‘high fat’.
• Response Variable : This is the dependent variable or the outcome that you are measuring.
• Within-group Variance : This is the variance or spread of scores within each level of your factor.
• Between-group Variance : This is the variance or spread of scores between the different levels of your factor.
• Grand Mean : This is the overall mean when you consider all the data together, regardless of the factor level.
• Treatment Sums of Squares (SS) : This represents the between-group variability. It is the sum of the squared differences between the group means and the grand mean.
• Error Sums of Squares (SS) : This represents the within-group variability. It’s the sum of the squared differences between each observation and its group mean.
• Total Sums of Squares (SS) : This is the sum of the Treatment SS and the Error SS. It represents the total variability in the data.
• Degrees of Freedom (df) : The degrees of freedom are the number of values that have the freedom to vary when computing a statistic. For example, if you have ‘n’ observations in one group, then the degrees of freedom for that group is ‘n-1’.
• Mean Square (MS) : Mean Square is the average squared deviation and is calculated by dividing the sum of squares by the corresponding degrees of freedom.
• F-Ratio : This is the test statistic for ANOVAs, and it’s the ratio of the between-group variance to the within-group variance. If the between-group variance is significantly larger than the within-group variance, the F-ratio will be large and likely significant.
• Null Hypothesis (H0) : This is the hypothesis that there is no difference between the group means.
• Alternative Hypothesis (H1) : This is the hypothesis that there is a difference between at least two of the group means.
• p-value : This is the probability of obtaining a test statistic as extreme as the one that was actually observed, assuming that the null hypothesis is true. If the p-value is less than the significance level (usually 0.05), then the null hypothesis is rejected in favor of the alternative hypothesis.
• Post-hoc tests : These are follow-up tests conducted after an ANOVA when the null hypothesis is rejected, to determine which specific groups’ means (levels) are different from each other. Examples include Tukey’s HSD, Scheffe, Bonferroni, among others.

Types of ANOVA

Types of ANOVA are as follows:

One-way (or one-factor) ANOVA

This is the simplest type of ANOVA, which involves one independent variable . For example, comparing the effect of different types of diet (vegetarian, pescatarian, omnivore) on cholesterol level.

Two-way (or two-factor) ANOVA

This involves two independent variables. This allows for testing the effect of each independent variable on the dependent variable , as well as testing if there’s an interaction effect between the independent variables on the dependent variable.

Repeated Measures ANOVA

This is used when the same subjects are measured multiple times under different conditions, or at different points in time. This type of ANOVA is often used in longitudinal studies.

Mixed Design ANOVA

This combines features of both between-subjects (independent groups) and within-subjects (repeated measures) designs. In this model, one factor is a between-subjects variable and the other is a within-subjects variable.

Multivariate Analysis of Variance (MANOVA)

This is used when there are two or more dependent variables. It tests whether changes in the independent variable(s) correspond to changes in the dependent variables.

Analysis of Covariance (ANCOVA)

This combines ANOVA and regression. ANCOVA tests whether certain factors have an effect on the outcome variable after removing the variance for which quantitative covariates (interval variables) account. This allows the comparison of one variable outcome between groups, while statistically controlling for the effect of other continuous variables that are not of primary interest.

Nested ANOVA

This model is used when the groups can be clustered into categories. For example, if you were comparing students’ performance from different classrooms and different schools, “classroom” could be nested within “school.”

ANOVA Formulas

ANOVA Formulas are as follows:

Sum of Squares Total (SST)

This represents the total variability in the data. It is the sum of the squared differences between each observation and the overall mean.

• yi represents each individual data point
• y_mean represents the grand mean (mean of all observations)

Sum of Squares Within (SSW)

This represents the variability within each group or factor level. It is the sum of the squared differences between each observation and its group mean.

• yij represents each individual data point within a group
• y_meani represents the mean of the ith group

Sum of Squares Between (SSB)

This represents the variability between the groups. It is the sum of the squared differences between the group means and the grand mean, multiplied by the number of observations in each group.

• ni represents the number of observations in each group
• y_mean represents the grand mean

Degrees of Freedom

The degrees of freedom are the number of values that have the freedom to vary when calculating a statistic.

For within groups (dfW):

For between groups (dfB):

For total (dfT):

• N represents the total number of observations
• k represents the number of groups

Mean Squares

Mean squares are the sum of squares divided by the respective degrees of freedom.

Mean Squares Between (MSB):

Mean Squares Within (MSW):

F-Statistic

The F-statistic is used to test whether the variability between the groups is significantly greater than the variability within the groups.

If the F-statistic is significantly higher than what would be expected by chance, we reject the null hypothesis that all group means are equal.

Examples of ANOVA

Examples 1:

Suppose a psychologist wants to test the effect of three different types of exercise (yoga, aerobic exercise, and weight training) on stress reduction. The dependent variable is the stress level, which can be measured using a stress rating scale.

Here are hypothetical stress ratings for a group of participants after they followed each of the exercise regimes for a period:

• Yoga: [3, 2, 2, 1, 2, 2, 3, 2, 1, 2]
• Aerobic Exercise: [2, 3, 3, 2, 3, 2, 3, 3, 2, 2]
• Weight Training: [4, 4, 5, 5, 4, 5, 4, 5, 4, 5]

The psychologist wants to determine if there is a statistically significant difference in stress levels between these different types of exercise.

To conduct the ANOVA:

1. State the hypotheses:

• Null Hypothesis (H0): There is no difference in mean stress levels between the three types of exercise.
• Alternative Hypothesis (H1): There is a difference in mean stress levels between at least two of the types of exercise.

2. Calculate the ANOVA statistics:

• Compute the Sum of Squares Between (SSB), Sum of Squares Within (SSW), and Sum of Squares Total (SST).
• Calculate the Degrees of Freedom (dfB, dfW, dfT).
• Calculate the Mean Squares Between (MSB) and Mean Squares Within (MSW).
• Compute the F-statistic (F = MSB / MSW).

3. Check the p-value associated with the calculated F-statistic.

• If the p-value is less than the chosen significance level (often 0.05), then we reject the null hypothesis in favor of the alternative hypothesis. This suggests there is a statistically significant difference in mean stress levels between the three exercise types.

4. Post-hoc tests

• If we reject the null hypothesis, we conduct a post-hoc test to determine which specific groups’ means (exercise types) are different from each other.

Examples 2:

Suppose an agricultural scientist wants to compare the yield of three varieties of wheat. The scientist randomly selects four fields for each variety and plants them. After harvest, the yield from each field is measured in bushels. Here are the hypothetical yields:

The scientist wants to know if the differences in yields are due to the different varieties or just random variation.

Here’s how to apply the one-way ANOVA to this situation:

• Null Hypothesis (H0): The means of the three populations are equal.
• Alternative Hypothesis (H1): At least one population mean is different.
• Calculate the Degrees of Freedom (dfB for between groups, dfW for within groups, dfT for total).
• If the p-value is less than the chosen significance level (often 0.05), then we reject the null hypothesis in favor of the alternative hypothesis. This would suggest there is a statistically significant difference in mean yields among the three varieties.
• If we reject the null hypothesis, we conduct a post-hoc test to determine which specific groups’ means (wheat varieties) are different from each other.

How to Conduct ANOVA

Conducting an Analysis of Variance (ANOVA) involves several steps. Here’s a general guideline on how to perform it:

• Null Hypothesis (H0): The means of all groups are equal.
• Alternative Hypothesis (H1): At least one group mean is different from the others.
• The significance level (often denoted as α) is usually set at 0.05. This implies that you are willing to accept a 5% chance that you are wrong in rejecting the null hypothesis.
• Data should be collected for each group under study. Make sure that the data meet the assumptions of an ANOVA: normality, independence, and homogeneity of variances.
• Calculate the Degrees of Freedom (df) for each sum of squares (dfB, dfW, dfT).
• Compute the Mean Squares Between (MSB) and Mean Squares Within (MSW) by dividing the sum of squares by the corresponding degrees of freedom.
• Compute the F-statistic as the ratio of MSB to MSW.
• Determine the critical F-value from the F-distribution table using dfB and dfW.
• If the calculated F-statistic is greater than the critical F-value, reject the null hypothesis.
• If the p-value associated with the calculated F-statistic is smaller than the significance level (0.05 typically), you reject the null hypothesis.
• If you rejected the null hypothesis, you can conduct post-hoc tests (like Tukey’s HSD) to determine which specific groups’ means (if you have more than two groups) are different from each other.
• Regardless of the result, report your findings in a clear, understandable manner. This typically includes reporting the test statistic, p-value, and whether the null hypothesis was rejected.

When to use ANOVA

ANOVA (Analysis of Variance) is used when you have three or more groups and you want to compare their means to see if they are significantly different from each other. It is a statistical method that is used in a variety of research scenarios. Here are some examples of when you might use ANOVA:

• Comparing Groups : If you want to compare the performance of more than two groups, for example, testing the effectiveness of different teaching methods on student performance.
• Evaluating Interactions : In a two-way or factorial ANOVA, you can test for an interaction effect. This means you are not only interested in the effect of each individual factor, but also whether the effect of one factor depends on the level of another factor.
• Repeated Measures : If you have measured the same subjects under different conditions or at different time points, you can use repeated measures ANOVA to compare the means of these repeated measures while accounting for the correlation between measures from the same subject.
• Experimental Designs : ANOVA is often used in experimental research designs when subjects are randomly assigned to different conditions and the goal is to compare the means of the conditions.

Here are the assumptions that must be met to use ANOVA:

• Normality : The data should be approximately normally distributed.
• Homogeneity of Variances : The variances of the groups you are comparing should be roughly equal. This assumption can be tested using Levene’s test or Bartlett’s test.
• Independence : The observations should be independent of each other. This assumption is met if the data is collected appropriately with no related groups (e.g., twins, matched pairs, repeated measures).

Applications of ANOVA

The Analysis of Variance (ANOVA) is a powerful statistical technique that is used widely across various fields and industries. Here are some of its key applications:

Agriculture

ANOVA is commonly used in agricultural research to compare the effectiveness of different types of fertilizers, crop varieties, or farming methods. For example, an agricultural researcher could use ANOVA to determine if there are significant differences in the yields of several varieties of wheat under the same conditions.

Manufacturing and Quality Control

ANOVA is used to determine if different manufacturing processes or machines produce different levels of product quality. For instance, an engineer might use it to test whether there are differences in the strength of a product based on the machine that produced it.

Marketing Research

Marketers often use ANOVA to test the effectiveness of different advertising strategies. For example, a marketer could use ANOVA to determine whether different marketing messages have a significant impact on consumer purchase intentions.

Healthcare and Medicine

In medical research, ANOVA can be used to compare the effectiveness of different treatments or drugs. For example, a medical researcher could use ANOVA to test whether there are significant differences in recovery times for patients who receive different types of therapy.

ANOVA is used in educational research to compare the effectiveness of different teaching methods or educational interventions. For example, an educator could use it to test whether students perform significantly differently when taught with different teaching methods.

Psychology and Social Sciences

Psychologists and social scientists use ANOVA to compare group means on various psychological and social variables. For example, a psychologist could use it to determine if there are significant differences in stress levels among individuals in different occupations.

Biology and Environmental Sciences

Biologists and environmental scientists use ANOVA to compare different biological and environmental conditions. For example, an environmental scientist could use it to determine if there are significant differences in the levels of a pollutant in different bodies of water.

Advantages of ANOVA

Here are some advantages of using ANOVA:

Comparing Multiple Groups: One of the key advantages of ANOVA is the ability to compare the means of three or more groups. This makes it more powerful and flexible than the t-test, which is limited to comparing only two groups.

Control of Type I Error: When comparing multiple groups, the chances of making a Type I error (false positive) increases. One of the strengths of ANOVA is that it controls the Type I error rate across all comparisons. This is in contrast to performing multiple pairwise t-tests which can inflate the Type I error rate.

Testing Interactions: In factorial ANOVA, you can test not only the main effect of each factor, but also the interaction effect between factors. This can provide valuable insights into how different factors or variables interact with each other.

Handling Continuous and Categorical Variables: ANOVA can handle both continuous and categorical variables . The dependent variable is continuous and the independent variables are categorical.

Robustness: ANOVA is considered robust to violations of normality assumption when group sizes are equal. This means that even if your data do not perfectly meet the normality assumption, you might still get valid results.

Provides Detailed Analysis: ANOVA provides a detailed breakdown of variances and interactions between variables which can be useful in understanding the underlying factors affecting the outcome.

Capability to Handle Complex Experimental Designs: Advanced types of ANOVA (like repeated measures ANOVA, MANOVA, etc.) can handle more complex experimental designs, including those where measurements are taken on the same subjects over time, or when you want to analyze multiple dependent variables at once.

Disadvantages of ANOVA

Some limitations or disadvantages that are important to consider:

Assumptions: ANOVA relies on several assumptions including normality (the data follows a normal distribution), independence (the observations are independent of each other), and homogeneity of variances (the variances of the groups are roughly equal). If these assumptions are violated, the results of the ANOVA may not be valid.

Sensitivity to Outliers: ANOVA can be sensitive to outliers. A single extreme value in one group can affect the sum of squares and consequently influence the F-statistic and the overall result of the test.

Dichotomous Variables: ANOVA is not suitable for dichotomous variables (variables that can take only two values, like yes/no or male/female). It is used to compare the means of groups for a continuous dependent variable.

Lack of Specificity: Although ANOVA can tell you that there is a significant difference between groups, it doesn’t tell you which specific groups are significantly different from each other. You need to carry out further post-hoc tests (like Tukey’s HSD or Bonferroni) for these pairwise comparisons.

Complexity with Multiple Factors: When dealing with multiple factors and interactions in factorial ANOVA, interpretation can become complex. The presence of interaction effects can make main effects difficult to interpret.

Requires Larger Sample Sizes: To detect an effect of a certain size, ANOVA generally requires larger sample sizes than a t-test.

Equal Group Sizes: While not always a strict requirement, ANOVA is most powerful and its assumptions are most likely to be met when groups are of equal or similar sizes.

About the author

Muhammad Hassan

Researcher, Academic Writer, Web developer

You may also like

Cluster Analysis – Types, Methods and Examples

Discriminant Analysis – Methods, Types and...

MANOVA (Multivariate Analysis of Variance) –...

Documentary Analysis – Methods, Applications and...

Graphical Methods – Types, Examples and Guide

Substantive Framework – Types, Methods and...