hypothesis variables dependent variable

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.

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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 ...

Very informative, concise and helpful. Thank you

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• v.43(2); 2021 Mar

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

Chittaranjan andrade.

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

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

Key Message:

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

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

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

Independent and Dependent Variables

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

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

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

Importance of Variables in Stating the Research Objectives

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

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

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

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

Importance of Variables in Framing Hypotheses

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

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

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

Combinations of Age with Dependent Variables in the Generation of Hypotheses

Operationalization of Variables

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

Possible Ways of Operationalization of Suicidality and Depression

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

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

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

Concluding Notes

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

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

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

Independent and Dependent Variables

Saul McLeod, PhD

Editor-in-Chief for Simply Psychology

BSc (Hons) Psychology, MRes, PhD, University of Manchester

Saul McLeod, PhD., is a qualified psychology teacher with over 18 years of experience in further and higher education. He has been published in peer-reviewed journals, including the Journal of Clinical Psychology.

Learn about our Editorial Process

Olivia Guy-Evans, MSc

Associate Editor for Simply Psychology

BSc (Hons) Psychology, MSc Psychology of Education

Olivia Guy-Evans is a writer and associate editor for Simply Psychology. She has previously worked in healthcare and educational sectors.

On This Page:

In research, a variable is any characteristic, number, or quantity that can be measured or counted in experimental investigations . One is called the dependent variable, and the other is the independent variable.

In research, the independent variable is manipulated to observe its effect, while the dependent variable is the measured outcome. Essentially, the independent variable is the presumed cause, and the dependent variable is the observed effect.

Variables provide the foundation for examining relationships, drawing conclusions, and making predictions in research studies.

Independent Variable

In psychology, the independent variable is the variable the experimenter manipulates or changes and is assumed to directly affect the dependent variable.

It’s considered the cause or factor that drives change, allowing psychologists to observe how it influences behavior, emotions, or other dependent variables in an experimental setting. Essentially, it’s the presumed cause in cause-and-effect relationships being studied.

For example, allocating participants to drug or placebo conditions (independent variable) to measure any changes in the intensity of their anxiety (dependent variable).

In a well-designed experimental study , the independent variable is the only important difference between the experimental (e.g., treatment) and control (e.g., placebo) groups.

By changing the independent variable and holding other factors constant, psychologists aim to determine if it causes a change in another variable, called the dependent variable.

For example, in a study investigating the effects of sleep on memory, the amount of sleep (e.g., 4 hours, 8 hours, 12 hours) would be the independent variable, as the researcher might manipulate or categorize it to see its impact on memory recall, which would be the dependent variable.

Dependent Variable

In psychology, the dependent variable is the variable being tested and measured in an experiment and is “dependent” on the independent variable.

In psychology, a dependent variable represents the outcome or results and can change based on the manipulations of the independent variable. Essentially, it’s the presumed effect in a cause-and-effect relationship being studied.

An example of a dependent variable is depression symptoms, which depend on the independent variable (type of therapy).

In an experiment, the researcher looks for the possible effect on the dependent variable that might be caused by changing the independent variable.

For instance, in a study examining the effects of a new study technique on exam performance, the technique would be the independent variable (as it is being introduced or manipulated), while the exam scores would be the dependent variable (as they represent the outcome of interest that’s being measured).

Examples in Research Studies

For example, we might change the type of information (e.g., organized or random) given to participants to see how this might affect the amount of information remembered.

In this example, the type of information is the independent variable (because it changes), and the amount of information remembered is the dependent variable (because this is being measured).

For the following hypotheses, name the IV and the DV.

1. Lack of sleep significantly affects learning in 10-year-old boys.

IV……………………………………………………

DV…………………………………………………..

2. Social class has a significant effect on IQ scores.

DV……………………………………………….…

3. Stressful experiences significantly increase the likelihood of headaches.

4. Time of day has a significant effect on alertness.

Operationalizing Variables

To ensure cause and effect are established, it is important that we identify exactly how the independent and dependent variables will be measured; this is known as operationalizing the variables.

Operational variables (or operationalizing definitions) refer to how you will define and measure a specific variable as it is used in your study. This enables another psychologist to replicate your research and is essential in establishing reliability (achieving consistency in the results).

For example, if we are concerned with the effect of media violence on aggression, then we need to be very clear about what we mean by the different terms. In this case, we must state what we mean by the terms “media violence” and “aggression” as we will study them.

Therefore, you could state that “media violence” is operationally defined (in your experiment) as ‘exposure to a 15-minute film showing scenes of physical assault’; “aggression” is operationally defined as ‘levels of electrical shocks administered to a second ‘participant’ in another room.

In another example, the hypothesis “Young participants will have significantly better memories than older participants” is not operationalized. How do we define “young,” “old,” or “memory”? “Participants aged between 16 – 30 will recall significantly more nouns from a list of twenty than participants aged between 55 – 70” is operationalized.

The key point here is that we have clarified what we mean by the terms as they were studied and measured in our experiment.

If we didn’t do this, it would be very difficult (if not impossible) to compare the findings of different studies to the same behavior.

Operationalization has the advantage of generally providing a clear and objective definition of even complex variables. It also makes it easier for other researchers to replicate a study and check for reliability .

For the following hypotheses, name the IV and the DV and operationalize both variables.

1. Women are more attracted to men without earrings than men with earrings.

I.V._____________________________________________________________

D.V. ____________________________________________________________

Operational definitions:

I.V. ____________________________________________________________

2. People learn more when they study in a quiet versus noisy place.

I.V. _________________________________________________________

D.V. ___________________________________________________________

3. People who exercise regularly sleep better at night.

Can there be more than one independent or dependent variable in a study?

Yes, it is possible to have more than one independent or dependent variable in a study.

In some studies, researchers may want to explore how multiple factors affect the outcome, so they include more than one independent variable.

Similarly, they may measure multiple things to see how they are influenced, resulting in multiple dependent variables. This allows for a more comprehensive understanding of the topic being studied.

What are some ethical considerations related to independent and dependent variables?

Ethical considerations related to independent and dependent variables involve treating participants fairly and protecting their rights.

Researchers must ensure that participants provide informed consent and that their privacy and confidentiality are respected. Additionally, it is important to avoid manipulating independent variables in ways that could cause harm or discomfort to participants.

Researchers should also consider the potential impact of their study on vulnerable populations and ensure that their methods are unbiased and free from discrimination.

Ethical guidelines help ensure that research is conducted responsibly and with respect for the well-being of the participants involved.

Can qualitative data have independent and dependent variables?

Yes, both quantitative and qualitative data can have independent and dependent variables.

In quantitative research, independent variables are usually measured numerically and manipulated to understand their impact on the dependent variable. In qualitative research, independent variables can be qualitative in nature, such as individual experiences, cultural factors, or social contexts, influencing the phenomenon of interest.

The dependent variable, in both cases, is what is being observed or studied to see how it changes in response to the independent variable.

So, regardless of the type of data, researchers analyze the relationship between independent and dependent variables to gain insights into their research questions.

Can the same variable be independent in one study and dependent in another?

Yes, the same variable can be independent in one study and dependent in another.

The classification of a variable as independent or dependent depends on how it is used within a specific study. In one study, a variable might be manipulated or controlled to see its effect on another variable, making it independent.

However, in a different study, that same variable might be the one being measured or observed to understand its relationship with another variable, making it dependent.

The role of a variable as independent or dependent can vary depending on the research question and study design.

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Statistics By Jim

Making statistics intuitive

Independent and Dependent Variables: Differences & Examples

By Jim Frost 15 Comments

In this post, learn the definitions of independent and dependent variables, how to identify each type, how they differ between different types of studies, and see examples of them in use.

What is an Independent Variable?

Independent variables (IVs) are the ones that you include in the model to explain or predict changes in the dependent variable. The name helps you understand their role in statistical analysis. These variables are independent . In this context, independent indicates that they stand alone and other variables in the model do not influence them. The researchers are not seeking to understand what causes the independent variables to change.

Independent variables are also known as predictors, factors , treatment variables, explanatory variables, input variables, x-variables, and right-hand variables—because they appear on the right side of the equals sign in a regression equation. In notation, statisticians commonly denote them using Xs. On graphs, analysts place independent variables on the horizontal, or X, axis.

In machine learning, independent variables are known as features.

For example, in a plant growth study, the independent variables might be soil moisture (continuous) and type of fertilizer (categorical).

Statistical models will estimate effect sizes for the independent variables.

Relate post : Effect Sizes in Statistics

Including independent variables in studies

The nature of independent variables changes based on the type of experiment or study:

Controlled experiments : Researchers systematically control and set the values of the independent variables. In randomized experiments, relationships between independent and dependent variables tend to be causal. The independent variables cause changes in the dependent variable.

Observational studies : Researchers do not set the values of the explanatory variables but instead observe them in their natural environment. When the independent and dependent variables are correlated, those relationships might not be causal.

When you include one independent variable in a regression model, you are performing simple regression. For more than one independent variable, it is multiple regression. Despite the different names, it’s really the same analysis with the same interpretations and assumptions.

Determining which IVs to include in a statistical model is known as model specification. That process involves in-depth research and many subject-area, theoretical, and statistical considerations. At its most basic level, you’ll want to include the predictors you are specifically assessing in your study and confounding variables that will bias your results if you don’t add them—particularly for observational studies.

For more information about choosing independent variables, read my post about Specifying the Correct Regression Model .

Related posts : Randomized Experiments , Observational Studies , Covariates , and Confounding Variables

What is a Dependent Variable?

The dependent variable (DV) is what you want to use the model to explain or predict. The values of this variable depend on other variables. It is the outcome that you’re studying. It’s also known as the response variable, outcome variable, and left-hand variable. Statisticians commonly denote them using a Y. Traditionally, graphs place dependent variables on the vertical, or Y, axis.

For example, in the plant growth study example, a measure of plant growth is the dependent variable. That is the outcome of the experiment, and we want to determine what affects it.

How to Identify Independent and Dependent Variables

If you’re reading a study’s write-up, how do you distinguish independent variables from dependent variables? Here are some tips!

Identifying IVs

How statisticians discuss independent variables changes depending on the field of study and type of experiment.

In randomized experiments, look for the following descriptions to identify the independent variables:

• Independent variables cause changes in another variable.
• The researchers control the values of the independent variables. They are controlled or manipulated variables.
• Experiments often refer to them as factors or experimental factors. In areas such as medicine, they might be risk factors.
• Treatment and control groups are always independent variables. In this case, the independent variable is a categorical grouping variable that defines the experimental groups to which participants belong. Each group is a level of that variable.

In observational studies, independent variables are a bit different. While the researchers likely want to establish causation, that’s harder to do with this type of study, so they often won’t use the word “cause.” They also don’t set the values of the predictors. Some independent variables are the experiment’s focus, while others help keep the experimental results valid.

Here’s how to recognize independent variables in observational studies:

• IVs explain the variability, predict, or correlate with changes in the dependent variable.
• Researchers in observational studies must include confounding variables (i.e., confounders) to keep the statistical results valid even if they are not the primary interest of the study. For example, these might include the participants’ socio-economic status or other background information that the researchers aren’t focused on but can explain some of the dependent variable’s variability.
• The results are adjusted or controlled for by a variable.

Regardless of the study type, if you see an estimated effect size, it is an independent variable.

Identifying DVs

Dependent variables are the outcome. The IVs explain the variability or causes changes in the DV. Focus on the “depends” aspect. The value of the dependent variable depends on the IVs. If Y depends on X, then Y is the dependent variable. This aspect applies to both randomized experiments and observational studies.

In an observational study about the effects of smoking, the researchers observe the subjects’ smoking status (smoker/non-smoker) and their lung cancer rates. It’s an observational study because they cannot randomly assign subjects to either the smoking or non-smoking group. In this study, the researchers want to know whether lung cancer rates depend on smoking status. Therefore, the lung cancer rate is the dependent variable.

In a randomized COVID-19 vaccine experiment , the researchers randomly assign subjects to the treatment or control group. They want to determine whether COVID-19 infection rates depend on vaccination status. Hence, the infection rate is the DV.

Note that a variable can be an independent variable in one study but a dependent variable in another. It depends on the context.

For example, one study might assess how the amount of exercise (IV) affects health (DV). However, another study might study the factors (IVs) that influence how much someone exercises (DV). The amount of exercise is an independent variable in one study but a dependent variable in the other!

How Analyses Use IVs and DVs

Regression analysis and ANOVA mathematically describe the relationships between each independent variable and the dependent variable. Typically, you want to determine how changes in one or more predictors associate with changes in the dependent variable. These analyses estimate an effect size for each independent variable.

Suppose researchers study the relationship between wattage, several types of filaments, and the output from a light bulb. In this study, light output is the dependent variable because it depends on the other two variables. Wattage (continuous) and filament type (categorical) are the independent variables.

After performing the regression analysis, the researchers will understand the nature of the relationship between these variables. How much does the light output increase on average for each additional watt? Does the mean light output differ by filament types? They will also learn whether these effects are statistically significant.

Related post : When to Use Regression Analysis

Graphing Independent and Dependent Variables

As I mentioned earlier, graphs traditionally display the independent variables on the horizontal X-axis and the dependent variable on the vertical Y-axis. The type of graph depends on the nature of the variables. Here are a couple of examples.

Suppose you experiment to determine whether various teaching methods affect learning outcomes. Teaching method is a categorical predictor that defines the experimental groups. To display this type of data, you can use a boxplot, as shown below.

The groups are along the horizontal axis, while the dependent variable, learning outcomes, is on the vertical. From the graph, method 4 has the best results. A one-way ANOVA will tell you whether these results are statistically significant. Learn more about interpreting boxplots .

Now, imagine that you are studying people’s height and weight. Specifically, do height increases cause weight to increase? Consequently, height is the independent variable on the horizontal axis, and weight is the dependent variable on the vertical axis. You can use a scatterplot to display this type of data.

It appears that as height increases, weight tends to increase. Regression analysis will tell you if these results are statistically significant. Learn more about interpreting scatterplots .

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Reader Interactions

April 2, 2024 at 2:05 am

Hi again Jim

Thanks so much for taking an interest in New Zealand’s Equity Index.

Rather than me trying to explain what our Ministry of Education has done, here is a link to a fairly short paper. Scroll down to page 4 of this (if you have the inclination) – https://fyi.org.nz/request/21253/response/80708/attach/4/1301098%20Response%20and%20Appendix.pdf

The Equity Index is used to allocate only 4% of total school funding. The most advantaged 5% of schools get no “equity funding” and the other 95% get a share of the equity funding pool based on their index score. We are talking a maximum of around $1,000NZD per child per year for the most disadvantaged schools. The average amount is around $200-$300 per child per year.

My concern is that I thought the dependent variable is the thing you want to explain or predict using one or more independent variables. Choosing the form of dependent variable that gets a good fit seems to be answering the question “what can we predict well?” rather than “how do we best predict the factor of interest?” The factor is educational achievement and I think this should have been decided upon using theory rather than experimentation with the data.

As it turns out, the Ministry has chosen a measure of educational achievement that puts a heavy weight on achieving an “excellence” rating on a qualification and a much lower weight on simply gaining a qualification. My reading is that they have taken what our universities do when looking at which students to admit.

It doesn’t seem likely to me that a heavy weighting on excellent achievement is appropriate for targeting extra funding to schools with a lot of under-achieving students.

However, my stats knowledge isn’t extensive and it’s definitely rusty, so your thoughts are most helpful.

Regards Kathy Spencer

April 1, 2024 at 4:08 pm

Hi Jim, Great website, thank you.

I have been looking at New Zealand’s Equity Index which is used to allocate a small amount of extra funding to schools attended by children from disadvantaged backgrounds. The Index uses 37 socioeconomic measures relating to a child’s and their parents’ backgrounds that are found to be associated with educational achievement.

I was a bit surprised to read how they had decided on the dependent variable to be used as the measure of educational achievement, or dependent variable. Part of the process was as follows- “Each measure was tested to see the degree to which it could be predicted by the socioeconomic factors selected for the Equity Index.”

Any comment?

Many thanks Kathy Spencer

April 1, 2024 at 9:20 pm

That’s a very complex study and I don’t know much about it. So, that limits what I can say about it. But I’ll give you a few thoughts that come to mind.

This method is common in educational and social research, particularly when the goal is to understand or mitigate the impact of socioeconomic disparities on educational outcomes.

There are the usual concerns about not confusing correlation with causation. However, because this program seems to quantify barriers and then provide extra funding based on the index, I don’t think that’s a problem. They’re not attempting to adjust the socioeconomic measures so no worries about whether they’re directly causal or not.

I might have a small concern about cherry picking the model that happens to maximize the R-squared. Chasing the R-squared rather than having theory drive model selecting is often problematic. Chasing the best fit increases the likelihood that the model fits this specific dataset best by random chance rather than being truly the best. If so, it won’t perform as well outside the dataset used to fit the model. Hopefully, they validated the predicted ability of the model using other data.

However, I’m not sure if the extra funding is determined by the model? I don’t know if the index value is calculated separately outside the candidate models and then fed into the various models. Or does the choice of model affect how the index value is calculated? If it’s the former, then the funding doesn’t depend on a potentially cherry picked model. If the latter, it does.

So, I’m not really clear on the purpose of the model. I’m guessing they just want to validate their Equity Index. And maximizing the R-squared doesn’t really say it’s the best Index but it does at least show that it likely has some merit. I’d be curious how the took the 37 measures and combined them to one index. So, I have more questions than answers. I don’t mean that in a critical sense. Just that I know almost nothing about this program.

I’m curious, what was the outcome they picked? How high was the R-squared? And what were your concerns?

February 6, 2024 at 6:57 pm

Excellent explanation, thank you.

February 5, 2024 at 5:04 pm

Thank you for this insightful blog. Is it valid to use a dependent variable delivered from the mean of independent variables in multiple regression if you want to evaluate the influence of each unique independent variable on the dependent variables?

February 5, 2024 at 11:11 pm

It’s difficult to answer your question because I’m not sure what you mean that the DV is “delivered from the mean of IVs.” If you mean that multiple IVs explain changes in the DV’s mean, yes, that’s the standard use for multiple regression.

If you mean something else, please explain in further detail. Thanks!

February 6, 2024 at 6:32 am

What I meant is; the DV values used as parameters for multiple regression is basically calculated as the average of the IVs. For instance:

From 3 IVs (X1, X2, X3), Y is delivered as :

Y = (Sum of all IVs) / (3)

Then the resulting Y is used as the DV along with the initial IVs to compute the multiple regression.

February 6, 2024 at 2:17 pm

There are a couple of reasons why you shouldn’t do that.

For starters, Y-hat (the predicted value of the regression equation) is the mean of the DV given specific values of the IV. However, that mean is calculated by using the regression coefficients and constant in the regression equation. You don’t calculate the DV mean as the sum of the IVs divided by the number of IVs. Perhaps given a very specific subject-area context, using this approach might seem to make sense but there are other problems.

A critical problem is that the Y is now calculated using the IVs. Instead, the DVs should be measured outcomes and not calculated from IVs. This violates regression assumptions and produces questionable results.

Additionally, it complicates the interpretation. Because the DV is calculated from the IV, you know the regression analysis will find a relationship between them. But you have no idea if that relationship exists in the real world. This complication occurs because your results are based on forcing the DV to equal a function of the IVs and do not reflect real-world outcomes.

In short, DVs should be real-world outcomes that you measure! And be sure to keep your IVs and DV independent. Let the regression analysis estimate the regression equation from your data that contains measured DVs. Don’t use a function to force the DV to equal some function of the IVs because that’s the opposite direction of how regression works!

I hope that helps!

September 6, 2022 at 7:43 pm

Thank you for sharing.

March 3, 2022 at 1:59 am

Excellent explanation.

February 13, 2022 at 12:31 pm

Thanks a lot for creating this excellent blog. This is my go-to resource for Statistics.

I had been pondering over a question for sometime, it would be great if you could shed some light on this.

In linear and non-linear regression, should the distribution of independent and dependent variables be unskewed? When is there a need to transform the data (say, Box-Cox transformation), and do we transform the independent variables as well?

October 28, 2021 at 12:55 pm

If I use a independent variable (X) and it displays a low p-value <.05, why is it if I introduce another independent variable to regression the coefficient and p-value of Y that I used in first regression changes to look insignificant? The second variable that I introduced has a low p-value in regression.

October 29, 2021 at 11:22 pm

Keep in mind that the significance of each IV is calculated after accounting for the variance of all the other variables in the model, assuming you’re using the standard adjusted sums of squares rather than sequential sums of squares. The sums of squares (SS) is a measure of how much dependent variable variability that each IV accounts for. In the illustration below, I’ll assume you’re using the standard of adjusted SS.

So, let’s say that originally you have X1 in the model along with some other IVs. Your model estimates the significance of X1 after assessing the variability that the other IVs account for and finds that X1 is significant. Now, you add X2 to the model in addition to X1 and the other IVs. Now, when assessing X1, the model accounts for the variability of the IVs including the newly added X2. And apparently X2 explains a good portion of the variability. X1 is no longer able to account for that variability, which causes it to not be statistically significant.

In other words, X2 explains some of the variability that X1 previously explained. Because X1 no longer explains it, it is no longer significant.

Additionally, the significance of IVs is more likely to change when you add or remove IVs that are correlated. Correlated IVs is known as multicollinearity. Multicollinearity can be a problem when you have too much. Given the change in significance, I’d check your model for multicollinearity just to be safe! Click the link to read a post that wrote about that!

September 6, 2021 at 8:35 am

nice explanation

August 25, 2021 at 3:09 am

it is excellent explanation

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How to Write a Great Hypothesis

Hypothesis Definition, Format, Examples, and Tips

Verywell / Alex Dos Diaz

• The Scientific Method

Hypothesis Format

Falsifiability of a hypothesis.

• Operationalization

Hypothesis Types

Hypotheses examples.

• Collecting Data

A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.

Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."

At a Glance

A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.

The Hypothesis in the Scientific Method

In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:

• Forming a question
• Performing background research
• Creating a hypothesis
• Designing an experiment
• Collecting data
• Analyzing the results
• Drawing conclusions
• Communicating the results

The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.

Unless you are creating an exploratory study, your hypothesis should always explain what you  expect  to happen.

In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.

Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.

In many cases, researchers may find that the results of an experiment  do not  support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.

In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."

In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."

Elements of a Good Hypothesis

So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:

• Is your hypothesis based on your research on a topic?
• Can your hypothesis be tested?
• Does your hypothesis include independent and dependent variables?

Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the  journal articles you read . Many authors will suggest questions that still need to be explored.

How to Formulate a Good Hypothesis

To form a hypothesis, you should take these steps:

• Collect as many observations about a topic or problem as you can.
• Evaluate these observations and look for possible causes of the problem.
• Create a list of possible explanations that you might want to explore.
• After you have developed some possible hypotheses, think of ways that you could confirm or disprove each hypothesis through experimentation. This is known as falsifiability.

In the scientific method ,  falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.

Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that  if  something was false, then it is possible to demonstrate that it is false.

One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.

The Importance of Operational Definitions

A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.

Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.

For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.

These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.

Replicability

One of the basic principles of any type of scientific research is that the results must be replicable.

Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.

Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.

To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.

Hypothesis Checklist

• Does your hypothesis focus on something that you can actually test?
• Does your hypothesis include both an independent and dependent variable?
• Can you manipulate the variables?
• Can your hypothesis be tested without violating ethical standards?

The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:

• Simple hypothesis : This type of hypothesis suggests there is a relationship between one independent variable and one dependent variable.
• Complex hypothesis : This type suggests a relationship between three or more variables, such as two independent and dependent variables.
• Null hypothesis : This hypothesis suggests no relationship exists between two or more variables.
• Alternative hypothesis : This hypothesis states the opposite of the null hypothesis.
• Statistical hypothesis : This hypothesis uses statistical analysis to evaluate a representative population sample and then generalizes the findings to the larger group.
• Logical hypothesis : This hypothesis assumes a relationship between variables without collecting data or evidence.

A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the  dependent variable  if you change the  independent variable .

The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."

A few examples of simple hypotheses:

• "Students who eat breakfast will perform better on a math exam than students who do not eat breakfast."
• "Students who experience test anxiety before an English exam will get lower scores than students who do not experience test anxiety."​
• "Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone."
• "Children who receive a new reading intervention will have higher reading scores than students who do not receive the intervention."

Examples of a complex hypothesis include:

• "People with high-sugar diets and sedentary activity levels are more likely to develop depression."
• "Younger people who are regularly exposed to green, outdoor areas have better subjective well-being than older adults who have limited exposure to green spaces."

Examples of a null hypothesis include:

• "There is no difference in anxiety levels between people who take St. John's wort supplements and those who do not."
• "There is no difference in scores on a memory recall task between children and adults."
• "There is no difference in aggression levels between children who play first-person shooter games and those who do not."

Examples of an alternative hypothesis:

• "People who take St. John's wort supplements will have less anxiety than those who do not."
• "Adults will perform better on a memory task than children."
• "Children who play first-person shooter games will show higher levels of aggression than children who do not." 

Collecting Data on Your Hypothesis

Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.

Descriptive Research Methods

Descriptive research such as  case studies ,  naturalistic observations , and surveys are often used when  conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.

Once a researcher has collected data using descriptive methods, a  correlational study  can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.

Experimental Research Methods

Experimental methods  are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).

Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually  cause  another to change.

The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.

Thompson WH, Skau S. On the scope of scientific hypotheses .  R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607

Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:].  Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z

Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004

Nosek BA, Errington TM. What is replication ?  PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691

Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies .  Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18

Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.

By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."

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Independent and Dependent Variables Examples

The independent and dependent variables are key to any scientific experiment, but how do you tell them apart? Here are the definitions of independent and dependent variables, examples of each type, and tips for telling them apart and graphing them.

Independent Variable

The independent variable is the factor the researcher changes or controls in an experiment. It is called independent because it does not depend on any other variable. The independent variable may be called the “controlled variable” because it is the one that is changed or controlled. This is different from the “ control variable ,” which is variable that is held constant so it won’t influence the outcome of the experiment.

Dependent Variable

The dependent variable is the factor that changes in response to the independent variable. It is the variable that you measure in an experiment. The dependent variable may be called the “responding variable.”

Examples of Independent and Dependent Variables

Here are several examples of independent and dependent variables in experiments:

• In a study to determine whether how long a student sleeps affects test scores, the independent variable is the length of time spent sleeping while the dependent variable is the test score.
• You want to know which brand of fertilizer is best for your plants. The brand of fertilizer is the independent variable. The health of the plants (height, amount and size of flowers and fruit, color) is the dependent variable.
• You want to compare brands of paper towels, to see which holds the most liquid. The independent variable is the brand of paper towel. The dependent variable is the volume of liquid absorbed by the paper towel.
• You suspect the amount of television a person watches is related to their age. Age is the independent variable. How many minutes or hours of television a person watches is the dependent variable.
• You think rising sea temperatures might affect the amount of algae in the water. The water temperature is the independent variable. The mass of algae is the dependent variable.
• In an experiment to determine how far people can see into the infrared part of the spectrum, the wavelength of light is the independent variable and whether the light is observed is the dependent variable.
• If you want to know whether caffeine affects your appetite, the presence/absence or amount of caffeine is the independent variable. Appetite is the dependent variable.
• You want to know which brand of microwave popcorn pops the best. The brand of popcorn is the independent variable. The number of popped kernels is the dependent variable. Of course, you could also measure the number of unpopped kernels instead.
• You want to determine whether a chemical is essential for rat nutrition, so you design an experiment. The presence/absence of the chemical is the independent variable. The health of the rat (whether it lives and reproduces) is the dependent variable. A follow-up experiment might determine how much of the chemical is needed. Here, the amount of chemical is the independent variable and the rat health is the dependent variable.

How to Tell the Independent and Dependent Variable Apart

If you’re having trouble identifying the independent and dependent variable, here are a few ways to tell them apart. First, remember the dependent variable depends on the independent variable. It helps to write out the variables as an if-then or cause-and-effect sentence that shows the independent variable causes an effect on the dependent variable. If you mix up the variables, the sentence won’t make sense. Example : The amount of eat (independent variable) affects how much you weigh (dependent variable).

This makes sense, but if you write the sentence the other way, you can tell it’s incorrect: Example : How much you weigh affects how much you eat. (Well, it could make sense, but you can see it’s an entirely different experiment.) If-then statements also work: Example : If you change the color of light (independent variable), then it affects plant growth (dependent variable). Switching the variables makes no sense: Example : If plant growth rate changes, then it affects the color of light. Sometimes you don’t control either variable, like when you gather data to see if there is a relationship between two factors. This can make identifying the variables a bit trickier, but establishing a logical cause and effect relationship helps: Example : If you increase age (independent variable), then average salary increases (dependent variable). If you switch them, the statement doesn’t make sense: Example : If you increase salary, then age increases.

How to Graph Independent and Dependent Variables

Plot or graph independent and dependent variables using the standard method. The independent variable is the x-axis, while the dependent variable is the y-axis. Remember the acronym DRY MIX to keep the variables straight: D = Dependent variable R = Responding variable/ Y = Graph on the y-axis or vertical axis M = Manipulated variable I = Independent variable X = Graph on the x-axis or horizontal axis

• Babbie, Earl R. (2009). The Practice of Social Research (12th ed.) Wadsworth Publishing. ISBN 0-495-59841-0.
• di Francia, G. Toraldo (1981). The Investigation of the Physical World . Cambridge University Press. ISBN 978-0-521-29925-1.
• Gauch, Hugh G. Jr. (2003). Scientific Method in Practice . Cambridge University Press. ISBN 978-0-521-01708-4.
• Popper, Karl R. (2003). Conjectures and Refutations: The Growth of Scientific Knowledge . Routledge. ISBN 0-415-28594-1.

Related Posts

Understanding Dependent and Independent Variables in Research Experiments and Hypothesis Testing

• First Online: 08 July 2024

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• Kingsley Okoye 3 &
• Samira Hosseini 4  

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This chapter describes what are the dependent and independent variables for conducting research experiments. It introduces the readers to the different conditions to the use of the two types of variables (dependent and independent) in scientific research and hypothesis testing. The differences between the two variables and examples of each use case scenario are provided in this chapter. The relationship between the independent (IV) and dependent (DV) variables is the key foundation of most statistical data analysis or scientific tests. The authors note that an easy way to identify the independent or dependent variable in an experiment is: independent variables (IV) are what the researchers change or changes on its own , whereas dependent variables (DV) are what changes as a result of the change in the independent variable (IV). Thus, independent variables (IV) otherwise known as the “predictor variable” are the cause while dependent variables (DV) or the “response variable” are the effect .

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Agravante, M. (2018). What Is the Meaning of Variables in Research? https://sciencing.com/meaning-variables-research-6164255.html.

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Okoye, K., Hosseini, S. (2024). Understanding Dependent and Independent Variables in Research Experiments and Hypothesis Testing. In: R Programming. Springer, Singapore. https://doi.org/10.1007/978-981-97-3385-9_5

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Dependent Variable: Definition and Examples

Types of Variable > Dependent Variable Definition

Contents (click to skip to the section):

• Dependent Variable General Definition.

Dependent Variable Examples.

Test your understanding..

• Dependent Variable Definition ( Statistical Modeling ).

Dependent Variables in Psychology.

• Dependent Variables in Cross Tabs.

Other Names for the Dependent Variable.

• Outcome Variable.

Dependent Variable Definition.

The dependent variable(DV) is just like the name sounds; it depends upon some factor that you, the researcher, controls. For example:

• How well you perform in a race depends on your training.
• How much you weigh depends on your diet.
• How much you earn depends upon the number of hours you work.

Whatever event you are expecting to change is always the dependent variable. In the first example above race performance is the variable you would expect to change if you changed your training, so that’s the dependent variable. In the second example, the dependent variable is weight and in the third example the dependent variable is the amount earned.

If you have trouble figuring out which of your variables is the independent one, and which is the dependent one, try inserting the variables into the following sentence:

“(Independent variable) causes a change in (Dependent Variable) and it isn’t possible that (Dependent Variable) could cause a change in (Independent Variable).”

When you run an experiment (I’m using the word “experiment” here loosely…it could be as simple as taking a survey or it could involve a complex scientific experiment), your independent variable stays fixed. In the next graph, the independent variable(IV) is the grade level and the dependent variable is the food rating. You can see that the food rating depends on what grade a student is (it looks like the higher grade levels have pickier eaters or perhaps students who choose their food more carefully).

Potential Confusion

You, the researcher, define your variables when you set up your experiment. Your hypothesis statement is what determines whether a variable is dependent or independent. Any variable can be and independent variable(IV) or dependent variable(DV). For example, let’s say you are interested in studying the health benefits of walking. You write the following two hypothesis statements:

• A more nutritious diet leads to more daily walking.
• More daily walking leads to increased happiness.

Both of the statements above are valid (assuming they correctly describe what you are trying to test with your experiment). However, walking is the DV in statement 1 and the IV in statement 2.

Example: The Brain as both Dependent and Independent Variables Much research has been conducted in the past that treats the brain as an IV. For example, the brain has a direct effect on behavior. However, more recent research has shown that the brain can also be a DV. for example, biofeedback is a type of learned behavior that helps you to control stress responses, like heart rate and muscle tension. The behavior makes subtle (and possibly permanent) changes in the brain. With biofeedback, the brain is the dependent variable, as it depends upon the behaviors practiced during biofeedback sessions. Although this is another example of how confusing the definition of an IV or DV can be, it also highlights how important it is to craft a good hypothesis statement for your experiment. Remember: the outcome of your experiment (i.e. your dependent variable) depends on how well you craft your hypothesis statement!

Back to Top

Example 1: A study finds that reading levels are affected by whether a person is born in the U.S. or in a foreign country. The IV is where the person was born and the DV is their reading level. The reading level depends on where the person was born.

Example 2: “In nonexperimental research, where there is no experimental manipulation, the IV is the variable that ‘logically’ has some effect on a DV. For example, in the research on cigarette-smoking and lung cancer, cigarette-smoking, which has already been done by many subjects, is the independent variable.” (Kerlinger, 1986, p.32) Lung cancer “depends” on smoking.

Tip : If you have trouble figuring out which of your variables is the independent one, and which is the dependent one, try inserting the variables into the following sentence:

Taking the two examples above, see how illogical it sounds to switch the places of the IV and DV in the bolded statements:

• Where a person is born depends on their reading level.
• Smoking “depends” on lung cancer.

Like most things in life though, if only it was that easy. Sometimes, it doesn’t work just to switch the phrase around to see if it works or not. Take the following two examples:

Example 3: A researcher studies how different drug doses affect the progression of a disease and compares the intensity and frequency of symptoms when different doses are given. The IV is the dose given and the DV is the intensity and frequency of symptoms. The intensity and frequency of symptoms “depends” on the dose of drug given.

Example 4: You are studying how tutoring affects SAT scores. Your independent variable(IV) is tutoring and the dependent variable(DV) is test scores. The test scores “depend” on the tutoring.

Switching them around also (sort of) makes sense:

• Dose of drug given depends on the intensity and frequency of symptoms.
• Tutoring depends on test scores.

That said, if you know what the hypothesis statement is–in other words, you know what is being tested–then you can decide which of the two versions make sense. This is one reason why it’s vital to craft a very clear hypothesis statement.

Dependent Variable Definition (Statistical Modeling)

For each question, choose the dependent variable. A tip for completing this quiz is first choose the two main variables from the statement. Then figure out which one is the DV (it’s the one that depends on the other one).

Q1: You are conducting an experiment to see if exposure to more sunlight increases happiness levels for workers who typically spend the entire day in windowless offices.

• Happiness level.
• Windowless offices.
• Time of day.

Click here for the answer. Q2: An experiment in a climate-controlled greenhouse concludes that water level, fertilizer and nutrient level in soil affects how tall plants grow. Plants grew an average of 12″ taller if treated with optimal resources.

• The greenhouse.
• Water level, fertilizer and nutrient levels.
• How tall the plants grow.
• Optimal resources.

Click here for the answer.

Q3: A researcher suspects that a cholera outbreak is happening because of tainted wells in the city. Most of the cases are clustered around public wells that draw their water from the underground aquifer.

• The underground aquifer.

Q4: Studies have shown that condom use is effective in controlling the spread of HIV. However, studies also show that a combination of two HIV medications (tenofovir and emtricitabine) can also control the spread of the disease.

• Emtricitabine.
• Both 1 and 2.

Solution to Q4 : Q4: The correct answer is 4, HIV. Controlling the spread of HIV depends upon condom use and the medications listed. Back to Quiz.

Back to Main Contents.

“In psychology studies, the dependent variable is usually a measurement of some aspect of the participants’ behavior. The IV is called independent because it is free to be varied by the experimenter. The DV is called dependent because it is thought to depend (at least in part) on the manipulations of the IV.” (Weiten, 2013)

Put another way, the dependent variable is the variable that is being measured by you, the experimenter. In psychology, the DV is often a score of some type. For example, a score on memorization task, an IQ test, or a depression scale.

Multiple Dependent Variables.

It’s common in psychology to investigate multiple dependent variables at the same time. Research can be a difficult process to set up–from gathering participants to obtaining funding and permissions–so making your research as broad as possible has many benefits. Researchers Simone Schnall and colleagues investigated how feeling disgust affected the harshness level of people’s moral judgment. The harshness of moral judgment was the DV, but several other DVs were measured, like how disgust affected people’s willingness to dine at a restaurant.

Back to Top.

Dependent Variables in Contingency Tables.

A dependent variable is also called:

• An experimental variable.
• An explained variable.
• A measured variable.
• An outcome variable.
• An output variable.
• A responding variable.
• A regressand (in regression analysis. )
• A response variable.

Outcome variable.

What is an Outcome variable?

The outcome variable and dependent variable are used synonymously. However, they are not exactly the same: the outcome variable is defined as the presumed effect in a non-experimental study , where the dependent variable is the presumed effect in an experimental study 1 .

Experimental vs. Non-experimental Studies.

In an experimental study, the researcher controls the allocation of resources to study participants. A non-experimental study is more like an observational study ; the researcher takes a look at what the participants are exposed to and then categorizes the individuals based on those exposures. Data registries and case studies are two examples of non-experimental; studies.

A simple example: let’s say you were interested on whether snack foods improved test scores. In an experimental study you could separate students into two groups, feed one group snacks while taking a test and deny the other group (the control group ) access to food. In the non-experimental case, you would find a group of students (say, in an entire college) and separate the students into those who eat snacks during a test and those who do not. You could then observe their performance on a test.

Measuring the Outcome Variable.

As outcome variables are involved in non-experimental studies, it’s practically impossible to put a numeric value on an outcome. Instead, non-numeric techniques are used 2 :

• Expert opinion.
• One or more case reports.
• Program evaluations. These are studies designed to see whether a program is meeting its goals.
• Quality improvement methods (Plan-Do-Study-Act), used to measure or redefine standards.
• Case control studies ; performed after an event has happened. Data is gathered and the researcher attempts to find the cause based on this historical data.
• Cohort studies : similar to case control but the participants are gathered before any event has happened. For example, a group of 1,000 people age 40-50 might be studied for 10 years to see who develops heart disease.

References: 1. Indiana University: Types of Variables. 2. Measuring Outcomes in Speech-language Pathology By Carol Frattali. 3. Kerlinger, F. N. (1986). Foundations of behavioral research (3rd ed.). Fort Worth: Holt,Rinehart and Winston, Inc. 4. Weiten, W. (2013). Psychology: Themes and variations, 9th ed. Belmont, CA: Wadsworth.

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• Types of Variables in Research & Statistics | Examples

Types of Variables in Research & Statistics | Examples

Published on September 19, 2022 by Rebecca Bevans . Revised on June 21, 2023.

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 .

If you want to test whether some plant species are more salt-tolerant than others, some key variables you might measure include the amount of salt you add to the water, the species of plants being studied, and variables related to plant health like growth and wilting .

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, other interesting articles, 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 variables 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 color-coded according to the type of variable: nominal , continuous , ordinal , and binary .

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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 ( causation ).

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 variables are listed below.

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

• Student’s  t -distribution
• Normal distribution
• Null and Alternative Hypotheses
• Chi square tests
• Confidence interval
• Cluster sampling
• Stratified sampling
• Data cleansing
• Reproducibility vs Replicability
• Peer review
• Likert scale

Research bias

• Implicit bias
• Framing effect
• Cognitive bias
• Placebo effect
• Hawthorne effect
• Hindsight bias
• Affect heuristic

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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 .

A confounding variable , also called a confounder or confounding factor, is a third variable in a study examining a potential cause-and-effect relationship.

A confounding variable is related to both the supposed cause and the supposed effect of the study. It can be difficult to separate the true effect of the independent variable from the effect of the confounding variable.

In your research design , it’s important to identify potential confounding variables and plan how you will reduce their impact.

Quantitative variables are any variables where the data represent amounts (e.g. height, weight, or age).

Categorical variables are any variables where the data represent groups. This includes rankings (e.g. finishing places in a race), classifications (e.g. brands of cereal), and binary outcomes (e.g. coin flips).

You need to know what type of variables you are working with to choose the right statistical test for your data and interpret your results .

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).

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15 Independent and Dependent Variable Examples

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An independent variable (IV) is what is manipulated in a scientific experiment to determine its effect on the dependent variable (DV).

By varying the level of the independent variable and observing associated changes in the dependent variable, a researcher can conclude whether the independent variable affects the dependent variable or not.

This can provide very valuable information when studying just about any subject.

Because the researcher controls the level of the independent variable, it can be determined if the independent variable has a causal effect on the dependent variable.

The term causation is vitally important. Scientists want to know what causes changes in the dependent variable. The only way to do that is to manipulate the independent variable and observe any changes in the dependent variable.

Definition of Independent and Dependent Variables

The independent variable and dependent variable are used in a very specific type of scientific study called the experiment .

Although there are many variations of the experiment, generally speaking, it involves either the presence or absence of the independent variable and the observation of what happens to the dependent variable.

The research participants are randomly assigned to either receive the independent variable (called the treatment condition), or not receive the independent variable (called the control condition).

Other variations of an experiment might include having multiple levels of the independent variable.

If the independent variable affects the dependent variable, then it should be possible to observe changes in the dependent variable based on the presence or absence of the independent variable.  

Of course, there are a lot of issues to consider when conducting an experiment, but these are the basic principles.

These concepts should not be confused with predictor and outcome variables .

Examples of Independent and Dependent Variables

1. gatorade and improved athletic performance.

A sports medicine researcher has been hired by Gatorade to test the effects of its sports drink on athletic performance. The company wants to claim that when an athlete drinks Gatorade, their performance will improve.

If they can back up that claim with hard scientific data, that would be great for sales.

So, the researcher goes to a nearby university and randomly selects both male and female athletes from several sports: track and field, volleyball, basketball, and football. Each athlete will run on a treadmill for one hour while their heart rate is tracked.

All of the athletes are given the exact same amount of liquid to consume 30-minutes before and during their run. Half are given Gatorade, and the other half are given water, but no one knows what they are given because both liquids have been colored.

In this example, the independent variable is Gatorade, and the dependent variable is heart rate.  

2. Chemotherapy and Cancer

A hospital is investigating the effectiveness of a new type of chemotherapy on cancer. The researchers identified 120 patients with relatively similar types of cancerous tumors in both size and stage of progression.

The patients are randomly assigned to one of three groups: one group receives no chemotherapy, one group receives a low dose of chemotherapy, and one group receives a high dose of chemotherapy.

Each group receives chemotherapy treatment three times a week for two months, except for the no-treatment group. At the end of two months, the doctors measure the size of each patient’s tumor.

In this study, despite the ethical issues (remember this is just a hypothetical example), the independent variable is chemotherapy, and the dependent variable is tumor size.

3. Interior Design Color and Eating Rate

A well-known fast-food corporation wants to know if the color of the interior of their restaurants will affect how fast people eat. Of course, they would prefer that consumers enter and exit quickly to increase sales volume and profit.

So, they rent space in a large shopping mall and create three different simulated restaurant interiors of different colors. One room is painted mostly white with red trim and seats; one room is painted mostly white with blue trim and seats; and one room is painted mostly white with off-white trim and seats.

Next, they randomly select shoppers on Saturdays and Sundays to eat for free in one of the three rooms. Each shopper is given a box of the same food and drink items and sent to one of the rooms. The researchers record how much time elapses from the moment they enter the room to the moment they leave.

The independent variable is the color of the room, and the dependent variable is the amount of time spent in the room eating.

4. Hair Color and Attraction

A large multinational cosmetics company wants to know if the color of a woman’s hair affects the level of perceived attractiveness in males. So, they use Photoshop to manipulate the same image of a female by altering the color of her hair: blonde, brunette, red, and brown.

Next, they randomly select university males to enter their testing facilities. Each participant sits in front of a computer screen and responds to questions on a survey. At the end of the survey, the screen shows one of the photos of the female.

At the same time, software on the computer that utilizes the computer’s camera is measuring each male’s pupil dilation. The researchers believe that larger dilation indicates greater perceived attractiveness.

The independent variable is hair color, and the dependent variable is pupil dilation.

5. Mozart and Math

After many claims that listening to Mozart will make you smarter, a group of education specialists decides to put it to the test. So, first, they go to a nearby school in a middle-class neighborhood.

During the first three months of the academic year, they randomly select some 5th-grade classrooms to listen to Mozart during their lessons and exams. Other 5 th grade classrooms will not listen to any music during their lessons and exams.

The researchers then compare the scores of the exams between the two groups of classrooms.

Although there are a lot of obvious limitations to this hypothetical, it is the first step.

The independent variable is Mozart, and the dependent variable is exam scores.

6. Essential Oils and Sleep

A company that specializes in essential oils wants to examine the effects of lavender on sleep quality. They hire a sleep research lab to conduct the study. The researchers at the lab have their usual test volunteers sleep in individual rooms every night for one week.

The conditions of each room are all exactly the same, except that half of the rooms have lavender released into the rooms and half do not. While the study participants are sleeping, their heart rates and amount of time spent in deep sleep are recorded with high-tech equipment.

At the end of the study, the researchers compare the total amount of time spent in deep sleep of the lavender-room participants with the no lavender-room participants.

The independent variable in this sleep study is lavender, and the dependent variable is the total amount of time spent in deep sleep.

7. Teaching Style and Learning

A group of teachers is interested in which teaching method will work best for developing critical thinking skills.

So, they train a group of teachers in three different teaching styles : teacher-centered, where the teacher tells the students all about critical thinking; student-centered, where the students practice critical thinking and receive teacher feedback; and AI-assisted teaching, where the teacher uses a special software program to teach critical thinking.

At the end of three months, all the students take the same test that assesses critical thinking skills. The teachers then compare the scores of each of the three groups of students.

The independent variable is the teaching method, and the dependent variable is performance on the critical thinking test.

8. Concrete Mix and Bridge Strength

A chemicals company has developed three different versions of their concrete mix. Each version contains a different blend of specially developed chemicals. The company wants to know which version is the strongest.

So, they create three bridge molds that are identical in every way. They fill each mold with one of the different concrete mixtures. Next, they test the strength of each bridge by placing progressively more weight on its center until the bridge collapses.

In this study, the independent variable is the concrete mixture, and the dependent variable is the amount of weight at collapse.

9. Recipe and Consumer Preferences

People in the pizza business know that the crust is key. Many companies, large and small, will keep their recipe a top secret. Before rolling out a new type of crust, the company decides to conduct some research on consumer preferences.

The company has prepared three versions of their crust that vary in crunchiness, they are: a little crunchy, very crunchy, and super crunchy. They already have a pool of consumers that fit their customer profile and they often use them for testing.

Each participant sits in a booth and takes a bite of one version of the crust. They then indicate how much they liked it by pressing one of 5 buttons: didn’t like at all, liked, somewhat liked, liked very much, loved it.

The independent variable is the level of crust crunchiness, and the dependent variable is how much it was liked.

10. Protein Supplements and Muscle Mass

A large food company is considering entering the health and nutrition sector. Their R&D food scientists have developed a protein supplement that is designed to help build muscle mass for people that work out regularly.

The company approaches several gyms near its headquarters. They enlist the cooperation of over 120 gym rats that work out 5 days a week. Their muscle mass is measured, and only those with a lower level are selected for the study, leaving a total of 80 study participants.

They randomly assign half of the participants to take the recommended dosage of their supplement every day for three months after each workout. The other half takes the same amount of something that looks the same but actually does nothing to the body.

At the end of three months, the muscle mass of all participants is measured.

The independent variable is the supplement, and the dependent variable is muscle mass.  

11. Air Bags and Skull Fractures

In the early days of airbags , automobile companies conducted a great deal of testing. At first, many people in the industry didn’t think airbags would be effective at all. Fortunately, there was a way to test this theory objectively.

In a representative example: Several crash cars were outfitted with an airbag, and an equal number were not. All crash cars were of the same make, year, and model. Then the crash experts rammed each car into a crash wall at the same speed. Sensors on the crash dummy skulls allowed for a scientific analysis of how much damage a human skull would incur.

The amount of skull damage of dummies in cars with airbags was then compared with those without airbags.

The independent variable was the airbag and the dependent variable was the amount of skull damage.

12. Vitamins and Health

Some people take vitamins every day. A group of health scientists decides to conduct a study to determine if taking vitamins improves health.

They randomly select 1,000 people that are relatively similar in terms of their physical health. The key word here is “similar.”

Because the scientists have an unlimited budget (and because this is a hypothetical example, all of the participants have the same meals delivered to their homes (breakfast, lunch, and dinner), every day for one year.

In addition, the scientists randomly assign half of the participants to take a set of vitamins, supplied by the researchers every day for 1 year. The other half do not take the vitamins.

At the end of one year, the health of all participants is assessed, using blood pressure and cholesterol level as the key measurements.

In this highly unrealistic study, the independent variable is vitamins, and the dependent variable is health, as measured by blood pressure and cholesterol levels.

13. Meditation and Stress

Does practicing meditation reduce stress? If you have ever wondered if this is true or not, then you are in luck because there is a way to know one way or the other.

All we have to do is find 90 people that are similar in age, stress levels, diet and exercise, and as many other factors as we can think of.

Next, we randomly assign each person to either practice meditation every day, three days a week, or not at all. After three months, we measure the stress levels of each person and compare the groups.

How should we measure stress? Well, there are a lot of ways. We could measure blood pressure, or the amount of the stress hormone cortisol in their blood, or by using a paper and pencil measure such as a questionnaire that asks them how much stress they feel.

In this study, the independent variable is meditation and the dependent variable is the amount of stress (however it is measured).

14. Video Games and Aggression

When video games started to become increasingly graphic, it was a huge concern in many countries in the world. Educators, social scientists, and parents were shocked at how graphic games were becoming.

Since then, there have been hundreds of studies conducted by psychologists and other researchers. A lot of those studies used an experimental design that involved males of various ages randomly assigned to play a graphic or non-graphic video game.

Afterward, their level of aggression was measured via a wide range of methods, including direct observations of their behavior, their actions when given the opportunity to be aggressive, or a variety of other measures.

So many studies have used so many different ways of measuring aggression.

In these experimental studies, the independent variable was graphic video games, and the dependent variable was observed level of aggression.

15. Vehicle Exhaust and Cognitive Performance

Car pollution is a concern for a lot of reasons. In addition to being bad for the environment, car exhaust may cause damage to the brain and impair cognitive performance.

One way to examine this possibility would be to conduct an animal study. The research would look something like this: laboratory rats would be raised in three different rooms that varied in the degree of car exhaust circulating in the room: no exhaust, little exhaust, or a lot of exhaust.

After a certain period of time, perhaps several months, the effects on cognitive performance could be measured.

One common way of assessing cognitive performance in laboratory rats is by measuring the amount of time it takes to run a maze successfully. It would also be possible to examine the physical effects of car exhaust on the brain by conducting an autopsy.

In this animal study, the independent variable would be car exhaust and the dependent variable would be amount of time to run a maze.

Read Next: Extraneous Variables Examples

The experiment is an incredibly valuable way to answer scientific questions regarding the cause and effect of certain variables. By manipulating the level of an independent variable and observing corresponding changes in a dependent variable, scientists can gain an understanding of many phenomena.

For example, scientists can learn if graphic video games make people more aggressive, if mediation reduces stress, if Gatorade improves athletic performance, and even if certain medical treatments can cure cancer.

The determination of causality is the key benefit of manipulating the independent variable and them observing changes in the dependent variable. Other research methodologies can reveal factors that are related to the dependent variable or associated with the dependent variable, but only when the independent variable is controlled by the researcher can causality be determined.

Ferguson, C. J. (2010). Blazing Angels or Resident Evil? Can graphic video games be a force for good? Review of General Psychology, 14 (2), 68-81. https://doi.org/10.1037/a0018941

Flannelly, L. T., Flannelly, K. J., & Jankowski, K. R. (2014). Independent, dependent, and other variables in healthcare and chaplaincy research. Journal of Health Care Chaplaincy , 20 (4), 161–170. https://doi.org/10.1080/08854726.2014.959374

Manocha, R., Black, D., Sarris, J., & Stough, C.(2011). A randomized, controlled trial of meditation for work stress, anxiety and depressed mood in full-time workers. Evidence-Based Complementary and Alternative Medicine , vol. 2011, Article ID 960583. https://doi.org/10.1155/2011/960583

Rumrill, P. D., Jr. (2004). Non-manipulation quantitative designs. Work (Reading, Mass.) , 22 (3), 255–260.

Taylor, J. M., & Rowe, B. J. (2012). The “Mozart Effect” and the mathematical connection, Journal of College Reading and Learning, 42 (2), 51-66.  https://doi.org/10.1080/10790195.2012.10850354

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Dependent Variable vs. Independent Variable: What Is the Difference?

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A dependent variable is the variable being tested in a scientific experiment.

The dependent variable is "dependent" on the independent variable. As the experimenter changes the independent variable, the change in the dependent variable is observed and recorded. When you take data in an experiment, the dependent variable is the one being measured.

Common Misspellings: Dependant variable

Dependent Variable Examples

• A scientist is testing the effect of light and dark on the behavior of moths by turning a light on and off. The independent variable is the amount of light and the moth's reaction is the dependent variable . A change in the independent variable ( amount of light ) directly causes a change in the dependent variable (moth behavior).
• You want to learn which kind of chicken produces the largest eggs . The egg size depends on the chicken breed, so breed is the independent variable and egg size is the dependent variable.
• You want to know whether or not stress affects heart rate . Your independent variable is the stress, while the dependent variable is heart rate . To experiment, you would provide stress and measure the subject's heartbeat . In a good experiment, you'd choose a stress you could control and quantify. Your choice could lead you to perform additional experiments since it might turn out that the change in heart rate after exposure to a decrease in temperature by 40 degrees ( physical stress ) might be different from the heart rate after failing a test ( psychological stress ). Even though your independent variable might be a number you measure, it's one you control, so it's not "dependent."

Distinguishing Between Dependent and Independent Variables

Sometimes it's easy to tell the two types of variables apart , but if you get confused, here are tips to help keep scientific variables straight:

• If you change one variable, which is affected? If you're studying the growth rate of plants using different fertilizers , can you identify the variables? Start by thinking about what you are controlling and what you will be measuring. The type of fertilizer is the independent variable. The rate of growth is the dependent variable. So, to experiment, you would fertilize plants with one fertilizer and measure the change in height of the plant over time, then switch fertilizers and measure the height of plants over the same period. You might be tempted to identify time or height as your variable, not the growth rate (distance per time). It may help to look at your hypothesis or purpose to remember your goal .
• Write out your variables as a sentence stating cause and effect. The independent variable causes a change in the dependent variable. Usually, the sentence won't make sense if you get them wrong. For example: (Taking vitamins) affects the number of (birth defects). = Makes sense. (Birth defects) affects the number of (vitamins). = Probably not much.

Graphing the Dependent Variable

When you graph data, the independent variable is on the X-axis, while the dependent variable is on the Y-axis. You can use the DRY MIX acronym to remember this:

D - dependent variable R - responds to change Y - Y-axis

M - manipulated variable (one you change) I - independent variable X - X-axis

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Definitions

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

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

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

Identifying Dependent and Independent Variables

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

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

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

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

Structure and Writing Style

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

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

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

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

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

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

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Independent vs Dependent Variables | Definition & Examples

Published on 4 May 2022 by Pritha Bhandari . Revised on 17 October 2022.

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

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

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

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

Table of contents

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

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

Independent variables are also called:

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

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

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There are two main types of independent variables.

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

Experimental variables

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

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

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

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

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

• A low-dose experimental group
• A high-dose experimental group
• A placebo group

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

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

Subject variables

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

It’s not possible to randomly assign these to participants, since these are characteristics of already existing groups. Instead, you can create a research design where you compare the outcomes of groups of participants with characteristics. This is a quasi-experimental design because there’s no random assignment.

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

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

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

In statistics , dependent variables are also called:

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

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

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

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

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

Here are some tips for identifying each variable type.

Recognising independent variables

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

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

Recognising dependent variables

Check whether you’re dealing with a dependent variable:

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

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

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

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

The type of test is determined by:

• Your variable types
• Level of measurement
• Number of independent variable levels

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

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

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

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

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

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

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

• Right-hand-side variables (they appear on the right-hand side of a regression equation)

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

In statistics, dependent variables are also called:

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

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

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

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

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

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

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

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

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How to Identify Dependent and Independent Variables

Last Updated: June 29, 2024 Fact Checked

This article was co-authored by Michael Simpson, PhD . Dr. Michael Simpson (Mike) is a Registered Professional Biologist in British Columbia, Canada. He has over 20 years of experience in ecology research and professional practice in Britain and North America, with an emphasis on plants and biological diversity. Mike also specializes in science communication and providing education and technical support for ecology projects. Mike received a BSc with honors in Ecology and an MA in Society, Science, and Nature from The University of Lancaster in England as well as a Ph.D. from the University of Alberta. He has worked in British, North American, and South American ecosystems, and with First Nations communities, non-profits, government, academia, and industry. There are 10 references cited in this article, which can be found at the bottom of the page. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 136,973 times.

Whether you’re conducting an experiment or learning algebra, understanding the relationship between independent and dependent variables is a valuable skill. Learning the difference between them can be tricky at first, but you’ll get the hang of it in no time.

Understanding Independent and Dependent Variables

• For example, if a researcher wants to see how well different doses of a medication work, the dose is the independent variable.
• Suppose you want to see if studying more improves your test scores. The amount of time you spend studying is the independent variable.

• Say a researcher is testing an allergy medication. Allergy relief after taking the dose is the dependent variable, or the outcome caused by taking the medicine.

Tip: When you encounter variables, plug them into this sentence: “ Independent variable causes Dependent Variable , but it isn't possible that Dependent Variable could cause Independent Variable .

For example: “A 5 mg dose of medication causes allergy relief, but it isn’t possible that allergy relief could cause a 5 mg dose of medication.”

Identifying Variables in Equations

• The $3 per chore is a constant. Your parents set that in stone, and that number isn't going to change. On the other hand, the number of chores you do and the total amount of money you earn aren't constant. They're variables that you want to measure.
• To set up an equation, use letters to represent the chores you do and the money you'll earn. Let t represent the total amount of money you earn and n stand for the number of chores you do.

• Notice that the amount of money you'll earn depends on the number of chores to do. Since it depends on other variables, it's the dependent variable.

Graphing Independent and Dependent Variables

• Say you sell apples and want to see how advertising affects your sales. The amount of money you spent in a month on advertising is the independent variable, or the factor that causes the effect you’re trying to understand. The number of apples you sold that month is the dependent variable.

• Suppose you’re trying to see if advertising more increases the number of apples you sold. Divide the x-axis into units to measure your monthly advertising budget.
• If you’ve spent between $0 and $500 a month in the last year on advertising, draw 10 dashes along the x-axis. Label the left end of the line “$0.” Then label each dash with a dollar amount in $50 increments ($50, $100, $150, and so on) until you’ve reached the last dash, or “$500.”

• Suppose your monthly apple sales have ranged between 60 and 250 over the last year. Draw 10 dashes across the y-axis, label the first “50,” and label the rest of the dashes in increments of 25 (50, 75, 100, and so on), until you’ve written 275 next to the last dash.

• For instance, if you spent $350 on advertising last month, find the dash labeled “350” on the x-axis. If last month’s apple sales totaled 225, find the dash labeled “225” on the y-axis. Draw a dot at the point at the graph coordinate ($350, 225), then continue graphing points for the rest of your monthly numbers.

• For example, say you’ve graphed your advertising expenses and monthly apple sales, and the dots are arranged in an upward sloped line. This means that your monthly sales were higher when you spent more on advertising.

Expert Q&A

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• ↑ Michael Simpson, PhD. Registered Professional Biologist. Expert Interview. 25 June 2021.
• ↑ https://researchbasics.education.uconn.edu/variables/
• ↑ https://libguides.usc.edu/writingguide/variables
• ↑ https://nces.ed.gov/nceskids/help/user_guide/graph/variables.asp
• ↑ https://www.khanacademy.org/math/algebra/introduction-to-algebra/alg1-dependent-independent/e/dependent-and-independent-variables
• ↑ https://www.mathsisfun.com/algebra/equations-solving.html
• ↑ https://www.khanacademy.org/math/pre-algebra/pre-algebra-equations-expressions/pre-algebra-dependent-independent/a/dependent-and-independent-variables-review
• ↑ https://www2.nau.edu/lrm22/lessons/graph_tips/graph_tips.html
• ↑ https://www.khanacademy.org/math/cc-sixth-grade-math/cc-6th-equations-and-inequalities/cc-6th-dependent-independent/v/dependent-and-independent-variables-exercise-example-2
• ↑ https://nces.ed.gov/nceskids/help/user_guide/graph/line.asp

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