# Encyclopedia of Personality and Individual Differences

Living Edition
| Editors: Virgil Zeigler-Hill, Todd K. Shackelford

# Dependent Variable

Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-28099-8_1296-1

## Keywords

Memory Test School Performance Independent Manner Grade Point Average Time Task
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Definition

The dependent variable is a variable whose variation is observed depending on variation in the independent variable.

## Introduction

When interpreting covariation of variables, it is often important to know what causes the covariation. To do this, in the case of two variables, one variable is regarded to vary in independent manner while variation in the other one is observed depending on variation in the independently varying one. In most cases, it is very hard to know which variable varies independently and which one varies dependently or if the covariation does occur without any apparent causality between the two variables. Consequently, an experimental approach is often taken: one variable is manipulated to vary, while the effect of this variation on the other variable is observed. The affected variable is called dependent variable Y and the manipulated variable is called independent variable X. As noted before, even though the terms “dependent” and “independent” imply a direction of effect, this direction must not be known in all cases – in some cases, the covariation might even be caused by a third variable Z, possibly not included in the statistical model (Fig. 1). Fig. 1 Forms of covariation. (a) X causes covariation in Y. (b) Y causes covariation in X. (c) X causes covariation in Y and vice versa. (d) Z causes covariation in X and Y

## Covariation

In contrast to a constant, a variable can take on at least two different states. When more than one variable is observed, the degree to which particular states of one or more variables tend to occur together with particular states of one or more other variables can be determined. This tendency of states of variables occurring together is called covariation. For the sake of simplicity, the case of covariation between only two variables will be discussed but is easily extendable to cases with more than three or more variables.

The covariation of two variables X and Y can be investigated systematically by altering the state of X while observing the associated states of Y (i.e., the states occurring together with the states of the manipulated variable X). Because – if the two variable do covary – the states of the Y are thought to be dependent on the manipulations of X, Y is called the “dependent” variable. The manipulated variable X is called the “independent” variable because its states are manipulated to change independently of states of Y. Mathematically, Y can, therefore, be expressed as a function of X:
$$Y= f(X).$$

## Examples of Dependent and Independent Variables

Examples for variables and their respective states are manifold. The independent variable may be of two groups in a psychological experiment with the states “being in group one” and “being in group two.” It is easy to interpret this variable as the independent variable: the two groups could be an experimental group receiving working memory training and the other group could be a control group performing simple reaction time tasks. The dependent variable could be the score in a subsequent working memory test. It is only logical to assume that the test score depends on the training but that the assignment to one of the two groups is independent of the score in the test after training – thus the names of the two variables. However, the distinction is not always this easy. If the two variables are the number of books a person has read (the possible states ranging from zero to infinity) and grade point average (GPA; the possible states ranging from minimally to maximally GPA), it is not clear which one of the two variables is independent and which one is dependent. It is reasonable to assume that knowledge obtained from literature influences school performance but it may also be that good grades provide a motivation to read more. There might even be a third variable, such as the parents’ socioeconomic status, that influences both the performance in school and the number of books a person reads. The third variable would be called a confounding variable or (experimental) confound, such as variable Z in Fig. 1d.

The classification of one variable as dependent and the other one as independent is therefore not always straightforward and has to be theoretically justified. In many cases of statistical modeling, the definition of variables as dependent and independent even leads to mathematically equivalent solutions: this means that an equation
$$g(Y)= X$$
can be formulated with g(•) = f −1(•) being the inverse function of f(•). Therefore, the correct labeling of the variables as “dependent” and “independent” is the responsibility of the researcher formulating the statistical model and can be of uttermost importance for the conclusions that can be drawn from an investigation.

## Conclusion

When investigating the covariation of variables, they are usually labeled as either “dependent” or “independent.” A statistical model, formulated to explain the covariation between the variables, also contains independent and dependent variables. This implies a direction of effect in terms of variation in independent variable causing variation in the dependent variable. The direction of this effect is not always clear and has to be defined, based on theoretical assumptions of the researcher postulating the model.

## Copyright information

© Springer International Publishing AG 2017

## Authors and Affiliations

1. 1.Department of PsychologyPsychological Methods and AssessmentMünchenGermany
2. 2.Faculty of Psychology, Educational Science, and Sport ScienceUniversity of RegensburgRegensburgGermany

## Section editors and affiliations

• Matthias Ziegler
• 1
1. 1.Humboldt University, GermanyBerlinGermany