# Dependent Variable

**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## Definition

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

## Introduction

*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).

## 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.

*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*:

## 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.

*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.