Abstract definition of independent variable and dependent variable
Most generally, a dependent variable (DV) is something which we think depends on one or more independent variables (IV). That is, we think that, if the IVs change, the DV will change. There is a causal element here – but statistics cannot test the causation, it can only see if there is a relationship.
The proper interpretation of IVs and DVs depends on whether we are doing an experiment, or conducting an observational study. In an experiment, the IV is under the control of the experimenter. In an observational study, it is not. Thus, the common notion that an independent variable is something which the researcher varies is not completely correct.
Examples of independent and dependent variables
That’s rather abstract; let’s look at some examples. If we wanted to look at the relationship between height and weight in adult humans, we could not control either variable; yet, it is quite clear which is the dependent variable and which is the independent variable. It makes sense to say that weight depends on height; it does not make sense to say that height depends on weight. If I say “If I were taller, I would weigh more” people will nod. If I say “If I weighed more, I would be taller” people will giggle. We might have other IVs as well – for example, we might include gender.
In an experiment, on the other hand, the IVs are under the control of the experimenter. For example, if we wanted to see if different diets affected weight gain, we might get volunteers, and randomly assign them to different diets. Here the IV is “diet” and the DV is “weight gain”.
Independent and dependent are context specific
It is also important to note that what is a DV in one study may be an IV in another study. For example, we looked above at weight being a DV and height an IV. But, if we looked at the relationship of weight and coronary disease, then weight would be the IV. Similarly, if we looked at subject height and parental height, then subject height would be the DV. It does not make sense to say that my parents are short because I am!
Finally, it is important to note that, in some cases, we do not have IVs and DVs, we are simply interested in relationship. One example would be looking at degree of prejudice and political preference. In other cases, we simply want to see how variables hang together – for example, when we give people a test with a lot of items, we may want to combine these items somehow into a single score.
Why you need to distinguish dependent variables from independent variables
One reason it is crucial to understand DVs and IVs is that the type of statistical analysis we undertake will depend (hehe) on this. When we have a DV and several IVs, one huge set of techniques is subsumed under the generalized linear model – this includes the many forms of regression, it also includes analysis of variance (ANOVA), and analysis of covariance (ANCOVA). When we do not have DV and IVs, then there are techniques such as the various kinds of correlation, and techniques based on these (e.g. factor analysis, principal components analysis), cross-tabs, and so on.