Variables

Variables and Constants

Some indicators capture traits that are ontologically variable: If a study were to be in some sense repeated, the score on this indicator for a given case could have been other than what it was. An intuitive example of a variable in this sense is the result of rolling a die. If the die were to be rolled again, there is no particular reason to believe that it would show the same number of dots as on an earlier roll. Hence, the number of dots shown on the die after a roll is a variable in the ontological sense. An equivalent example in social science research involves random experimental assignment of a subject to one of a number of treatments: If the process of assignment were to be repeated, one may reasonably expect that many subjects would get a different assignment than they did in the initial iteration of the study. For this reason, one may conclude that experimental assignment is a variable, not a constant.

A second common usage of the distinction between variables and constants involves describing the data actually produced by a particular study, rather than the ontological characteristics of the data-generating process. In this usage, an indicator is said to be a variable if the cases included in the study have more than one score on the indicator. Thus, a research design in which only political activists are selected for analysis may be described as one in which political participation is a constant; in contrast, if some apolitical individuals are added to the research design, participation would then be said to be a variable. This is the usage employed in the common aphorism that it is impossible to explain a variable with a constant.

These two usages are nonequivalent. An indicator may be ontologically variable while still producing the same score for every case in a given study. As a simple example, consider an extremely unfair coin that shows heads in 99.9% of flips and tails in 0.1%. The study involves flipping the coin 100 times, recording 1 for each instance of heads and 0 for tails. With this setup, the probability of observing a score of one for each of the 100 cases of flipping the coin is about 90.5%, so it is quite probable that the resulting indicator will be a constant in the second sense. However, each coin flip obviously involves a variable in the ontological sense: It is not impossible (although obviously unlikely) that a given flip will show tails rather than heads.

...