Constant

The term constant simply refers to something that is not variable. In statistics, and survey research in particular, responses are typically described as random variables, roughly meaning that the responses cannot be predicted with certainty. For example, when people are asked whether they approve or disapprove of a particular political leader, typically there is uncertainty about what the response will be. As another example, in a survey regarding whether individuals approve or disapprove of the death penalty, responses are not constant simply because some individuals will approve and others will not.

Although at some level, the difference between a constant and a random variable is clear, the distinction between the two often becomes blurred. Consider, for example, the population mean, μ. That is, μ is the average of all individuals of interest in a particular survey if they could be measured. The so-called frequentist approach to statistical problems views μ as a constant. It is some fixed but unknown value. However, an alternative view, reflected by a Bayesian approach to statistics, does not view μ as a constant, but rather as a quantity that has some distribution. The distribution might reflect prior beliefs about the likelihood that μ has some particular value.

As another example, p might represent the probability that an individual responds “Yes” when asked if he or she is happily married. In some sense this is a constant: at a particular moment in time one could view p as fixed among all married couples. Simultaneously, p could be viewed as a random variable, either in the sense of prior beliefs held by the investigator or perhaps as varying over time.

Another general context in which the notion of constant plays a fundamental role has to do with assumptions made when analyzing data. Often it is assumed that certain features of the data are constant in order to simplify technical issues. Perhaps the best-known example is homoscedasticity. This refers to the frequently made assumption that the variance among groups of individuals is constant. In regression, constant variance means that when trying to predict Y based on some variable X, the (conditional) variance of Y, given X, does not vary. So, for example, if X is amount of solar radiation associated with a particular geographic region, and Y indicates breast cancer rates, constant variance means that the variance of Y does not differ among the geographic regions that are of interest.