Constant

The term constant simply refers to something that is not variable. In statistics, responses are typically described as RANDOM VARIABLES, roughly meaning that the responses cannot be predicted with certainty. For example, how much weight will the typical adult lose following some particular diet? How will individuals respond to a new medication? If we randomly pick some individual, will he or she approve of the death penalty?

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 study if they could be measured. The so-called frequentist approach to statistical problems views μas 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 [Page 180]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 to simplify technical issues. Perhaps the best-known example is HOMOSKEDASTICITY. 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 aggression in the home and Y is a measure of cognitive functioning, constant variance means that the variance of Y among homes with an aggression score of, for example, X = 10 is the same as homes with X = 15, X = 20, and any other value for X we might choose.