1. a relationship in which the values for one variable vary according to the values of another variable raised to a power. In mathematics, it is expressed by the equation y = axb, where x and y are the variables and a and b are numerical constants. Power functions have been used to characterize the scales relating perceived and physical intensity, for example, as well as to characterize the relationship between response speed and practice. 2. a formula relating different factors, such as sample size, effect size, and significance level, to the likelihood that use of a particular statistical procedure will lead to rejection of the null hypothesis when it is in fact false (see power). For example, a researcher may plan to use a specific statistical test to detect a medium-sized effect, evaluate the effect at the .001 significance level, and reach a desired
statistical power level of .80. Using a power function, the researcher could determine the sample size needed under those conditions. Power functions may be presented in tabular form or shown graphically as power curves.