Definition of POWER FUNCTION. 1. : a function of a parameter under statistical test whose value for a particular value of the parameter is the probability of rejecting the null hypothesis if that value of the parameter happens to be true. 2.: a function (as f(x) = axk) that equals the product of a constant and a power of the independent variable. a function of a parameter under statistical test whose value for a particular value of the parameter is the probability of rejecting the null hypothesis if that value of the parameter happens to be true. 2.