The power function of the analysis of variance tests, with tables and illustrations of their use
Statistical Research Memoirs, (1938)Abstract
After formulating the criterion for testing the general linear hypothesis (of analysis of variance tests) it is shown that if the hypothesis tested is not true the distribution depends upon a sum of noncentral squares. The properties of this sum and the application of the squares in the derivation of the exact distribution of the squares of the coefficient of variation are studied. Methods are given for calculating the probability integral of the square of the joint probability distribution of all the independent variates in the general case where the hypothesis tested is not true. Discussion and tables of the probability of failing to reject the hypothesis when a second hypothesis is true are presented. (PsycINFO Database Record (c) 2016 APA, all rights reserved)