On the Distribution of theF-Type Statistics in the Analysis of a Group of Experiments

Abstract

Particular matrix representations are given for the usual sums of squares in the analysis of a group of experiments. Box's theorems on quadratic forms in normal variables are applied to study the distributions of the sums of squares and of the usual variance ratio statistics. The behaviour of these statistics under heterogeneity of the error variance and of the interaction variance is considered and approximateF-tests are suggested.