The distribution of the sphericity test criterion

Abstract

The exact distribution of Mauchly's sphericity test criterion W = S/[trS/p]p, when S is the sum of product matrix from a sample of size N taken from a p-variate normal population, is obtained using contour integration and methods similar to those of Nair and Box. Tables of percentage points for p = 4(1)10, [alpha] = 0.01 and 0.05, and various values of N (including small) are given and comparisons made with approximate percentage points using methods of Box, Mauchly, Tukey and Wilks, and Davis.Exact distribution sphericity test criterion contour integration factorial series percentage points approximations