The distribution of the sphericity test criterion

Abstract

The exact distribution of Mauchly's sphericity test criterion W = | S|/[tr S/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, α = 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.