Probability Bounds for a Union of Hyperspherical Cones

Abstract

In this paper are given two methods of obtaining bounds on the probability content of a union of hyperspherical cones in EuclideanN-space when the underlying distribution is normal. The results of a small numerical study are tabulated to indicate the range of applicability of the methods. These methods can be used to obtain bounds on the overall significance level and power-like probabilities in the analysis of variance when many treatment sums of squares are tested against the same error sum of squares.