Tests for departure from normality. Empirical results for the distributions of b2 and √b1

Abstract

This paper is a preliminary to a detailed survey of the relative powers of a number of omnibus and directional tests of nonnormality. The probability integrals of √ b 1 and b 2 , the standardized third and fourth moment statistics, are found for random samples from a normal distribution. Main attention is given to b 2 . Extensive computer simulation and curve fitting have been used to provide charts of probability levels out to the 0.1% point, for 20 ≤ n ≤ 200. For √ b 1 , the parameters of Johnson's symmetrical S U approximation are tabled for values of n between 8 and 1000. An illustration is given of two ‘omnibus’ tests applying the charts and table, involving the joint use of √ b 1 and b 2 .