Omnibus test contours for departures from normality based on b1 and b2

Abstract

The test statistic X2(√b1)+X2(b2), where X(√b1) and X(b2) are standardized normal equivalents to the ample skewness, √b1, and kurtosis, b2, statistics, is considered in normal sampling. Using the Johnson system, SU, and SB, as approximate normalizing distributions, contours in the (√b1, b2) plane of the test statistic are set up for sample sizes ranging from 20 to 1000.