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

Abstract

The test statistic X 2 (√ b 1 )+ X 2 ( b 2 ), where X (√ b 1 ) and X ( b 2 ) are standardized normal equivalents to the ample skewness, √ b 1 , and kurtosis, b 2 , statistics, is considered in normal sampling. Using the Johnson system, S U , and S B , as approximate normalizing distributions, contours in the (√ b 1 , b 2 ) plane of the test statistic are set up for sample sizes ranging from 20 to 1000.