The Joint Assessment of Normality of Several Independent Samples

Abstract

Statistical methods are presented for the joint assessment of the supposed normality of a collection of independent (small) samples, which may derive from populations having differing means and variances. The procedures are based on the use of the W statistic (Shapiro and Wilk, 1965) as a measure of departure from normality. Two modes of combination of a collection of W statistics are considered, namely the standardized mean of the normal transforms of W and the sum of the x 2(2) transforms of the significance levels of w; and these are proposed for use in conjunction with the probability plotting of the collection of these transforms. Tables and formulae for practical implementation are provided. Some summary empirical sampling results are given on the comparative sensitivities of these procedures, along with detailed consideration of several specific examples which illustrate the additional informative value of probability plotting. The proposed techniques appear to have substantial data analysis value ...