Distribution of the Normal Scores Statistic for Nonparametric One-Way Analysis of Variance

Abstract

Abstract The normal scores test for one-way analysis of variance is studied. Exact critical values are given for the three-sample case when the total number of observations is 15 or less. An accurate small-sample approximation to the true distribution is developed by using the method of moments and the beta probability law. This fitting distribution is used in a heuristic evaluation of other fitting schemes. For moderate sample sizes, the asymptotic chi-squared distribution fits poorly, but an approximation based on the F distribution works fairly well.