Accuracy of Normal and Edgeworth Approximations to the Distribution of the Wilcoxon Signed Rank Statistic

Abstract

Abstract Cumulative probabilities from the null distribution of the Wilcoxon signed rank statistic were approximated by the normal approximation and by Edgeworth expansions to terms of order 1/N and of order 1/N 2 for selected values of the statistic for values of N from 30 through 100. Use of the usual correction for continuity is advantageous at all probability levels in the Edgeworth expansions and in the normal approximation for probability levels greater than about 0.035. The accuracy of these approximations is summarized in terms of percent relative error incurred as a function of the exact probability being approximated.