Sequential One-Sample Grouped Signed Rank Tests for Symmetry: Basic Procedures

Abstract

Independent groups, each of N independent observations on a random variable Z, are taken sequentially with signed ranks obtained within groups. Two tests of symmetry of the parent cdf F about the origin are developed, one based on the within-group configurations of signed ranks and the other based on the within-group sums of positive signed ranks. Some properties of F are F₊(z) = 1 - [1-F_-(z)]^k, x≥0, k>0, and F(0) = k/(k+1) where F₊ and F_- are respectively the conditional cdf's of non-negative and absolute negative values of Z. Properties and examples of the two procedures are given.