A Sequential Signed-Rank Test for Symmetry

Abstract

A sequential procedure for testing the hypothesis that the distribution of a sequence of i.i.d. random variables is symmetric about zero is given, where the test statistic is a function of the signs and the rank of the absolute values of the observations. Necessary and sufficient conditions that the individual signed ranks be independent are given. The critical region, power, and expected sample size of the test are determined approximately by using the fact that the test statistic behaves asymptotically like a Brownian motion process.