A class of sequential grouped signed rank tests

Abstract

A class of nonparametric sequential tests for testing symmetry about a specified value is developed for the case where observations are taken in groups. Signed rank statistics are computed indepently for each group and the test is based on the sum of these statistics used with linear boundaries. The procedure is formulated as a Markov chain so that the exact small sample properties of the test can be evaluated. The asymtotic OC and ASN functions are developed for local alternatives. For the case where Wilcoxon scores are used tables are given which make it easy to design a test to achieve specified error probabilities.

Keywords:

• sequential nonparametric test
• Wilcoxon statistic
• sequential probability ratio test
• Markov chain