Consideration of power for some two sample tests with censoring based on a given order statistic

Abstract

SUMMARY This paper deals with some properties of three nonparametric tests which can be used for detecting a difference in location of two populations wlhen samples are censored on the occurrence of a given order statistic. The null distributions of the test statistics are presented together with some tables of critical values. Exact expressions are obtained for the powers of the tests under exponential and rectangular alternatives. Finally, the expected durations of the tests are compared. A number of tests which permit early termination of an experiment have been proposed for detecting a difference in the location of two populations. These tests have important applications in life-testing situations where testing time may be costly. The criterion for termination may be a preselected period of time from the start of the experiment or the occurrence of a given order statistic in one of the samples or the two samples combined. In this paper we consider three nonparametric tests which may be used to provide a one-sided test for difference in location of two populations. The common feature of the tests is that the experiment is terminated on or before the occurrence of a preselected order statistic in one of the samples. We first consider the distributions of the test statistics under the null hypothesis that the two samples have been drawn randomly from populations with identical cumulative distribution functions. Some tables of critical values are presented. Expressions are given for the test powers under the alternative of a translation in an exponential distribution and for changes in the location and scale parameters of a rectangular distribution. Finally some results are given for the expected durations of the tests.