Two Sequential Two-Sample Grouped Rank Tests with Applications to Screening Experiments

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Abstract
Two sequential two-sample grouped rank tests are developed and designated as the Configural Rank Test and the Rank-Sum Test. For both tests, observations are taken in groups of m X-observations and n Y-observations with the observations ranked within the groups. The sequential procedures relate to the usual decisions at the end of each group, namely to accept a null hypothesis, to accept an alternative hypothesis, or to take another group of observations. The hypotheses involved are H0:G(x) = F(x) and H1:G(x) = Fk(x) when f(x) is the cumulative distribution function of the X-population and G(y) that for the Y-population. The implications of these hypotheses are discussed. The sequential methods are direct applications of Wald sequental analysis. The configural rank test depends on a probability-ratio statistic based on probabilities of the particular configuration of ordered observations obtained; the rank-sum test uses the within-group rank sum for the Y-sample and probability ratios based on the probabilities for the rank sums. Values of the operating characteristic functions and of the average sample number functions for the two tests are given with discussions of the properties of the tests.

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