K-Sample Analogues of the Kolmogorov-Smirnov Statistics and Binomial Group Tests

Abstract

<p> The Kolmogorov-Smirnov tests of homogeneity or goodness-of-fit and the binomial group tests for eliminating defectives are of different nature. But they are both popular in applications. The former are widely used in nonparametric comparison, while the later are usually adopted in the group screening problems. When the experimenter has k populations, k-sample statistics should be considered for the testing of homogeneity or goodness-of-fit. On the other hand, when there are k experimenters available for performing group testing on a given population, a k-sample group testing procedure should be used.</p> <p> In this thesis, the distribution functions of k-sample analogues of the Kolmogorov-Smirnov statistics have been found under certain conditions and a k-sample group testing procedure has been defined. This procedure has also been shown to be optimal in the sense that it requires a minimum expected number of k-sample group tests for finding a single defective from a binomial population.</p> <p> Our methods are mainly combinatorial: matrix enumeration, tree counting and construction algorithms are explored as a foundation of our study.</p>