Components of Pearson's Phi-Squared Distance Measure for the k-Sample Problem
Abstract A general approach to the k-sample problem for continuous random variables, based on a generalization of Pearson's classical φ2 measure, is presented. Tests are developed by considering an analysis of variance type of orthogonal decomposition of a distance measure for a k-population goodness-to-fit hypothesis. Estimates of some of these components are shown to provide test statistics for the hypothesis that the k-populations have a common distribution. Several classical parametric and nonparametric tests are found to be quadratic functions of these component estimates. In addition, a new class of test statistic is derived that possesses aspects of both parametric and nonparametric methods.