| Abstract: | A general approach to the k-sample problem for continuous random variables, based on a generalization of Pearson's classical [phi-squared] measure, is presented. Tests are developed by considering an ANOVA type orthogonal decomposition of a distance measure for a k-population goodness-of-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 components. Also, a new class of test statistics is derived that possesses aspects of both parametric and nonparametric methods. The power properties of the various statistics for detecting local shifts are explored using large sample and Monte Carlo methods. |
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