Abstract
This paper discusses a functional approach to the problem of comparison of multi-samples (two samples or c samples, where c ≥ 2). The data consists of c random samples whose probability distributions are to be tested for equality. A diversity of statistics to test equality of c samples are presented in a unified framework with the aim of helping the researcher choose the optimal procedures which provide greatest insight about how the samples differ in their distributions. Concepts discussed are: sample distribution functions; ranks; mid-distribution function; two-sample t test and nonparametric Wilcoxon test; multi-sample analysis of variance and Kruskal Wallis test; Anderson Darling and Cramer von Mises tests; components and linear rank statistics; comparison distribution and comparison density functions, especially for discrete distributions; components with orthogonal polynomial score functions; chi-square tests and their components.
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