Match tests for nonparametric analysis of variance problems - Worthington, P.L.B. (1982)
The thesis is presented in two parts, (a) "Nonparametric Analysis of Variance", and (b) "An Asymptotic Expansion of the Null Distributions of Kruskal and Wallis's and Friedman's Statistics". In the first part we present a number of new nonparametric tests designed for a variety of experimental situations. These tests are all based on a so-called "matching" principle. The range of situations covered by the tests are: (i) Two-way analysis of variance with a general alternative hypothesis (without interaction). (ii) Two-way analysis of variance with an ordered alternative hypothesis (without interaction). (iii) Interaction in two-way analysis of variance, both the univariate and. multivariate cases. (iv) Latin square designs. (v) Second-order interaction in three-way analysis of variance. (vi) Third-order interaction in four-way analysis of variance. The validity of the tests is supported by a series of simulation studies which were performed with a number of different distributions.