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Home  >  Volume 26 (March 2014)

47. Empirical permutation paradigm for two-way repeated measures ANOVA by Justice IghodaroOdiase. Volume26, (March, 2014), pp 344 – 356.
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Exact test of significance can only be guaranteed by the use of the distribution of a test statistic resulting from an exhaustive enumeration of all the distinct permutations of the observations in an experiment, especially when threshold p-values are involved.  The permutation paradigm requires no distributional assumptions and works well with values that are normal, almost normal and non-normally distributed.  Under the truth of the null hypothesis, permutation test only requires exchangeability of observations either within pairs, between samples, or within blocks.  This paper examines empirically the permutation distribution of the observations in an experiment in the context of exchangeability within blocks as applicable to two-way repeated measures analysis of variance.  The methodology developed in this paper enumerates all the distinct permutations of the observations or ranks of observations in an experiment and is illustratively applied to the Friedman test statistic.  The Friedman test is used to detect differences in treatments across multiple test attempts and only requires exchangeability (or, if variances differ, compound symmetry) and the ability to rank the data.  The exact distribution of the Friedman test statistic for small samples is therefore generated empirically, leading to the production of exact critical values at different levels of significance.

Keywords:Permutation test, Friedman test, p-value, two-way ANOVA, exchangeability AMS Classification:62E15, 62G10