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I am testing the statistical significance of 60 strong correlated quantitative variables in 2 groups, with small sample size, non normality and presence of outliers. I have implemented a permutation test based in the t-test statistic for deal correctly the correlation structure of the variables; but I think this permutation test could be also based in the statistic of the nonparametric Wilcoxon test, due to the presence of the outliers. Is it correct?

Jesus Herranz Valera
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    The Wilcoxon test is a permutation test already. It computes the permutation distribution of (a monotonic function of) a t-test on the ranks. Your permutation test based off a t- is already nonparametric; perhaps your concern is to make it more robust to outliers rather than to make it nonparametric. What are the response values measuring? – Glen_b Sep 06 '13 at 23:00
  • The data are expression of peptides in proteins. They are normalized with similar techniques of genetic expression data, but the results are very inestable and generate outliers. – Jesus Herranz Valera Sep 09 '13 at 08:40
  • Are these values a measurement or a count or some other thing? – Glen_b Sep 09 '13 at 09:44
  • There are a measurement. The problema is your comment: "the Wilcoxon test is a permutation test", but I want to use as basic statistic is my permutation test because I want to treat the correlation structure between the variables. – Jesus Herranz Valera Sep 09 '13 at 14:46
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    (I am completely in favor of doing permutation tests with the most suitable statistic for your problem; that comment was simply clarifying that the Wilcoxon isn't distinct from permutation tests.) If you're looking for robustness to outliers, simply construct a permutation statistic that has the robustness properties you want, while retaining the other properties you need it to have. – Glen_b Sep 09 '13 at 23:07

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