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I have searched far and wide for a non-parametric test for the 2x2 between subjects MANOVA I would like to do. So far I have found non-parametric equivalents for factorial ANOVA with corresponding R packages (see here). Does anyone have any ideas on how to do the same analysis, but with multiple DVs?

iamnarra
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As far as I know there is no non-parametric equivalent to MANOVA (or even ANOVAs involving more than one factor). However, you can use MANOVA in combination with bootstrapping or permutation tests to get around violations of the assumption of normality/homoscedascity.

mzunhammer
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    There is something called PERMANOVA. – amoeba Feb 13 '17 at 12:22
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    Have a look [here](http://stats.stackexchange.com/questions/259432/tests-of-significance-for-vector-valued-distributions/260295#260295) – zlon Feb 13 '17 at 12:29
  • Thanks. The issue though is that one could argue that my data is ordinal (scores from a rubric), so it's not a matter of violation of assumptions. Would it be a fair rationale to say that I conducted a parametric MANOVA due to the lack of nonparametric alternatives? – iamnarra Feb 13 '17 at 12:39
  • It is not ok to stick with your "plain vanilly" MANOVA. Being ordinal, your data is likely to violate the distributional assumption of your inference. Permutation testing gets you around this problem by sampling the distribution under the null directly from your data-set. It's really easy to implement when you got your MANOVA already set up (just have a look at the example linked by zlon). – mzunhammer Feb 13 '17 at 12:50