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Oct 3, 2019 at 19:56 vote accept JoZ
Oct 1, 2019 at 11:47 comment added Frank Harrell The central limit theorem does not work well enough for that to hold. This is especially true for skewed distributions for which the standard deviation is not even a valid measure of dispersion.
Sep 30, 2019 at 20:39 comment added André.B You should not use any formal tests for normality; they are typically overly-sensitive, while ANOVAs are very robust to deviations from normality. Moreover, you can rely on the central limit theorem as far as inferences of 'significant' effects go. MANOVAs are similarly robust, so I would not worry about looking for non-parametric alternatives.
Sep 30, 2019 at 14:43 comment added JoZ If I understand the answer correctly, it seems the way we apply the BH procedure is not correct. Are their any non-parametric parallel to MANOVA that we can utilize and make the adjustment using BH method? Also, after selecting the significant groups, does that mean either we can do a ad hoc test (Dunn test for example) or we can follow what @FrankHarrell suggest, applying proportional odds ordinal logistic model to each individual hormones? Mank thanks for your answers.
Sep 30, 2019 at 14:32 comment added JoZ Thank you so much for your answer and also thanks @FrankHarrell for the useful add on. We did the normality test and rejected the normality assumption first. Therefore we only conducted the K-W test but only for each individual hormone. The R return each one hormone a p-value, and what our group did is to apply BH procedure directly to the p-value returned. Then we select the groups that are still significant after adjustment and do the ad hoc test (Dunn's test) to furthur investigate the inter-group differences.
Sep 30, 2019 at 11:19 comment added Frank Harrell The idea of 'rejecting' 'hypotheses' is coming under fire, for good reasons. Regardless of the result of a hypothesis test it is a better strategy to estimate differences (point + interval estimates; even better the whole Bayesian posterior distribution). For rank tests this can be done with the proportional odds ordinal logistic model, which generalizes the K-W test.
Sep 30, 2019 at 8:55 history edited BruceET CC BY-SA 4.0
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Sep 30, 2019 at 8:19 history answered BruceET CC BY-SA 4.0