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I have performed certain statistical tests (ANOVA, DMRT, t-test, etc.) assuming my data is normal as well as with homogeneous variance. Now my paper is almost accepted in a reputed journal, reviewer asked me,"Is your data normal and with homogeneous variance". On performing Shapiro-Wilk test I came to know that a part of my data (one out of four treatments, each treatment has three replicates) is not normal. Similarly, a part of my data does not have equal variance. What should be my reply to the reviewer? Do I have to analyse my data again?

P.S. I am not a statistician.

Nick Cox
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kgpnerd
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    What's the sample size? I think that test is sensitive to sample size. Also, what does the skew (and kurtosis) look like? Did you look at histograms, q-q plots, etc.? It doesn't sound to me like your whole analysis has been invalidated by the one significant test among 4 treatments... – Patrick Coulombe Mar 04 '15 at 05:16
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    What did you test when you used Shapiro-Wilk? Did you test the residuals? What about other tests of normality? ANOVA is robust against minor departures from normality. – StatsStudent Mar 04 '15 at 05:38
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    How many observations did you have in the subgroup that you rejected normality for? – Glen_b Mar 04 '15 at 08:00
  • If the reviewer is asking the question, the implication is that you are not showing the data directly and perhaps over-focusing on significance tests, which is the tone of your question too. Showing normal probability plots as well as looking at Shapiro-Wilk tests is a way to try to satisfy everyone. You might even get ideas to improve your analyses. – Nick Cox Mar 04 '15 at 10:12
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    My answer to [this question](http://stats.stackexchange.com/questions/121852/a-principled-method-for-choosing-between-t-test-or-non-parametric-e-g-wilcoxon) gives a reference that clearly comes out against performing formal tests of assumptions (including of normality) when choosing a test. It gives links to posts with several references that make the same point about equality of variance (homogeneity of variance). There's some explanation in respect of homogeneity tests [here](http://stats.stackexchange.com/questions/100934/does-testing-for-assumptions-affect-type-i-error/100941#100941). – Glen_b Mar 04 '15 at 11:18
  • There are many more posts on site relating to tests of assumptions that will be relevant. – Glen_b Mar 04 '15 at 11:18

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