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I have a repeated-measures anova (Two-way), and I want to check for normality; my plots show this: 

lmerabsolute <- aov(Proportionofundershoots~ Target*Experiment + (ID/(Target*Experiment)), data=overallundershootproportion)

enter image description here

However, my shapiro test shows this:

shapiro.test(resid(lmerabsolute))

    Shapiro-Wilk normality test

data:  resid(lmerabsolute)
W = 0.98896, p-value = 0.001789

What do I do? I would be so grateful for some advice!

When I arcsine transform the data, my new shapiro test result looks like this:

Shapiro-Wilk normality test

data:  resid(lmerabsolute)
W = 0.98975, p-value = 0.003128

Here is the arcsine transformed normality plot:

enter image description here

So definitely an improvement! I have not managed to get a more significant P-value than this!

kjetil b halvorsen
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Caledonian26
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  • Please say more about the details of your data and experimental design. If your outcome is a proportion, as the name `Proportionofundershoots` suggests, then a mixed-effects ANOVA such as you have done might not be the best analysis to pursue. Also, please say more about why you are doing normality testing; see [this page](https://stats.stackexchange.com/q/2492/28500) for an introduction to why such testing often can be unnecessary or even misleading. – EdM Mar 10 '20 at 21:10
  • Why would you use a *test* when the conditional response is obviously not continuous? The null is immediately false. What could the test tell you that you don't already know for sure? The QQ plot addresses a somewhat more useful question ("how far from normal" in some sense), though there are still issues with choosing analyses by looking at your data. – Glen_b Mar 11 '20 at 05:39

1 Answers1

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Based on your first graph, your problem is granularity; there is a limited number of values that happen often. It is impossible to (meaningfully) fix that using a transformation. So, the second graph suggests to me that you made an error when applying the arcsine transformation. Appart from the granularity, the original distribution does not look bad, so I would stick with that. Based on eyeballing your graph, the number of observations is large enough, such that a statistically "significant" result could easily be the result of a substantively insignificant deviation from the null hypothesis. So the tests are not that meaningful in your case.

Maarten Buis
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