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I am trying to run a mixed anova with the following factors..

between subject factors: group (3 levels: groups 1,2 and 3) education (2 levels : low education/ high education)

within subject factors: task (2 levels)

so there are 12 conditions.

Shapiro Wilk test indicates that 4/12 conditions are not normally distributed (p=0.006, p<0.001, p=0.040, p=0.002).

I've been told that it might be okay to proceed with this anova seeing as its only 4/12 conditions which are not normally distributed, and of these, one of them is quite close to being normally distributed (p=0.04). Am I right to proceed?

If so - how do I justify/explain this in my write up? I'm finding it quite hard to know how to word, e.g. I am not too sure I can write "Although 4/12 conditions are not normally distributed, I decided to proceed with the anova regardless because my supervisor told me I could". haha

And then when I'm analysing the results of the ANOVA, should I write some sort of disclaimer that my results might be invalid? Also if this is not the case, and I shouldn't proceed, is there a better test that I can use?

Any help or tips would be much appreciated, I'm new at this :)

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In ANOVA, the residuals should be normally distributed, so you will run the Shapiro Wilk test just one time (and not for each condition you have). But you have a within subject (two levels) and i think you should measure the residual for each task and then use Shapiro Wilk test. So you will have 2 Shapiro Wilk tests for these two residuals.

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  • $\begingroup$ Sorry I don't understand your comment. What's a residual? I've already run the Shapiro wilk test, are you saying I should've done it differently $\endgroup$
    – reckrockaree
    Commented Jul 29, 2017 at 17:34
  • $\begingroup$ @reckrockaree For ANOVA, you dont run Shapiro Wilk test for each factor. If residuals are normally distributed, your data will be. In a classical ANOVA you have to calculate the unstandardized residuals and runs the Shapiro Wilk test. Because you have a within subject factor i think the test will be a little different (because residuals may be dependent with the within subject factor). Take a look on how to perform ANOVA´s assumptions for split plot or nested experiments. $\endgroup$
    – Fabio Janoni
    Commented Jul 31, 2017 at 10:48

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