I think the title is representative enough. I have an experiment that is between two groups and within those two groups there is a within comparison that is randomized.

So i want to use mixed ANOVA, but my data is not normally distributed. However, i found this:

Assumption #5: Your dependent variableshould be approximately normally distributed for each combination of the groups of your two factors (i.e., your within-subjects factor and between-subjects factor). Whilst this sounds a little tricky, it is easily tested for using SPSS Statistics. Also, when we talk about the mixed only requiring approximately normal data, this is because it is quite "robust" to violations of normality, meaning that assumption can be a little violated and still provide valid results. You can test for normality using, for example, the Shapiro-Wilk test of normality (for 'actual data') or Q-Q Plots (for 'studentized residuals'), both of which are simple procedures in SPSS Statistics. In addition to showing you how to do this in our enhanced mixed ANOVA guide, we also explain what you can do if your data fails this assumption (i.e., if it fails it more than a little bit).

This is from a tutorial that i don't have access to. I was wondering if anyone knows:

  1. What does it mean that this assumption can be "a little violated"?
  2. What can i do since my data violates this assumption?

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