# Unsure whether normality is mildy or severely violated, can I still use repeated measures ANOVA?

I am trying to run a repeated measures ANOVA in Stata on a dataset with 149 participants that each gave answers to 4 valuation questions (496 observations in total). I need to measure whether there is a difference in mean for the given valuations. I am only allowed to use repeated measures ANOVA or Friedman for this.

A lot of people have filled in 0 as their valuation and thus the data is right skewed. Sphericity is violated as well (Mauchly's test, p = 0.000). The histogram, Q-Q plot and Shapiro-Wilk test for this variable look as following:

Using the logarithmic transformation y = ln(1+y) I transformed the data to make it more normally distributed. Sphericity is not violated anymore after the transformation (Mauchly's test, p = 0.0629). The histogram, Q-Q plot and Shapiro-Wilk test for this new variable look as following:

As you can see in the histogram and Q-Q plot, the data follows the normal distribution better than before. But, as the p value of the Shapiro-Wilk test is still 0.000, the assumption of normality is still violated. However, I read that repeated measures ANOVA is robust in cases of mild violation of normality and thus can still be performed even if normality is mildly violated. But I am unsure whether my data mildly violates it or severely. Can I continue with the repeated measures ANOVA with the logarithmic transformed data or is the Friedman test a better idea in this case?

• You need to provide more details. For example, what do you mean that the 4 questions have to measured against one another? If you want to analyze data with repeated measures I suggest you read about generalized linear mixed models (GLMM), which are much more flexible, providing ways of modelling data with various distributions. Jul 19 at 13:54
• @UkiBuki sorry I probably used the wrong wording, so I edited it. I have 4 different questions that ask for valuation of a product and those answers need to be compared within the subject. I need to measure whether there is a difference in mean for the valuation of these products. I am only allowed to use repeated measures ANOVA or Friedman for this.
– Zzz
Jul 19 at 14:01
• What were the questions and what answers were possible? Jul 19 at 14:13
• @UkiBuki All four questions were open questions and would yield a continuous variable (although most participants have given a whole number so that's probably measured as count). The valuations that are given by the participants range from 0 to 500 dollars.
– Zzz
Jul 19 at 14:20
• If you must choose between the two, I would go for the Friedman test, because means are not meaningful for your data. However, you might consult someone more experienced in the analysis of panel data to get more alternatives. Jul 19 at 14:33