I am currently analysing my quantitative data. My sample size is 157 students who sat for a survey in 2 phases after an intervention. The same students sat for the same survey on positive outcomes on peer feedback (this is just one of the 7 dependent variables). I did RM ANOVA and test on the normality. It shows that there is a non normal distribution and a few with no value at all not even p<.01. Someone suggested that I should do transformation and the result is still non normal distribution. Then I did the non parametric Friedman test but because it is only 2 phases, it automatically used the Wilcoxon test. I understand that the Wilcoxon test will not allow me to test my variables based on my independent variables which are gender and class. I am interested to find out whether under the dependent variable postive outcomes on peer feedback, whether female or male students change in terms of whether they find peer feedback helpful or which class is more favourable towards peer feedback. My question is should I go back to 2 Way RM ANOVA for this even though my test for normality is non normal? since Wilcoxon does not give me the option to use my independent variables. Are there any reference that can support my decision to go back to RM ANOVA?
(Just to summarize the comments so that this question isn't counted as officially 'unanswered'... )
The raw data, $y$, needn't be normally distributed. Primarily, the residuals need to be normally distributed (this is discussed in my answer here). However, even when discussing the residuals, with a big enough sample, they can deviate somewhat from true normality and the Central Limit Theorem will provide you with a little slack. In addition, repeated measures ANOVA typically assumes that the random effects are normally distributed, although I believe it is possible to use other distributions.