Hi everyone,

I have a three-group experiment design with two data collection times (baseline and retention). Some data violate the assumptions of normality and homogeneity of variance. But for the data that meets assumptions, I am using repeated measures ANOVA to show three points:

First, all subjects are coming from the same population (using the normality test of Shapiro-Wilk [also skewness value] and homogeneity of variance of Levene's test). Second, the impact of treatment (between-subjects), and third, if there is a significant difference between baseline and retention sessions where the significance lies (within-subjects).

Besides normality and homogeneity of variance tests, I am not conducting any other tests (like unpaired t-tests) for the first point. I am conducting ANOVA for the second and third points. I believe this is correct but I would like to confirm this?

My main question here is; what are non-parametric tests that I need to conduct to show the same three points for the parametric tests?

Here is what I am planning and would appreciate any feedback or any suggestion on what to use.

I am planning to run a set of pairwise Mann-Whitney U tests to show that all three groups are coming from the same population. Use Friedman's test to show the impact of treatment. Then run another set of pairwise Mann-Whitney U tests to show where the differences are. Is this the right approach?

Thank you and appreciate your help!

- Hawkar