I have an experiment with three groups of subjects (i.e., three conditions) while each group was tested twice (see attachment; each dot represents data of a single subject; dark blue are the means and MSE). Using Lilliefors test I found that data in Group 2, day 2 is not normal. I tried to make a log-transform, but the data still failed to comply the normality assumption. For the analysis of each of two days separately, I am fine to use non-parametric statistics (Kruskal-Wallis test instead of one-way ANOVA and Mann–Whitney U test instead of two-samples t-test). The question is that I need to test the interaction between conditions and days, which is a mixed ANOVA in a parametric universe (within-subject factor is time of the measurement and between subject factor is a condition). What is the a non-parametric solution for that? If there is a way that still somehow can use parametric tests, I would be happy with this solution either.

Many thanks!

Vadim