I have run two psychological experiments. The dependent variable is a rating provided by the participant, that is, an integer number from 0 to 100.

The first experiment is a mixed 2x2 design, with one between-subject factor (treatment) and one within-subject factor (question). Each of these factors has two levels. That is, participants are asked two questions in the experiment (Q1 and Q2), while a factor varies systematically between the two groups (Treatment1 and Treatment2).

The second experiment is identical, except for that the design becomes completely within-subjects. That is, it is a repeated measures 2x2 design; participants are asked four questions that encode the two manipulations in a factorial form: Q1Treatment1, Q1Treatment2, Q2Treatment1, and Q2Treatment2.

I am interested in the potential interactions between the two factors (question and treatment).

Normally, I would conduct repeated measures ANOVAs for these experiments. However, the problem is that my data deviate strikingly from normality (in fact, so do the residuals). Therefore, I am looking for nonparametric equivalents to ANOVA for these two designs.