Nonparametric equivalent to Mixed Anova?

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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.

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关键词：Parametric equivalent nonpara Metric Mixed equivalent provided question between factors

       
These aren't exactly nonparametric, but there are nonlinear mixed effect models that may suit your problem.

You may be able to come up with permutation procedures that encode your null hypotheses, in which case you can use a permutation test. In general, however, testing interactions via nonparametrics is difficult, because it intrinsically involves a deviation from additivity, which seems (??) impossible to reconcile with the kind of arbitrary rescalability that goes with nonparametric procedures. In your position I would be inclined to see if there's some parametric model that works. What are your responses? Likert? Binary?

Ben Bolker