I'm wondering whether it's possible to do a Kruskal-Wallis test on difference scores, since I can't seem to find an example of this online. I think it would make sense conceptually, but I would like to confirm if it makes sense statistically?
I'd like to know whether groups differ on the dependent variable across time. I searched for a nonparametric equivalent for a mixed-measures ANOVA, but did not seem to find something suitable.
Info about the dataset:
-small sample (9 participants)
-residuals not normally distributed
-1 between subjects factor with 3 levels (interventions)
-1 within subjects factor with 2 levels (time; pre- and post-measurement)
-dependent variable=continuous (bin weight)
Question also posted at: https://stats.stackexchange.com/questions/554517/kruskal-wallis-on-difference-scores
The other issue is how you use the pre-scores, whether creating difference scores (post - pre) or post - B*pre where the B is found usually by least squares. See the discussions of Lord's paradox (e.g., https://www.degruyter.com/document/doi/10.1515/edu-2020-0107/html)
As far as whether to use K-W or more powerful rank based tests like van der Waerden's tests (e.g., vanWaerdenTest in PMCMRplus in R), it depends if you want to be able to detect effects more efficiently or not.
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