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Repeated measures data occur when more than one measurement is collected on the same unit (e.g. subject). Use this tag for RM-ANOVA together with [anova] tag.
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Should I control for random effects of participant in an individual differences design?
You're correct that the second model reduces the power to detect associations between the individual difference measure and the trial-level outcome by including a random intercept for each participant …
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vote
How to test a treatment had a positive effect on the experimental group?
Because it's a small sample, this question and answer(s) are relevant. You're correct that you don't want to conduct a paired samples t-test on only the experiment group, because a comparison to a con …