Hi! I am doing data analysis for a repeated measures design. However when looking into the assumptions for RM-ANOVA I come across two ways checking for this assumption.
1. Check normality for each condition across participants like you would do for a between-subject ANOVA.
2. Check normality for within-subjects difference scores between conditions (i.e. normality distribution of a difference variable -> condition A - condition B).
I cannot find a conclusive answer to which option is required, it seems to me option 2 since I am researching within-subject changes across conditions but I am unsure.
Thanks in advance!
One way to look at the assumptions of a repeated measures anova is that they're the same as for any general linear model (like anova), plus the assumption of sphericity.
So, you can assess the normality by examining the residuals from the analysis.
I had a difficult time finding a page on the internet on the assumptions of RM anova that wasn't misleading. Most just say, "the dependent variable is normally distributed" which is either wrong or misleading, depending on what they intend.
A more detailed discussion on normality in RM anova is here:
https://stats.stackexchange.com/questions/151689/repeated-measures-anova-what-is-the-normality-assumption
Great answer, Sal Mangiafico. 👍 I'll just add a Thom Baguley's nice explanation of sphericity.
https://psychologicalstatistics.blogspot.com/2006/05/what-is-all-this-stuff-about.html
Sal Mangiafico has answered clearly. I'll just add that the normality of residuals and normality of scores within conditions have the same distributions in simple designs because they differ only by a constant (the condition mean). Once you add in covariates or a random effect for participants (as in a within/repeated design) they can differ greatly (though often - but not always - pronounced skew or kurtosis is detectable in both).
Edit. Further context for my post. This means there are situations when normality of the outcome variable and normality of residuals are essentially the same thing (hence advice in many introductory texts). The issue with the advice is that it doesn't generalise. So checking normality of residuals is a better option and should be taught at introductory level also to minimise confusion. This is also exactly the sort of advice that AI LLMs will likely get confused or wrong for a while yet because they are drawing from a pool of text resources that are potentially inconsistent.
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