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# Classical Frequentist RM ANOVA - implemented method

From reading texts on longitudinal data analysis (chapter 2 of Hedeker & Gibbons, 2006 https://doi.org/10.1002/0470036486 or chapter 3 of Fitzmaurice, Laird & Ware, 2011 https://doi.org/10.1002/9781119513469), I understand there are basically two broad approaches to (classical) RM ANOVA: the univariate approach and the multivariate (MANOVA) approach. Each has different properties and potential pitfalls. It's not clear to me which approach is implemented in JASP RM ANOVA.

According to this information, the MANOVA approach constructs derived variables from the repeated measures (of a single outcome variable) and treats these as multiple dependent variables, applying the MANOVA procedure. This strictly precludes unbalanced datasets, with missing data requiring respondent deletion. Statistical power is also reduced (compared with the univariate RM ANOVA). However, the within-subjects correlation structure allowed in this approach is more general than the univariate version.

The univariate RM ANOVA is restricted to a compound symmetry covariance structure, but can be designed to accommodate some missing data. It is more prone to issues with sphericity, but (when sphericity holds) has greater statistical power than the MANOVA approach.

Which of these approaches forms the implementation adopted in JASP (>=0.18)?

• I'm figuring from this discussion https://github.com/jasp-stats/jasp-issues/issues/1660 that it is the univariate approach that is currently implemented.

• I'll ask to make sure

EJ

• My recollection from doing RM Measures ANOVA in SPSS is that SPSS always produced univariate output along with multivariate output, and the results for the univariate approach were always identical to the results for the multivariate approach.

R

• Also, in JASP as well as any other standard stats package I can think of, the RM ANOVA algorithm does not accommodate missing data. For example, if you have . . .

subject#1 trial #1 = 39

subject#1 trial #2 = 33

subject#1 trial #3 = 47

subject#2 trial #1 = 52

subject#2 trial #2 = missing

subject#2 trial #3 = 76

subject#3 trial #1 = 23

subject#3 trial #2 = 80

subject#3 trial #3 = 25

then the RM ANOVA automatically deletes from the analysis all of subject #2's data.

R