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Test with ",{"type":42,"tag":55,"props":761,"children":762},{},[763],{"type":48,"value":506},{"type":48,"value":765},": if p \u003C 0.05, sphericity is violated and you must apply ",{"type":42,"tag":55,"props":767,"children":768},{},[769],{"type":48,"value":770},"Greenhouse-Geisser",{"type":48,"value":772}," (conservative, use when ε \u003C 0.75) or ",{"type":42,"tag":55,"props":774,"children":775},{},[776],{"type":48,"value":777},"Huynh-Feldt",{"type":48,"value":779}," (less conservative, use when ε ≥ 0.75) correction to the degrees of freedom; with only 2 conditions sphericity is automatically satisfied (there is only one pair of differences)",{"type":42,"tag":118,"props":781,"children":782},{},[783,788,790,795],{"type":42,"tag":55,"props":784,"children":785},{},[786],{"type":48,"value":787},"Normality of difference scores",{"type":48,"value":789}," — RM-ANOVA assumes the differences between conditions are normally distributed (not the raw scores); test with Shapiro-Wilk on each pairwise difference; with n ≥ 30 the test is robust to non-normality by the central limit theorem; for small n with clearly non-normal differences, use the ",{"type":42,"tag":55,"props":791,"children":792},{},[793],{"type":48,"value":794},"Friedman test",{"type":48,"value":796}," (non-parametric alternative)",{"type":42,"tag":118,"props":798,"children":799},{},[800,805],{"type":42,"tag":55,"props":801,"children":802},{},[803],{"type":48,"value":804},"No outliers in difference scores",{"type":48,"value":806}," — extreme outliers in the within-subject differences inflate the error term and reduce power; inspect with boxplots of difference scores and consider whether outliers represent data entry errors or genuine unusual participants",{"type":42,"tag":118,"props":808,"children":809},{},[810,815],{"type":42,"tag":55,"props":811,"children":812},{},[813],{"type":48,"value":814},"Independence of subjects",{"type":48,"value":816}," — observations from different participants must be independent; this assumption is about between-person independence, not within-person — RM-ANOVA explicitly models within-person correlation; violations occur if subjects are related (e.g., sibling pairs) and should be addressed with multilevel models",{"type":42,"tag":118,"props":818,"children":819},{},[820,825],{"type":42,"tag":55,"props":821,"children":822},{},[823],{"type":48,"value":824},"Complete data or appropriate handling of missing values",{"type":48,"value":826}," — RM-ANOVA requires complete data for each subject across all conditions by default (listwise deletion); with substantial missing data, use linear mixed models which can handle missing at random (MAR) missingness without listwise deletion",{"type":42,"tag":43,"props":828,"children":830},{"id":829},"related-tools",[831],{"type":48,"value":832},"Related Tools",{"type":42,"tag":51,"props":834,"children":835},{},[836,838,844,846,852,854,860,862,868],{"type":48,"value":837},"Use the ",{"type":42,"tag":169,"props":839,"children":841},{"href":840},"/tools/one-way-anova",[842],{"type":48,"value":843},"Online ANOVA calculator",{"type":48,"value":845}," when participants are different people in each condition (between-subjects design) — repeated measures ANOVA is for within-subject designs where the same participants appear in all conditions. Use the ",{"type":42,"tag":169,"props":847,"children":849},{"href":848},"/tools/two-way-anova",[850],{"type":48,"value":851},"Online two-way ANOVA calculator",{"type":48,"value":853}," for factorial between-subjects designs; for mixed designs (one within, one between factor) the repeated measures approach handles the within-subject component. Use the ",{"type":42,"tag":169,"props":855,"children":857},{"href":856},"/tools/t-test",[858],{"type":48,"value":859},"Online t-test calculator",{"type":48,"value":861}," (paired t-test) for the two-condition special case — a repeated measures ANOVA with exactly 2 conditions gives the same p-value as a paired t-test (F = t²). Use the ",{"type":42,"tag":169,"props":863,"children":865},{"href":864},"/tools/power-analysis",[866],{"type":48,"value":867},"Power Analysis Calculator",{"type":48,"value":869}," to determine sample size needed to detect a specified effect size (η²) with desired power — repeated measures designs require fewer participants than between-subjects designs for the same power.",{"type":42,"tag":43,"props":871,"children":873},{"id":872},"frequently-asked-questions",[874],{"type":48,"value":875},"Frequently Asked Questions",{"type":42,"tag":51,"props":877,"children":878},{},[879,884,886,891],{"type":42,"tag":55,"props":880,"children":881},{},[882],{"type":48,"value":883},"When should I use repeated measures ANOVA instead of regular (between-subjects) ANOVA?",{"type":48,"value":885},"\nUse repeated measures ANOVA whenever the ",{"type":42,"tag":55,"props":887,"children":888},{},[889],{"type":48,"value":890},"same participants",{"type":48,"value":892}," provide data in each condition — for example, measuring the same patients at baseline, 3 months, and 6 months; testing the same subjects under three different drug doses in a crossover trial; or comparing reaction times in three experimental conditions in a within-subjects psychology experiment. The key benefit is statistical power: by removing between-person variability from the error term, repeated measures ANOVA can detect smaller effects with fewer participants than between-subjects ANOVA. Use between-subjects ANOVA when different participants are in each group (separate treatment and control groups) — using repeated measures ANOVA on independent groups is incorrect.",{"type":42,"tag":51,"props":894,"children":895},{},[896,901,903,908,910,915,917,922],{"type":42,"tag":55,"props":897,"children":898},{},[899],{"type":48,"value":900},"What do I do if Mauchly's test is significant (sphericity is violated)?",{"type":48,"value":902},"\nApply a degrees-of-freedom correction rather than abandoning the test. The ",{"type":42,"tag":55,"props":904,"children":905},{},[906],{"type":48,"value":907},"Greenhouse-Geisser correction",{"type":48,"value":909}," multiplies both numerator and denominator df by ε (the sphericity estimate), producing a more conservative F-test. When ε \u003C 0.75, use Greenhouse-Geisser; when ε ≥ 0.75, use the less conservative ",{"type":42,"tag":55,"props":911,"children":912},{},[913],{"type":48,"value":914},"Huynh-Feldt correction",{"type":48,"value":916},". With only 2 df for the within-subject factor (3 conditions), the corrections have minimal impact. Alternatively, use ",{"type":42,"tag":55,"props":918,"children":919},{},[920],{"type":48,"value":921},"multivariate ANOVA (MANOVA)",{"type":48,"value":923}," on the repeated measures, which does not require sphericity — MANOVA is preferred when n is large relative to the number of conditions. Report both the uncorrected and corrected F-statistics, and always state which correction was applied.",{"type":42,"tag":51,"props":925,"children":926},{},[927,932,937,939,944],{"type":42,"tag":55,"props":928,"children":929},{},[930],{"type":48,"value":931},"What is the difference between eta-squared (η²) and partial eta-squared (ηₚ²)?",{"type":42,"tag":55,"props":933,"children":934},{},[935],{"type":48,"value":936},"Eta-squared (η²)",{"type":48,"value":938}," is the proportion of total variance explained by the factor: η² = SS_factor / SS_total. It includes between-subjects variance in the denominator, making it smaller (and arguably more honest). ",{"type":42,"tag":55,"props":940,"children":941},{},[942],{"type":48,"value":943},"Partial eta-squared (ηₚ²)",{"type":48,"value":945}," excludes between-subjects variance: ηₚ² = SS_factor / (SS_factor + SS_error), making it larger and more comparable to effect sizes from between-subjects ANOVA. Most software (SPSS, R's ez package) reports ηₚ² by default for repeated measures designs, which is why repeated measures effect sizes often look larger than between-subjects effect sizes for equivalent phenomena. Always specify which effect size you are reporting. For benchmarks: ηₚ² ≈ 0.01 small, 0.06 medium, 0.14 large (Cohen, 1988).",{"type":42,"tag":51,"props":947,"children":948},{},[949,954,956,961,963,968],{"type":42,"tag":55,"props":950,"children":951},{},[952],{"type":48,"value":953},"Can I use repeated measures ANOVA with missing data?",{"type":48,"value":955},"\nStandard RM-ANOVA uses listwise deletion — any participant missing data at any time point is excluded entirely, which reduces power and can introduce bias if data are not missing completely at random (MCAR). With substantial missing data (> 10–15%), consider ",{"type":42,"tag":55,"props":957,"children":958},{},[959],{"type":48,"value":960},"linear mixed models (LMM)",{"type":48,"value":962}," instead — LMM handles missing at random (MAR) data without case exclusion by using maximum likelihood estimation, and produces valid estimates as long as the missing data mechanism is not related to unobserved values. Ask the AI to ",{"type":42,"tag":153,"props":964,"children":965},{},[966],{"type":48,"value":967},"\"use a linear mixed model with random intercept for subject instead of repeated measures ANOVA to handle missing data\"",{"type":48,"value":969},".",{"title":7,"searchDepth":971,"depth":971,"links":972},2,[973,974,975,976,977,978,979,980],{"id":45,"depth":971,"text":49},{"id":109,"depth":971,"text":112},{"id":187,"depth":971,"text":190},{"id":406,"depth":971,"text":409},{"id":578,"depth":971,"text":581},{"id":742,"depth":971,"text":745},{"id":829,"depth":971,"text":832},{"id":872,"depth":971,"text":875},"markdown","content:tools:074.repeated-measures-anova.md","content","tools/074.repeated-measures-anova.md","tools/074.repeated-measures-anova","md",{"loc":4},1775502472528]