# Differences between MANOVA and Repeated Measures ANOVA?

• What is the difference between a repeated measures ANOVA over some factor (say experimental condition) and a MANOVA?
• In particular one website I stumbled across suggested that MANOVA does not make the same assumption of sphericity that repeated measures ANOVA does, is that true?
• If so, why would one not just always use MANOVA?
• I am trying to conduct a repeated measures ANOVA with multiple DVs, what is the appropriate approach?

Thank you.

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The multivariate approach to repeated measures does not treat each factor level as a separate DV. Instead, it treats all unique differences between factor levels as separate DVs and then tests the hypothesis that the theoretical centroid of these DVs is the 0-vector. If there are $p$ levels, there are p over 2 differences, and $p-1$ unique differences (involving $p-1$ different factor levels). –  caracal Jul 18 '11 at 20:43
I've edited the question to remove the offending phrase, but I'm not sure I understand your comment entirely, and it seems like it might be a relevant point to make clear as an answer to the first bullet point question. –  rpierce Jul 19 '11 at 15:03
Chapter 13 of Maxwell & Delaney (2004) "Designing Experiments and Analyzing Data" provides an in-depth treatment of exactly the answers you are looking for in your first two bullet points. –  caracal Jul 19 '11 at 17:13

Having several repeated-measures DVs one can apply a univariate approach (also called Repeated Measures sensu stricto or split-plot approach) or multivariate approach (or MANOVA). In univariate approach, RM levels are treated as deviations from one variable, their average level. In multivariate approach, RM levels are treated as covariates of each other. Univariate approach requires sphericity assumption while multivariate approach does not, and because of this it is becoming more popular indeed. However, it spends more df and thus needs larger sample size. Also, univariate approach retains its popularity because it generalizes to Mixed models. When sphericity assumption (and beyond expectation more general compound symmetry assumption too) holds results by both approaches are very similar, as far as I know.

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