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6
  • 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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1  
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. – Russell S. Pierce Jul 19 '11 at 15:03
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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

2 Answers

up vote 7 down vote accepted

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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up vote 3 down vote

I prefer a repeated measures model. Not only is it easier to interpret the results, it is more flexible in that you can specify a covariance structure.

This reference may be of use as it works through an example: Mixed or MANOVA

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I suppose by "repeated measures model" you mean a mixed model (as in the link you provided). It is really important to be specific here: You do NOT seem to prefer repeated measures ANOVA (as in the question), you prefer mixed models for repeated measures. And as pointed out in the blog post, mixed models really are preferable in most cases. – wolf.rauch Jul 19 '11 at 17:05
The link to the reference has changed; it can now be found here. On a different note, I think it's fair to think of RM ANOVA as a special case of linear mixed models. – gung Jun 26 '12 at 16:54
Yes a repeated measures model is a mixed model. One can see the chapter in SAS for Mixed Models. – Glen Jul 6 '12 at 1:52

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