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MANOVA Mechanics

MANOVA Mechanics. MANCOVA and Factorial MANOVA. Regular Anova. Ancova*. Mancova. In Mancova the linear combination of DVs is adjusted for one or more covariates.

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MANOVA Mechanics

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  1. MANOVA Mechanics MANCOVA and Factorial MANOVA

  2. Regular Anova Ancova*

  3. Mancova • In Mancova the linear combination of DVs is adjusted for one or more covariates. • The adjusted linear combinations of the DVs is the combination that would have been had all of the subjects scored the same on the covariate.

  4. Mancova • Compare to before • Now we kick it in to matrix gear yo • The general approach (recall how we square matrices and do matrix division) for constructing an adjustment matrix (S)

  5. Testing interactions • A factorial MANOVA may be used to determine whether or not two or more categorical independent variables (and their interactions) significantly affect optimally weighted linear combinations of two or more normally distributed dependent variables. • As in univariate factorial ANOVA, we will first take note of the interaction, as it will inform us as to qualify any main effects or not

  6. Recall Anova • When you have more than one IV the interaction looks something like this: • SSbg breaks down into main effects and interaction

  7. In Manova • Main effects are dealt with as we have in the one-way design • Consider two main effects A and B with two levels each and three DVs Y1 – Y3 • For A we have a column matrix (vector) of means on the DVs for each of the two levels of A Means for group 1 Means for group 2

  8. We then would have the same situation for our 2 levels of treatment B, as well as a vector of grand means • We find effects by calculating the SSCP matrices of interest e.g. A (k levels)

  9. In Manova • With Main effects A and B, the interaction breaks down into the following… • We have a vector of AkBm cell means • And error is still the deviations of an individual’s scores on the DVs about their cell means Such that Main effect A Main effect B

  10. Test Statistic – Wilk’s Lambda • As before, this can be seen as the percent of non-overlap between the effect and the DVs

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