MANOVA. Dig it!. Comparison to the Univariate. Analysis of Variance allows for the investigation of the effects of a categorical variable on a continuous IV We can also look at multiple IVs, their interaction, and control for the effects of exogenous factors (Ancova)
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Cole, Maxwell, Arvey 1994
Psy Program Silliness Pranksterism
1 8 60
1 7 57
1 13 65
1 15 63
1 12 60
2 15 62
2 16 66
2 11 61
2 12 63
2 16 68
3 17 52
3 20 59
3 23 59
3 19 58
3 21 62
You might for practice verify that multiplying this matrix by W will result in a matrix
of 1s on the diagonal and zeros off-diagonal
Canonical Correlation output
Test that remaining correlations are zero:
Wilk's Chi-SQ DF Sig.
1 .073 30.108 4.000 .000
2 .815 2.346 1.000 .126
The Roy-Bargman step down procedure is another method that can be used as a follow-up to MANOVA to assess DV importance or as alternative to it all together.
If one has a theoretical ordering of DV importance, then this may be the method of choiceAssessing DVs
Roy-Bargman step down procedure can be used as a follow-up to MANOVA to assess DV importance or as alternative to it all together.
The theoretically most important DV is analyzed as an individual univariate test (DV1).
The next DV (DV2) in terms of theoretical importance is then analyzed using DV1 as a covariate. This controls for the relationship between the two DVs.
DV3 (in terms of importance) is assessed with DV1 and DV2 as covariates, etc.
At each step you are asking: are there group differences on this DV controlling for the other DVs?
In a sense this is a like a stepwise DFA, but here we have a theoretical reason for variable entry rather than some completely empirically based criterion
Also, one will want to control type I error for the number of tests involved
The stepdown analysis is available in SPSS ‘Manova’ syntaxRoy-Bargman
If one has a theoretical (a priori) basis of how the group differences are to be compared planned contrasts or trend analysis can be conducted in the multivariate setting
E.g. Maybe you thought those clinical types were weirdos all along
Note that all the post-hocs and contrasts in the SPSS menu for MANOVA regard the univariate Anovas, not the Manova
Planned comparisons will require SPSS syntaxSpecific Comparisons and Trend Analysis
Cripes! Where is this going??