Univariate repeated measures are based on somewhat different assumptions from multivariate tests. The latter assume multivariate normality and equal variance covariance matrices across groups. The former does not assume multivariate normality, just normality of the residuals, but do assume, in addition to equal variance covariance matrices, that the pooled variance covariance matrix is spherical. Another way of saying this is that all pair wise differences between the repeated observations have the same variance. Interestingly enough, the univariate repeated measures is typically more liberal than the multivariate tests, especially when the sphericity assumption is not met. The measure of this assumption is epsilon and there should be a test of epsilon less than zero. The smaller it is, the more the assumption is violated. There are adjustments to the degrees of freedom to reduce this effect but they do depend on how you estimate epsilon. The Huynh-Feldt correction is more liberal than the Geisser-Greenhouse estimate.
Dr. Paul R. Swank,
Children's Learning Institute
Professor, Department of Pediatrics, Medical School
Adjunct Professor, School of Public Health
University of Texas Health Science Center-Houston
From: SPSSX(r) Discussion [mailto:[hidden email]] On Behalf Of Zdaniuk, Bozena
Sent: Wednesday, November 30, 2011 10:28 PM
To: [hidden email]
Subject: FW: multi vs univariate tests in GLM RM anova
hello, i received a couple answers to my post which made me realize i may not have explained my issue well. I understand the difference between the multivariate and univariate tests in the MANOVA (multiple dependent variables) but I am not sure i understand it in the RM Anova (the same DV measured multiple times). In MANOVA, the multivariate tests tell us if there are effects across all DVs. Then the univariate tests show us the effects separately for each DV. But in RM Anova, the univariate tests are not showing us effects separately for each measure. We still have exactly the same set of effects that include the within-subject factor as we have in the multivariate tests. So, how are they different?
bozena
On Wed, Nov 30, 2011 at 9:03 PM, Zdaniuk, Bozena <[hidden email]> wrote:
Hello, i am running one within, two between subject RM ANOVA using GLM. The multivariate tests show all within-subject effects as significant but the univariate tests show two of those effects as non-significant. My intuition is to use the univariate tests but I don't know exactly why (and whether it is what I should do). Why would there be such a difference between the two types of tests? My N is very large (70, 000)
thanks in advance for help.
bozena zdaniuk
From: Carlos Mora [[hidden email]]
Sent: Wednesday, November 30, 2011 6:36 PM
To: Zdaniuk, Bozena
Subject: Re: multi vs univariate tests in GLM RM anova
The null hypothesis of the multivariate test is that all means are equal. If two of those are not equal, the test yields significant results at he chosen level of confidence. One way of peeling down the onion of pairwise difference is through contrasts. If you are going to use univariate tests, then you should extract random samples from your large data set and run the test on a fresh subsample.
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