Posted by
Swank, Paul R on
Apr 12, 2011; 3:00pm
URL: http://spssx-discussion.165.s1.nabble.com/Questions-about-ANOVAs-and-Sphericity-tp4297706p4298435.html
ANOVA with repeated measures has an additional assumption in addition to the typical ones of independence, normality, and homogeneity of variance. It is referred to as sphericity. It means that the variance-covariance matrix must assume a certain patter for the usual F tests to be appropriate. Another approach to repeated measures is to treat it as a multivariate model, typically with some type of transform on the dvs. That is the multivariate test. So one decides whether to use the univariate (ANOVA) result or the multivariate result. It should be pointed out however, that 1) there are adjustments that can be made for the univariate tests if sphericity is a problem and 2) although the multivariate test does not rely on a sphericity assumption, it does have an assumption of multivariate normality that the univariate test does not have.
Dr. Paul R. Swank,
Professor and Director of Research
Children's Learning Institute
University of Texas Health Science Center-Houston
-----Original Message-----
From: SPSSX(r) Discussion [mailto:
[hidden email]] On Behalf Of rohanp16
Sent: Tuesday, April 12, 2011 3:17 AM
To:
[hidden email]
Subject: Questions about ANOVAs and Sphericity
Hello everyone !! :)
I had a few questions about ANOVAs and sphericity. I am conducting a 2 way
ANOVA with one factor (A) having two levels and the other factor (B) having
21 levels.
Q1) In the 'Within Subjects effects' Table I see there is a main effect of
factor B. One should then go to 'planned comparisons' to see where the
effect lies right ? However SPSS throws out a 'multivariate tests' output
just below the 'planned comparisons' table. What does this table mean ?
Below the table it says
"Each F tests the multivariate effect of Factor B. These tests are based on
the linearly independent pairwise comparisons among the estimated marginal
means"
What does this table mean ? I'm 90% sure there is no need to look at this
table, but REALLY want to know what it means.
Q2) I have a significant interaction effect (A*B) and I used the following
syntax to see where the difference lied,
/EMMEANS=TABLES(A*B) COMPARE(B) ADJ(BONFERRONI)
/EMMEANS=TABLES(B*A) COMPARE(A) ADJ(BONFERRONI)
The output that SPSS throws out, I should first look at the 'Multivariate
tests' table and only if that is significant do I see which direction the
differences lie in the 'Planned comparisons' table right ?
Q3) While conducting the Mauchly's Test of Sphericity, I realize one
requires more than 2 levels of a variable for sphericity to be an issue. So
for factor A I get a value of 1 for Mauchly's W which means sphericity is
not an issue (and a . in the 'significance' column). However for my other
factor, I get a 0.000 and no significance value (i.e - once again there is .
in the significance column). Does that mean sphericity is an issue or is not
an issue ? If it was an issue, why didn't it just spit out some value <0.05
in the significance column?
Thanks a lot, take care :)
--
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