SPSS MANOVA output question - Why 2 different sets of "Within-Subjects" Effects?
Jeff
Can someone please explain the difference between two multivariate
tests of "within subjects effects" produced by SPSS's GLM command?
Details below. Thanks for your time.
The experimental design has 2 independent groups of 100 subjects
each. Within each group, each subject is measured at each of 3 time
points on each of four noncommensurate DVs (total of 12 data values
per subject).
Here is the syntax for the GLM command producing the output in
question:
GLM
dv1time1 dv1time2 dv1time3 dv2time1 dv2time2 dv2time3
dv3time1 dv3time2 dv3time3 dv4time1 dv4time2 dv4time3 BY group
/WSFACTOR = Time 3 Polynomial
/MEASURE = DV1 DV2 DV3 DV4
/METHOD = SSTYPE(3)
/EMMEANS = TABLES(group)
/EMMEANS = TABLES(Time)
/EMMEANS = TABLES(group*Time)
/PRINT = DESCRIPTIVE HOMOGENEITY
/CRITERIA = ALPHA(.05)
/WSDESIGN = Time
/DESIGN = group .
The output produced by this command includes two separate tables of
"Multivariate" tests. Each table displays the results of multivariate
tests (eg Wilks' lambda) for the two Within-Subjects effects (i.e.,
Time and Time*group), but the two tables give different values. I am
wondering, what are these two different sets of Within-Subjects tests?
More specifically:
The first table appears early in the output, and it includes one
section for "Between Subjects" effects (i.e., intercept & group) and
another section for "Within Subjects" effects (i.e., Time and
Time*group).
The second table appears later in the output (after Mauchley's test)
under the major heading "Tests of Within-Subjects Effects". This table
includes only a section for "Within Subjects" effects (i.e., again,
Time and Time*group). SPSS marks the second table with the note "d.
Tests are based on averaged variables". The first table has no such
note, so I suspect this note is crucial. Unfortunately, I cannot
figure out what it means (another MANOVA on averaged DV1-DV4 values
does not produce the results shown in this table, so it doesn't mean
that).
As I mentioned earlier, the two tables give different values---both
for the test statistics and for their df's. For the Time factor, for
example, the first table gives Wilks' lambda = 0.129 with dfe=191,
whereas the second table gives Wilks' lambda=0.221 with dfe=788.
In sum, my question is, what is different about these two separate
multivariate tests of within-subjects effects? For example, what
exactly are the null hypotheses tested in each case? Why are the error
df's different? What would it mean if the first table's test of Time
was significant and the second table's was not, or vice versa?
My background in MANOVA is pretty limited, so it will help if the
explanation is as nontechnical as possible.
Thanks very much,
Jeff Miller
lsro...@gmail.com
The IBM website http://www-01.ibm.com/support/docview.wss?uid=swg21476707 on
"Doubly-multivariate repeated measures and tests based on averaged variables" says:
"The first table entitled Multivariate Tests carries the true doubly-multivariate test statistics. The averaged results appear in the table entitled Multivariate that is listed under the heading Tests of Within-Subjects Effects. Averaged results are like those you would have obtained had you set up a multivariate model with a data set that is configured for the univariate approach to repeated measures (e.g., a split-plot approach).
...
Example
...
The results of this analysis would replicate the averaged multivariate results from the original doubly multivariate run in the table entitled Multivariate Tests. Note that these tests (also known as Scheffe's multivariate mixed model tests) assume a type of multivariate sphericity for which SPSS does not currently offer a test. The fully or doubly multivariate tests do not require this assumption to be met. Note also that when there are only two levels of the within subjects factor, the two sets of tests are the same."
I'm not sure what to make of that. But since Mauchly's Test of Sphericity is significant, I think I cannot assume multivariate sphericity.
Should I then ignore the Multivariate "Tests based on averaged variables" table?