At 10:19 AM -0500 3/4/01, jim clark on edstat-l wrote:
>By default in SPSS, the error term used to test the significance
>of each contrast is specific to the particular contrast. So with
>a two-group comparison, it amounts to a paired-difference t-test...
>Whether other packages adopt the same approach or default to
>other error terms, I do not know.
Thanks Jim. I should have made it clear why I asked this question.
It's all to do with precision of the estimate (or the p value
thereof). If the error term was based on all levels of the
repeated-measures factor, then it would obviously have more degrees
of freedom than the error term from just the t test for the two
levels in question. Now, if you have a large sample size, it makes
no difference to the precision of the estimate (or p value) of the
contrast of interest, but if you have a small sample size, it does
make a difference. The person I am helping has only 5 subjects, but
he has 4 levels. So the t value for the contrast of two levels would
have 4 degrees of freedom (paired t test, because no control group),
but if the error term was based on all four levels, there would be 12
degrees of freedom. The confidence limits with 4 degrees of freedom
are wider than those for 12 degrees of freedom by a factor 2.78/2.18,
of 1.27. That's a big difference. For p-value people, it would
probably be the difference between p=0.04 and p=0.20, for example.
So it looks like all the hoohaa about Greenhouse-Geiser corrections
for sphericity are just for the overall significance of the
repeated-measures factor. The approach is therefore based on the
old-fashioned and misguided "thou shalt not test specific contrasts
unless the overall term is statistically significant". Well, that's
disappointing, especially when you end up testing with an error term
that has fewer degrees of freedom than you have available.
Of course, if you're going to use all the levels to get your error
term, you have to be happy that the error is uniform across the
levels. Hence my question about getting residuals vs predicteds out
of a repeated-measures ANOVA. So far I have had no response to that
query.
Will
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