Dear Linling Li,
> I understand there is strong correlation between group effect and frequency.
> But I still don't understand it clearly.
> I mean that what about the within-group one-sample t-tests with frequency as
> covariate? In this situation, we want to abstract common activation of all
> the subjects of one group, so we can include frequency in this model to
> exclude the variance which could be explained by the different frequencies
> within this group.But in between-group analysis like two-sample t-test, we
> want to get the group differences like group A > Group B or A < B. However,
> if we include a single frequency vector of two groups in this two-samplt
> t-test model, the variance that the frequency covariate can explain has
> large overlap with the real activation differences of these two group. So,
> this means that the group effect and frequency effect are highly correlated,
> and I cannot do two-sample t-test to exclude the frequency effect. Am I
> right?
Yes, exactly—at least, probably. ;-) The more correlated the group
and frequency regressors are, the less able you will be to tell them
apart, and thus the less well this test will work. Based on what you
said about your data (i.e. that you tried the two-sample t-test and
the results are not what you would want or expect), I suspect that you
cannot do a two-sample t-test with a covariate on your data, because
the correlation is too hight. (Or rather, not that you "can't" do it,
but that it is not going to be helpful in looking at your group
effect, which is what you are interested in.)
In the one-sample t-test for a single group, this isn't a problem, and
the frequency regressor may indeed explain some more variance, and
thus give you more significant results (as long as that isn't offset
by losing a degree of freedom).
In a group analysis, you could include two regressors: one (mean
centered) to explain frequency in group A, a second (mean centered) to
explain frequency in group B. This may reduce variance, and would not
get rid of your group effect (because you're coding in two
regressors). However, it would also NOT enable you to say that you
have a group effect after controlling for effects of frequency, since
you've just controlled for that within each group independently.
Hope this helps!
Jonathan
--
Dr. Jonathan Peelle
Department of Neurology
University of Pennsylvania
3 West Gates
3400 Spruce Street
Philadelphia, PA 19104
USA
http://jonathanpeelle.net/
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