On Wed, 1 Apr 2009 11:31:50 +0200, Radek Mareček <[log in to unmask]>
wrote:
<snip>
>When the subject effect is included the inter-subject variability
>doesn't end up in residuals (or at least not all) which induce higher
>t-values. But isn't the inter-subject variability crucial for assesing
>of significance of tested effect?
Yes and no.
There are different types of inter-subject variability. The type that's
being "regressed out" when you include the effect of subject is the "main
effect of subject," if you will. Just the average response of subject, over all
conditions.
But there's other sources of variability between subjects which can be used to
test significance.
Consider "ANOVAs and SPM" (an unpublished monograph by Henson and
Penny). For simplicity of discussion, look at section 3 on p. 5, where they
consider a design with no group factor and only one within-subject factor
(i.e., one "condition"). The equation modeling the design is
y_nk = tau_k + pi_n + e_nk
Here, y is the data, tau is the effect of "treatment" (i.e., condition, the within-
subject effect), and pi is the effect of subject. e is the residual. (n and k are
appropriate indexes.)
Clearly, this model includes the effect of subject, yet there is still variation
that can be used to test the effect of condition: the term e_nk.
You can think of e_nk as a term modeling the interaction of subject and
treatment.
So, while the "main effect" of subject is regressed out, the interaction of
subject and treatment still remains and is used to compute significance of the
condition effect.
I found a relatively clear exposition on ANOVA to be _Statistical Methods for
Psychology_ (Howell); it was a reference listed in the Henson/Penny
monograph (the current, revised edition of which left out the reference list,
though). At least here in the US I was able to get an old edition used for very
little money; certainly the 3rd and 4th editions are useful on these topics.
Only warning is that like most of conventional statistics, the book assumes
you will usually use "partitioned errors" not "pooled errors" the way SPM does.
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