On Sat, 4 Apr 2009 20:18:17 +0100, Laura Menenti
<[log in to unmask]> wrote:
>Dear Stephen,
After a first read of what you wrote, I think you're absolutely correct in what
you state below. In particular:
>However, when modeling between-subject effects, as you state:
>
>"In terms of breaking down variance, the intersubject variance is split
between
>group differences and differences between subjects _within groups_."
>
>The first part is the variance we are trying to explain with a main effect of
>group, the second part is the error variance that gives an indication of how
>reliable the group effect is. By inserting the subject factor, this variance is
>removed from the residual - which leaves only within-subject variance.
The model itself, on paper, really is OK. (Well, if you accept the fact that it's
using a pooled error instead of a partitioned error, but that's another issue,
though one which I suspect has contributed to this confusion.) But SPM
doesn't know where to "pick out" the appropriate error to test against
(namely, within-group-between-subjects, which is still there but not in the
residual but rather implicitly in the subject terms); it "blindly" uses the residual
(e_ijk in my model below).
Thanks for pointing out my error (no pun intended :) !) and for making your
point vigorously and getting the rest of us back on the right track.
Best,
S
>Thanks for pointing us out again to the tutorial - and to the topic we
>ourselves started when we noted what Radek noted: suspiciously strong
>between-group effects. Since then we got convinced of what we stated in
>our previous email, that you should not model the subject factor when
making
>between-subject comparisons, i.e. modeling main effects of group. I remain
>convinced of that after your replies, though IANASE (I am not a statistician
>either) I will try to explain why.
>
>The trouble is not, as you state in a previous email:
>
>"You're absolutely right that specifying the effect of subject will remove the
>effect of group if you're not careful."
>
>The problem is, it removes variance from the error term that should not be
>removed. Your explanation shows this:
>
>>
>>The model is
>>
>> y_ijk = s_i + g_j + c_k + gc_jk + e_ijk
>>
>>where
>> s = subject term
>> g = group term (and j = j(i) depends on i)
>> c = condition term
>> gc = interaction of group and condition term
>> e = residual
>>
>>After estimating and fitting, we have (I'm omitting hats and carats, and not
>>taking into account prewhitening/nonsphericity correction)
>>
>> y_ijk = s_i + g_j + c_k + gc_jk
>>
>
>So, the subject means are modeled, are therefore not in the residual, which
is
>removed after estimating.
>
>Now, I fully agree the above model provides a better model for the y-term.
>However, the whole point of ANOVA's is testing any difference in means
>against the appropriate error term. When testing for within-subjects effects,
>the appropriate term is within-subject variance - it is then appropriate to
>remove the between-subject variance from the residual by modeling it.
>
>However, when modeling between-subject effects, as you state:
>
>"In terms of breaking down variance, the intersubject variance is split
between
>group differences and differences between subjects _within groups_."
>
>The first part is the variance we are trying to explain with a main effect of
>group, the second part is the error variance that gives an indication of how
>reliable the group effect is. By inserting the subject factor, this variance is
>removed from the residual - which leaves only within-subject variance. Jan
>made the same claim in his reply to us last summer:
>
>"It is these subject constants that absorb much of the inter-subject
>variability present in most imaging data, which in turns leads to more
>sensitivity for the experimental effects (including group differences)."
>
>In conclusion, though no doubt including the subject means in the model
>provides a better fit (and therefore stronger group effects), I think this is
not
>appropriate _when looking at between-subject effects_.
>
>Laura
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