Well, "reasonably" sure, although happy for someone else to chime in to
the contrary. Many different contrasts can be technically valid (i.e.,
"estimable"). In the example in question, the contrast I proposed would
test for an expected difference between the mean of condition A and B of
zero, whereas in your original contrast the expected value of the
contrast would not be zero under the null hypothesis of no difference
between A and B.
In effect, I believe that by using a factor of 6/5 on the 5 A
conditions, one achieves the desired "upweighting" of the variance
associated with the condition A estimate (relative to the condition B
estimate).
cheers,
MH
On Tue, 20110201 at 13:56 +0000, Cyril Pernet wrote:
> Hi Michael
>
> r u sure? ok beta = pinv(X)*Y so we don't really care about the bias (I
> was referring to nb of stimuli and variance estimation)
>
> for the contrast with 5A and 6B using 1/5 1/6 you average 5 sessions vs
> 6 which of course works as well but you may want to somehow put this
> unbalance in your contrast? I guess it's a matter of choice  note that
> C is unchanged by the post multiplication by inv(X'X')X'X using my
> contrast so it is still valid too .. contrast don't have to sum up to 0
> (oh yeh my full contrast wasn't right since I copied/pasted 6 times ..
> but I'm sure you got the gesture).
>
> I actually never had this problem  was offering a possible solution but
> yours seems good too  anybody out there checked this up before?
>
> Cyril
>
>
> > Hi Cyril,
> > Even if you don't have equal numbers, the estimated betas are themselves
> > still unbiased. Thus, if you are going to compare two conditions, it
> > seems to me that you still want the contrast to sum to 0. In the example
> > you gave, if you wanted to compare the mean level of A to the mean level
> > of B, with no estimate of A available from session 3, I think that you
> > would want the following contrast:
> > 1/5 1/6 0 1/5 1/6 0 0 1/6 0 1/5 1/6 0 1/5 1/6 0 1/5 1/6 0
> > or multiplying by 6:
> > 6/5 1 0 6/5 1 0 0 1 0 6/5 1 0 6/5 1 0 6/5 1 0
> > (note the 0 in the "A" position of the 3rd session).
> >
> > cheers,
> > MH
> >
> >> Reem
> >>
> >> It doesn't really matter that in each session you don't have the same
> >> number of stimuli per condition as long as across your 6 sessions you
> >> end up with equal numbers (will work as well if not but it's not as good
> >> because variance estimation can be biased). As for the different number
> >> of conditions you can weight your contrast accordingly. Simply create 6
> >> sessions in SPM and your 2 or 3 conditions in each sessions. Let say
> >> your design runs like this:
> >>
> >> Session 1 A B C
> >> Session 2 A B
> >> Session 3 B C
> >> Session 4 A B C
> >> Session 5 A B C
> >> Session 6 A B
> >> = 5*A 6*B 4*C
> >> = 30/6*A 36/6*B 26/6*C (I choose to have 6 as denominator because you
> >> have 6 sessions)
> >>
> >> Let say you want to test A  B then use a contrast [30/36 1 0 30/36
> >> 1 0 30/36 1 0 30/36 1 0 30/36 1 0 30/36 1 0]
> >> How do I end up with 30/36 and 1 > 1/6 * 30/6 = 30/36 and 1/6 * 36/6
> >> = 1 (I use 1/6 for each session since you have 6 sessions)
> >> The sum doesn't end up to 1 but the contrast should still be valid ..
> >> (at least using a simple design on my machine with unbalanced design and
> >> manual checking the contrast is valid  check in SPM I think it is ok)
> >>
> >> Good luck
> >> Cyril
> >>
> >>
> >>
> >>> Dear SPMers
> >>>
> >>> I am trying run first level analysis on fMRI data in SPM8.
> >>>
> >>> The experiment design involves 6 runs/sessions, each run/session
> >>> consists of 8 stimuli (48 stimuli in total).
> >>>
> >>> There are 3 experimental conditions spread out equally across stimuli
> >>> i.e. There are 16 stimuli of each condition in total.
> >>>
> >>> Because the stimuli were presented at random and are eventrelated, I am
> >>> now running into a problem because in some of the runs of 8 stimuli,
> >>> there happens to be only 2 of the conditions presented and not 3. In
> >>> these cases, I'm not sure what to input in the 'onsets' tab of first
> >>> level model specification for the 3rd condition.
> >>>
> >>> Is there a way around this problem. I'd be very appreciative of some
> >>> help.
> >>>
> >>> Kind regards
> >>> Reem
> >>>
> >>
> >> 
> >> The University of Edinburgh is a charitable body, registered in
> >> Scotland, with registration number SC005336.
> >>
> >
> >
>
>
