Dear Jack,
If you have a single column for each of your four conditions, then your
approach is essentially correct.
> Here we defined them with following contrasts for each subjects:
> A1 A2 B1 B2
> effect of task 1 1 -1 -1 (A>B)
> and -1 -1 1 1 (B>A)
> effect of stimuli 1 -1 1 -1 (1>2)
> and -1 1 -1 1 (2>1)
> then, do a second level analysis for each contrast.
>As in some published papers, people may use two different ways to analyze
>the main effect and interaction in the factorial design: one is the
>F-test, the other is T-test (we use t-contrast here). Could anyone help me
>to clarify the usage of these two methods? When and how?
T contrasts are best applied if conditions are modeled with a single
covariate (for example, if one convolves using only the canonical hrf in an
event-related design, or when one models a block design using a simple
boxcar function). F contrasts are best applied if each condition is modeled
by more than one covariate (i.e. using basis functions). The advantage of
T-contrasts is that one is able to specify the direction of signal change
in each condition. F contrasts are not able to do this; the resultant
F-maps show activity that is different between conditions, regardless of
direction. The advantage of F-contrasts is that one can use them in
conjunction with basis functions such as gamma or fourier basis sets,
which, unlike the canonical hrf, make minimal assumptions about the form of
evoked haemodynamic responses. Possibly one major disadvantage of using
F-contrasts is that second-level group analyses are not possible: con*
images are not generated and cannot be taken on to second level as far as I
know. Therefore, only fixed effects group analyses are possible using
F-contrasts.
> interaction 1 -1 -1 1
> or -1 1 1 -1 (these two are different, right?)
In the case of your interaction, the t-contrast 1 -1 -1 1 will show a t-map
different from -1 1 1 -1. In the case of an F contrast, the F-maps will be
identical. F contrasts are specified differently from T-contrasts. They may
be generated and visualised using the matlab code
c=[eye(n) eye(n*)-1 eye(n)*-1 eye(n)];
imagesc(c)
where n is the number of basis functions you have employed.
If you have modeled with 5 basis functions, for example, then the
F-contrast for 1 -1 -1 1 will take the form...
1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 0
0 1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0 0
0 0 1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0 0
0 0 0 1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 1 0 0 0 0 0
0 0 0 0 1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 1 0 0 0 0
Hope this is useful,
Narender Ramnani
Dr. Narender Ramnani
Centre for fMRI of the Brain,
Department of Clinical Neurology,
(University of Oxford),
John Radcliffe Hospital,
Headley Way,
Oxford OX3 9DU
United Kingdom
Tel. +44 (0)1865 222704
Fax. +44 (0)1865 222717
email: [log in to unmask]
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