Dear Donald McLaren,
thank you for your answer to the email below.
>The assumption is that the estimated covariance is correct and that any violation of sphericity is eliminated by using the variance-covariance matrix. If you still have non-sphericity, then you >have violated the assumption of repeated-measure ANOVAs.
Is there any way I could test whether the assumptions for using pooled variance hold? Or would I simply have to assume this in case I report the flexible factorial analysis?
Best
Vera
Vera Ludwig, M.Sc.
Forschungsbereich Mind and Brain
Klinik für Psychiatrie und Psychotherapie
Charité– Universitätsmedizin Berlin
Charitéplatz 1
D-10117 Berlin
Telefon.: +49 / 30 / 450 517235
http://mindandbrain.charite.de/
________________________________________
Von: MCLAREN, Donald [[log in to unmask]]
Gesendet: Sonntag, 1. April 2012 08:15
An: Ludwig, Vera
Cc: [log in to unmask]
Betreff: Re: [SPM] 2x2 within-subjects ANOVA: Flexible Factorial and hierarchical approach produce different results
See inline responses below.
Best Regards, Donald McLaren
=================
D.G. McLaren, Ph.D.
Postdoctoral Research Fellow, GRECC, Bedford VA
Research Fellow, Department of Neurology, Massachusetts General Hospital and
Harvard Medical School
Website: http://www.martinos.org/~mclaren
Office: (773) 406-2464
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On Fri, Mar 30, 2012 at 8:59 AM, Ludwig, Vera <[log in to unmask]<mailto:[log in to unmask]>> wrote:
Dear everyone,
I am analysing a 2x2 within-subjects design in SPM8. I used two different approaches which produce slightly different results and I wonder which one I should use.
APPROACH 1: I set up a flexible factorial with 3 factors: subject, within-subject factor A, within-subject factor B. In the design matrix I include the main effect of subject, and the interaction of A x B.
What I get is the design matrix attached. As I understand, this would be the correct design matrix for a 2x2 within-subject ANOVA?
For the subject factor, I use independence = yes und variance = equal.
For the two within-subject factors, I use independence: no, and variance = equal.
I entered four con-images per subject (i.e., a con-image for each condition against baseline from the first level). When I now test for my main effect of interest in the flexible factorial, I get FWE-corrected significance in the region we predicted.
I presume your main effect is either 1 1 -1 -1 or 1 -1 1 -1. In testing these two main effects, you are using the pooled variance across both factors. This is in contrast to the more traditional approach of using partitioned variance for each within-subject effect. If you want to get the partitioned error effects, you should use GLM Flex. This will be slightly weaker in significance.
APPROACH 2: I calculate the main effect of interest on the first level, and then use a one-sample t-test on the second level. I still get activation in the same region as for approach 1, but it is considerably less significant.
A main effect is an F-test and as such has nothing that could be brought to the second level. If you used a t-contrast of 1 1 -1 -1 or 1 -1 1 -1, then you would bring the con_ image to the second level.
Why do I get different results?
This is identical to the partitioned variance approach; approach 1 used pooled variance.
Does approach 2 have less statistical power than approach 1?
Yes.
Is it correct to use the first approach?
Potentially. The assumption is that the estimated covariance is correct and that any violation of sphericity is eliminated by using the variance-covariance matrix. If you still have non-sphericity, then you have violated the assumption of repeated-measure ANOVAs. The safer, and more conservative approach, would be to use partitioned variance. In some simulations that I have done, the difference seems to amount to about 2 subjects.
I would be very grateful for advice.
Best wishes
Vera
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