Mixed design + permutation test

[Guillaume Rousselet]

Hey Margriet,

given your design, and if you don't plan on doing >>all<< the pairwise  
comparisons
anyway, then you could do an ANOVA. One way to make your analysis  
robust to non-normality
is:

1) compute F for your data
2) center your data independently for each of your 6 conditions, i.e.  
if your measure of
central tendency is the mean then subtract the mean of one condition  
from each member of
that condition, so that the new mean is zero
3) you just created a new dataset in which the null hypothesis is  
true. Now you can
sample with replacement subjects (paired design) or trials (unpaired  
design), compute the
F, and store it.
4) repeat 3) x times, for instance 1000 times. You will obtain a data  
driven distribution
of F under the null hypothesis.
5) compare the one-tail, let say 95% confidence interval of the F  
under the null
hypothesis to the original F obtained for non-centered data. If the  
original F is larger
than the 95% F, then your effect is significant.

This bootstrap procedure + it's validation is described here:
BOOTSTRAP RESAMPLING APPROACHES FOR
REPEATED MEASURE DESIGNS: RELATIVE ROBUSTNESS
TO SPHERICITY AND NORMALITY VIOLATIONS
BERKOVITS et al. 2000
Educational and Psychological Measurement, Vol. 60 No. 6, December  
2000 877-892

More advanced coverage of robust analysis of variance can be found here:
Wilcox, R. R. (2005). Introduction to Robust Estimation and Hypothesis  
Testing (2nd Ed.
ed.): Academic Press.

hope this help,

GAR



On 19 Mar 2008, at 13:44, Margriet Groen wrote:

> Hi,
>
> please excuse my ignorance, but is it possible to use permutation  
> tests with a mixed (3 conditions x 2 groups) design?
>
> Thanks,
> Margriet
>
> -- 
> =================================
> Dr. Margriet A. Groen
> Post-doctoral researcher
> University of Hamburg
> Biological Psychology and Neuropsychology
> Von-Melle-Park 11
> 20146 Hamburg
> Germany
>
> Phone: +49-40-42838-5838
> Fax: +49-40-42838-6591
> Email: margriet.groen at uni-hamburg.de
> Website: http://bpn.uni-hamburg.de/groen_e.html
> =================================
>
> ----------------------------------
> The aim of this list is to facilitate the discussion between users  
> of the FieldTrip  toolbox, to share experiences and to discuss new  
> ideas for MEG and EEG analysis. See also http://listserv.surfnet.nl/archives/fieldtrip.html 
>  and http://www.ru.nl/fcdonders/fieldtrip.





************************************************************************************
Guillaume A. Rousselet, Ph.D.

Lecturer
Department of Psychology
University of Glasgow
58 Hillhead Street
Glasgow, UK
G12 8QB

http://web.mac.com/rousseg/iWeb/

Email: g.rousselet at psy.gla.ac.uk
Fax. +44 (0)141 330 4606
Tel. +44 (0)141 330 6652
Cell +44 (0)791 779 7833


“Computers in the future may weigh no more than 1.5 tons.”
	
	Popular Mechanics, 1949
************************************************************************************



----------------------------------
The aim of this list is to facilitate the discussion between users of the FieldTrip  toolbox, to share experiences and to discuss new ideas for MEG and EEG analysis. See also http://listserv.surfnet.nl/archives/fieldtrip.html and http://www.ru.nl/fcdonders/fieldtrip.
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