# Mixed design + permutation test

Suresh Muthukumaraswamy sdmuthu at CARDIFF.AC.UK
Thu Mar 20 11:38:13 CET 2008

```Hi Margriet,
If your data is in analyse format or you can get in analyse/nifti format then FSL's randomise
function can do all this for you....if you set your design matrix up properly
- Suresh

Suresh Muthukumaraswamy, PhD
CUBRIC
Cardiff University
Park Place
Cardiff, CF10 3AT
United Kingdom
email: sdmuthu at cardiff.ac.uk
Phone: +44 (0)29 2087 0353

>>> Guillaume Rousselet <g.rousselet at PSY.GLA.AC.UK> 19/03/2008 17:38:47 >>>
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.
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.

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
>  and http://www.ru.nl/fcdonders/fieldtrip.

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

Lecturer
Department of Psychology
University of Glasgow
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
************************************************************************************

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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
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----------------------------------
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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