Question about permutation testing of an interaction in a two by two design

Matthew Nelson nelsonmj at CALTECH.EDU
Thu Nov 19 16:10:07 CET 2009

After the terrific help I received following the last question, I thought I
would post an additional question I am currently pondering.

I’m also interested in comparing the coherence of a pair of signals in a 2x2
design. I am specifically interested in testing the interaction in this
design and would like to do so using the cluster-based permutation tests to
do so across time and frequency. I’m curious to receive feedback and input
about the proper way to go about this.

Performing the tests across sessions seems to me to be a bit easier to
conceive and to write code for. In this case the design would be a
within-sessions design, as all of the four trial types occur in each
session. My impression is that the proper test could then be to calculate
for each session the difference along one factor for each condition of the
other factor, and then performing a permutation test of that difference
among the conditions of the other factor with the test statistic merely
being the mean difference of eth differences. It struck me that a 4-way
permutation of the four trial types, but this would instead be more
appropriate if the test statistic I was interested in was an omnibus anova
test, not to test strictly the interaction which is my interest here.

I am less sure how to perform the test if one wanted to do it within a
single session where there may be different numbers of trials in each

I know this question relates more to permutation tests than to frequency
analysis. If someone could even just point me towards a good reference where
I can learn more about these more detailed aspects of permutation tests, I
would appreciate it. Thanks.

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