control variables / cfg.cvar

[Michael Wibral]

Dear Eric,

I have a question with respect to the use of cfg.cvar and permutation testing. In particular, I am thinking about a design where subjects have to perform a task that involves giving two responses, say left and right hand button presses. I want to test two conditions against each other within subjects. If I have counterbalanced response hand assignment over subjects, you suggested to use cfg.cvar:
"The theory of permutation tests also applies to statistical testing problems
that involve control variables (e.g., response hand). In this case, the
mechanics of the permutation test involves randomly permuting the data sets
(single trials or subject averages) within each of the levels of the control
variable (conditional permutation). To increase statistical sensitivity in
the presence of control variable, it also is good to use a special test
statistic that partials out the variance explained by the control variable.
This is implemented in Fieldtrip for a couple of statfuns, but not for all
of them. Conditional permutation is implemented via cfg.cvar."

So in my design I have two levels of the control variable: L1 are subjects with c1-R/c2-L pairing and L2 are subjects with c1-L/c2-R pairing (?). If I now permute only within the levels (which I would do anyway if I used a dependend samples test?) then still there are perumtations where response hands are sorted on the two sets to be compared, giving rise to large unwanted clusters in this particular permutation and other that are similar to it.  Sure, this will not result in false positives, but decrease the sensitivity of my experiment.

But maybe I misunderstand the meaning of  "permuting the data sets (single trials or subject averages) within each of the  levels of the control variable" . Does a permutation within the levels mean, I permute left hand responses only with left hand repsonses and right hand responses only with right hand responses? In this case I would have to give up my dependend samples testing (within subjcets) and use independent samples testing (across) subjects, because I can only exchange left hand responses in condition 1 and left hand responses in condition 2 between subjects, correct?

Thanks for your help on this,
Michael

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