randomization vs. permutation
Robert Oostenveld
r.oostenveld at FCDONDERS.KUN.NL
Mon Aug 16 13:15:49 CEST 2004
Hi FieldTrippers,
As you all know, we are already heavily using randomization methods for
our statistics (e.g. in SOURCEANALYSIS or in RANDCLUSTERANALYSIS).
Likewise, jacknife and bootstrap estimates of variance are available in
SOURECANALYSIS and FREQANALYSIS (for coherence).
These methods (i.e. jacknife, bootstrap, randomization) can all be
shared under the common umbrella of resampling theory, and there is
another obvious resampling that sofar was not implemented yet:
PERMUTATION. Whereas in randomization you throw all trials over both
conditions together and then randomly re-assigned them to the two
conditions, in permutation the trials in condition A and B are
selectively swapped (at random) between conditions. Therefore the
number of trials should be the same. Permutation actually is a specific
instance of randomization.
The null-hypothesis that you are testing using either the randomization
or permutation is slightly different. Using randomization, you assume
that all trials in condition A and condition B come from the same
distribution. Using permutation, you only assume that the i-th trial of
condition A comes from the same distribution as the i-th trial of
condition B. Therefore permutation is a more natural choise for
baseline vs. active comparisons (comparing the pre- and post-stimulus
interval of every trial) and I also suspect that the permutation based
approach will result in more statistical power. Of course you can only
apply the permutation method if your data contains trials in A and B
that can be directly compared.
best regards,
Robert
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