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

Eric Maris e.maris at DONDERS.RU.NL
Tue Nov 24 12:11:18 CET 2009

```Dear Stephan,

It is sometimes possible to reformulate an interaction effect null
hypothesis such that it becomes a main effect null hypothesis (however, for
a different dependent variable, obtained be calculating the difference
between conditions). Such a reformulation is possible for a two-factorial
your case, this is condition), and the other between subjects (in your case,
this is group). You do this by calculating subject-specific difference
scores, [condition1 - condition2], and using these as the dependent variable
in a between-groups comparison. This is possible by means of the standard
independent-samples T-test, but also by means of a permutation test
(involving permutation of the difference scores), which allows you to deal
with the multiple comparison problem.

For a factorial design that only involves between-subject independent
variables, such a reformulation is not possible (at least, I am not aware of
it).

Best,

Eric

> -----Oorspronkelijk bericht-----

> Van: FieldTrip discussion list [mailto:FIELDTRIP at NIC.SURFNET.NL] Namens

> Stephan Moratti

> Verzonden: dinsdag 24 november 2009 10:20

> Aan: FIELDTRIP at NIC.SURFNET.NL

> Onderwerp: Re: [FIELDTRIP] Question about permutation testing of an
interaction

> in a two by two design

>

> Hi all,

>

> Thanks for the interesing discussion about the interaction with respect to

> permutation. I have been also struggling with this question. As we want to

> test the interaction (and not the main effect condition), I am not sure if

> resampling condition would produce the distribution of our null
hypothesis.

> Regarding the interaction, we want to check if the mean values across

> conditions follow the same pattern in two groups (if we consider a group x

> condition interaction). If we make a line plot an interaction would be
indicated

> by a line crossing if each line represents a group (ideally). No
interaction

> would be represented by parallel lines for each group. So I wonder if by

> resampling the subject values between the groups keeping the condition

> structure intact, would create our null distribution for the interaction.
If we

> resample condition, we would destroy the condition structure.

>

> What do you think? I would be happy for any input.

>

> Best,

>

> Stephan

>

> ----------------------------------

> 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.