[FieldTrip] Two-way permutation test

[Fritsche, M. (Matthias)]

Dear Fieldtrip mailing list,

my name is Matthias Fritsche and I'm a research intern in Floris de Lange's 'Prediction & Attention' group at the Donders Center for Cognitive Neuroimaging. I'm currently working on my Master's project and have got a question I hope you might be able to help me with.

I'm currently at the data analysis stage of a behavioral experiment and wondered whether there is a possibility to conduct a two-way permutation test (ANOVA-style, but without actually using ANOVAs/F-values).

My experiment has two independent variables, let’s call them A and B, and one dependent variable. Every participant was tested in all of the four conditions, A1B1, A2B1, A1B2 and A2B2. The dependent variable is a parameter of a model that is fit to the data. However, due to unstable fitting at the subject level, I can only obtain this parameter from the group-averaged data.

When only interested in effects between two specific conditions, e.g. A1B1 vs A2B1, the test is straightforward. In order to create the null distribution, I randomly swap the condition labels, A1B1 and A2B1, for each participant and compute the resulting group test statistic (difference of the dependent variable between A1B1 and A2B1) for that permutation. One option would be to test the difference between every two conditions in this way.

However, I wondered whether there is also a way to use a permutation test similar to a 2-way ANOVA, i.e. testing the main effects of factor A and factor B, as well as the interaction effect. For that purpose, there seem to be permutation tests that use ANOVAs to generate permutation distributions of F-values. However, I cannot use ANOVAs since I only have the dependent variable for the whole group and not for individual participants. Do you know of any method to solve this?

Thanks for your help.

Best,
Matthias
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