P-value correction in nilearn.mass_unvariate.permuted_ols

I want to conduct a mass univariate analysis comparing male and female sMRI. For that I want to use nilearn.mass_univariate.permuted_ols. I find the documentation concerning the p-value correction unclear. In the documentation of nilearn.mass_univariate.permuted_ols it says:

A max-type procedure is used to obtain family-wise corrected p-values.

I cannot find anything in the internet when I search for “max-type procedure”. Can someone explain what this “max-type procedure” ‘is’ and how exactly it is done?

It looks like the docstring contains a few references that should describe the method:

[1] Anderson, M. J. & Robinson, J. (2001). Permutation tests for linear models. Australian & New Zealand Journal of Statistics, 43(1), 75-88.

[2] Winkler, A. M. et al. (2014). Permutation inference for the general linear model. Neuroimage.

[3] Freedman, D. & Lane, D. (1983). A nonstochastic interpretation of reported significance levels. J. Bus. Econ. Stats., 1(4), 292-298

From what I understand of the method and the code, it involves running a bunch of permutations to build regressor-specific null distributions for coefficient t-statistics. In each permutation, it shuffles the IV matrix (both regressors of interest and confounds) across samples (e.g., participants), runs the GLM, and then returns the maximum coefficient t-statistic for each regressor (the max being across voxels, I believe) to build regressor-specific null distributions against which to compare the original coefficient t-statistics.

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