Permutation methods are commonly used to test significance of regressors of interest in general linear models (GLMs) for functional (image) data sets, in particular for neuroimaging applications as they rely on mild assumptions. Permutation inference for GLMs typically consists of three parts: choosing a relevant test statistic, computing pointwise permutation tests and applying a multiple testing correction. We propose new multiple testing methods as an alternative to the commonly used maximum

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... value of test statistics across the image. The new methods improve power and robustness against inhomogeneity of the test statistic across its domain. The methods rely on sorting the permuted functional test statistics based on pointwise rank measures; still they can be implemented even for large brain data. The performance of the methods is demonstrated through a designed simulation experiment, and an example of brain imaging data. We developed the R package GET which can be used for computation of the proposed procedures.