False discovery rate (FDR) is commonly used for correction for multiple testing in neuroimaging studies. However, when using two-tailed tests, making directional inferences about the results can lead to vastly inflated error rate, even approaching 100% in some cases. This happens because FDR only provides weak control over the error rate, meaning that the proportion of error is guaranteed only globally over all tests, not within subsets, such as among those in only one or another direction. Here we consider and evaluate different strategies for FDR control with two-tailed tests, using both synthetic and real imaging data. Approaches that separate the tests by direction of the hypothesis test, or by the direction of the resulting test statistic, more properly control the directional error rate and preserve FDR benefits, albeit with a doubled risk of errors under complete absence of signal. Strategies that combine tests in both directions, or that use simple two-tailed p-values, can lead to invalid directional conclusions, even if these tests remain globally valid. To enable valid thresholding for directional inference, we suggest that imaging software should allow the possibility that the user sets asymmetrical thresholds for the two sides of the statistical map. While FDR continues to be a valid, powerful procedure for multiple testing correction, care is needed when making directional inferences for two-tailed tests, or more broadly, when making any localized inference.
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