  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.
