Nonparametric statistical testing of coherence differences

Abstract

Many important questions in neuroscience are about interactions between neurons or neuronal groups. These interactions are often quantified by coherence, which is a frequency-indexed measure that quantifies the extent to which two signals exhibit a consistent phase relation. In this paper, we consider the statistical testing of the difference between coherence values observed in two experimental conditions. We pay special attention to problems induced by (1) unequal sample sizes and (2) the fact that coherence is typically evaluated at a large number of frequency bins and between large numbers of pairs of neurons or neuronal groups (the multiple comparisons problem). We show that nonparametric statistical tests provide convincing and elegant solutions for both problems. We also show that these tests allow to incorporate biophysically motivated constraints in the test statistic, which may drastically increase the sensitivity of the test. Finally, we explain why the nonparametric test is formally correct. This means that we formulate a null hypothesis (identical probability distribution in the different experimental conditions) and show that the nonparametric test controls the false alarm rate under this null hypothesis. The proposed methodology is illustrated by analyses of data collected in a study on cortico-spinal coherence [Schoffelen JM, Oostenveld R, Fries P. Neuronal coherence as a mechanism of effective corticospinal interaction. Science 2005;308(5718):111-3].