A critique of the use of the Kolmogorov-Smirnov (KS) statistic for the analysis of BOLD fMRI data

Abstract

The use of the Kolmogorov-Smirnov (KS) statistic for testing hypotheses regarding activation in blood oxygenation level-dependent functional MRI data is critiqued on both theoretical and empirical grounds. Theoretically, it is argued that the KS test is formally unable to support inferences of interest to most neuro-imaging studies and has reduced sensitivity compared with parametric alternatives. Empirically, false-positive rates yielded by the KS test in human data collected under the null hypothesis were significantly in excess of tabular values. These excessive false-positive rates could be explained by the presence of temporal autocorrelation. We also present evidence that the distribution of blood oxygenation level-dependent functional MRI data is only slightly nonnormal, questioning the initial impetus for the use of the KS test in this context. Finally, it is noted that parametric alternatives exist that do provide adequate control of the false-positive rate and can support inferences of interest.