The two-sample Kolmogorov-Smirnov (K-S) test is used to compare two independent ‘samples’ (or ‘data sets’) to test the null hypothesis that the distributions from which the samples are drawn are identical. For example, the K-S test can be used to compare two sets of miniature synaptic event amplitudes to see if they are statistically different. The Student’s t-test (which assumes data are normally distributed) and the nonparametric Mann-Whitney (which does not) are sensitive only to differences in means or medians. The K-S test, however, is sensitive only to a wider range of differencees in the data sets (such as changes in the shape of distribution) as it makes no assumptions about the distribution of the data. This wider sensitivity comes at the cost of power — the K-S test is less likely to detect small differences in the mean that the Student’s t-test or Mann-Whitney test might otherwise have detected.
The K-S test should be used on data that are not normally distributed. If the data conform to a normal distribution, the Student’s t-test is more sensitive.