6 Kolmogorov-Smirnov (K-S) Test

The K-S test is non-parametric test of the equality of continuous, one dimensional probability distribution that can be used to compare a sample with reference probability distribution (one-sample K-S test), or to compare two samples with one another (two-sample K-S test).
The K-S statistic quantifies the distance between the empirical distribution function (edf) of the sample and the cdf of the reference distribution, or between the edfs of two samples.
The null distribution of the test statistic is calculated under the \(H_0\) that the sample is drawn from the reference distribution (in 1-sample case) or that both samples are drawn from the same distribution (in the two-sample case)
Null distribution of test statistic under \(H_0\) is true.
In each case distribution considered under \(H_0\) are continuous distributions, otherwise unrestricted.
The two sample K-S test is one of the most useful and general non parametric for comparing two samples as it is sensitive to difference in both scale and shape of edf of the two samples.
The K-S test can be modified to save as goodness-of-fit test. In the special case for testing for normality in distribution, samples are standardised and compared to the normal distribution.

Questions on this section

Stuck on something here? Ask below and it stays attached to this topic.