The Kolmogorov-Smirnov test is a non-parametric test used to determine if two samples come from the same distribution or if a sample comes from a specified distribution. In the R statistical programming environment, this test is implemented as a function within the base stats package. For example, one might compare the distribution of reaction times from two different experimental conditions to ascertain if they differ significantly.
Its significance stems from its distribution-free nature, meaning it does not require assumptions about the underlying distribution of the data, such as normality. This characteristic makes it valuable when dealing with data that violates the assumptions of parametric tests. Furthermore, the test has a rich history, having been developed in the first half of the 20th century, and it continues to be a fundamental tool in statistical analysis across numerous disciplines. Its application ensures robustness in statistical inference, particularly when distributions are unknown or non-standard.