What is the role of the Kolmogorov-Smirnov test in statistics?

The Kolmogorov-Smirnov test is a non-parametric statistical test used primarily to assess the goodness-of-fit of a sample distribution to a specified reference probability distribution. This test compares the empirical distribution function of the sample data with the cumulative distribution function of the reference distribution. It quantifies the maximum difference between these two functions, helping to determine whether the sample data follows the expected distribution.

This is particularly valuable in various applications, such as assessing whether a dataset can be assumed to conform to a normal distribution before performing certain statistical analyses or modeling. The test provides a clear statistical framework for evaluating how well your sample aligns with theoretical expectations, making it a crucial tool in both hypothesis testing and exploratory data analysis.