KSvärden

KSvärden is a term used in statistics to refer to the values produced by the Kolmogorov–Smirnov (KS) test. The KS test is a nonparametric method for assessing whether a sample comes from a specified distribution (one-sample KS test) or whether two samples come from the same distribution (two-sample KS test). The central quantity in the KS test is the D-statistic, often called the KS-value. For a one-sample test, D = sup_x |F_n(x) - F(x)|, where F_n is the empirical distribution function of the sample and F is the hypothesized CDF. For a two-sample test, D = sup_x |F_n(x) - G_m(x)|, with F_n and G_m being the empirical CDFs of the two samples. The significance of the observed D is expressed as a p-value, computed via asymptotic results or exact methods in small samples.

In practice, KS-values are interpreted as a measure of the maximum discrepancy between distributions; smaller KS-values indicate closer agreement with the reference distribution or with the other sample. KS-values are widely used in goodness-of-fit testing and in comparing distributions across fields such as quality control, finance, and biology. They are valuable because they require relatively few assumptions about the distributions involved, and they provide a straightforward metric of agreement between distributions.

Limitations include sensitivity to sample size, reduced power for certain alternatives, and the potential effect of estimating distribution parameters from the data, which can alter the null distribution of D. Software packages routinely compute KS-values via built-in functions in statistical environments.

See also: Kolmogorov–Smirnov test, empirical distribution function.