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Illustration of the Kolmogorov–Smirnov statistic. The red line is a model CDF, the blue line is an empirical CDF, and the black arrow is the KS statistic.. In statistics, the Kolmogorov–Smirnov test (also K–S test or KS test) is a nonparametric test of the equality of continuous (or discontinuous, see Section 2.2), one-dimensional probability distributions.
The Kolmogorov–Smirnov test uses the supremum of the absolute difference between the empirical and the estimated distribution functions (Parr & Schucany 1980, p. 616).
Kolmogorov–Smirnov test: this test only works if the mean and the variance of the normal distribution are assumed known under the null hypothesis, Lilliefors test: based on the Kolmogorov–Smirnov test, adjusted for when also estimating the mean and variance from the data, Shapiro–Wilk test, and; Pearson's chi-squared test.
Kolmogorov–Smirnov test; L. Lilliefors test; N. Normal probability plot; P. Pearson's chi-squared test; S. Shapiro–Francia test; Shapiro–Wilk test This ...
The sup-norm in this expression is called the Kolmogorov–Smirnov statistic for testing the goodness-of-fit between the empirical distribution ^ and the assumed true cumulative distribution function F. Other norm functions may be reasonably used here instead of the sup-norm.
This score is a Kolmogorov–Smirnov-like statistic. [1] [2] Estimate the statistical significance of the ES. This calculation is done by a phenotypic-based permutation test in order to produce a null distribution for the ES. The P value is determined by comparison to the null distribution. [1] [2]
Together with Andrey Kolmogorov, Smirnov developed the Kolmogorov–Smirnov test and participated in the creation of the Cramér–von Mises–Smirnov criterion. Smirnov made great efforts to popularize and widely disseminate methods of mathematical statistics in the natural sciences and engineering.
In the statistical analysis of observational data, propensity score matching (PSM) is a statistical matching technique that attempts to estimate the effect of a treatment, policy, or other intervention by accounting for the covariates that predict receiving the treatment.