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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.
Scaling of data: One of the properties of the tests is the scale of the data, which can be interval-based, ordinal or nominal. [3] Nominal scale is also known as categorical. [6] Interval scale is also known as numerical. [6] When categorical data has only two possibilities, it is called binary or dichotomous. [1]
Kolmogorov–Smirnov test: tests whether a sample is drawn from a given distribution, or whether two samples are drawn from the same distribution. Kruskal–Wallis one-way analysis of variance by ranks: tests whether > 2 independent samples are drawn from the same distribution.
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.
In one-sample applications ... The Cramér–von Mises test is an alternative to the Kolmogorov–Smirnov test (1933). [4] Cramér–von Mises test (one sample)
Lilliefors test is a normality test based on the Kolmogorov–Smirnov test.It is used to test the null hypothesis that data come from a normally distributed population, when the null hypothesis does not specify which normal distribution; i.e., it does not specify the expected value and variance of the distribution. [1]
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The one-sample test statistic, , for Kuiper's test is defined as follows. Let F be the continuous cumulative distribution function which is to be the null hypothesis . Denote by F n the empirical distribution function for n independent and identically distributed (i.i.d.) observations X i , which is defined as