Nonparametric Statistics

The nonparametric statistics , nonparametric statistics , or distribution-free statistics deals with non-parametric statistical models and non-parametric statistical tests . It contrasts with parametric statistics .

Models and methods

Parameter-free models differ from parametric models in that the model structure is not determined a priori , but is determined from the data. The term parameter-free does not mean that such models have no parameters at all. Rather, the type and number of parameters is flexible and not fixed in advance.

Parameter-free statistical methods are mathematical procedures for testing statistical hypotheses. In contrast to parametric statistical tests, they do not make any assumptions about the probability distribution of the examined variables and can therefore also be used if the distribution requirements necessary for many statistical statements are not met. The results of parameter-free methods and tests are invariant to transformations of the variables with any strictly monotonic functions .

Common parameter-free methods are:

Parameters

• Median
• Quantiles
• Rank correlation coefficient

Procedure

• Kernel density estimator

Testing

• Anderson Darling Test
• Binomial test
• Cochran's Q (after William Gemmell Cochran )
• Cohen's Kappa
• Chi-square test
• Cramér von Mises test
• Fisher's exact test
• Friedman two-sided analysis of variance in ranks
• Kendall's concordance coefficient
• Kolmogorow-Smirnow test and Lilliefors test
• Kruskal-Wallis test and Scheirer-Ray-Hare test in ranks
• Kuipers test (after Nicolaas Kuiper )
• Mann-Whitney U test or Wilcoxon rank sum test
• McNemar test (a special case of the chi-square test )
• Median test
• Quade test
• Siegel-Tukey Test (after Sidney Siegel and John Tukey )
• Sign test
• Wald-Wolfowitz run test or iteration test
• Wilcoxon signed rank test

Parameter-free tests can have a greater test strength than parametric tests if the assumptions on which the parametric tests are based are not met.

Classification procedure

Common classification methods are:

• Cuboid classifier
• Distance classifier
• Bayesian classifier
• Nearest neighbor classification
• Fuzzy classifier
• Cluster process
• Support vector machines

See also

• Hierarchy

literature

• Sheskin, David J. (2003)  Handbook of parametric and nonparametric statistical procedures . crc Press. ISBN 1-58488-440-1
• Sidney Siegel (1956): Nonparametric Statistics for the Behavioral Sciences . New York, Toronto, London: McGraw-Hill (German translation by the specialist bookshop for psychology, Frankfurt am Main 1976).