Non-parametric statistics

The branch of statistics known as nonparametric statistics, deals with non-parametric statistical models and non-parametric statistical tests. Other common names are non-parametric statistics, or distribution-free statistics. She is the parametric statistics against.

Models and Methods

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

Nonparametric statistical methods are mathematical procedures for testing statistical hypotheses. Unlike parametric statistical tests make no assumptions about the probability distribution of the variables under study and are therefore also applicable when the necessary in many statistical distribution statements have not been fulfilled. The results of parameter-free methods and tests are invariant with respect to transformations of the variables with arbitrary strictly monotone functions.

Common nonparametric methods are:

Parameters

  • Median
  • Quantiles
  • Quartiles
  • Rank correlation coefficient

Method

  • Kernel density estimator

Tests

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

Nonparametric tests may have greater statistical power than parametric tests when the assumptions underlying the parametric tests are based are not met.

Classification methods

  • Square classifier
  • Abstandsklassifikator
  • Bayes classifier
  • Nearest Neighbor Classification
  • Fuzzy classifier
  • Cluster method
  • Artificial neural network
  • Support Vector Machines
Binomialtest Cohen's kappa Kendall's W McNemar's test Wald–Wolfowitz runs test Naive Bayes classifier Statistical classification
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