Non-parametric statistics
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The branch of statistics known as non-parametric statistics is concerned with non-parametric statistical models and non-parametric statistical tests.
Nonparametric models differ from parametric models in that the model structure is not specified a priori, but is instead determined from data. The term nonparametric is not meant to imply that such models completely lack parameters; rather, the number and nature of the parameters is flexible and not fixed in advance. Nonparametric models are therefore also called distribution free.
Non-parametric (or distribution-free) inferential statistical methods are mathematical procedures for statistical hypothesis testing which, unlike parametric statistics, make no assumptions about the frequency distributions of the variables being assessed. The most widely used of these methods is probably the chi-square test. Other widely used non-parametric methods include:
- binomial test
- Anderson-Darling test
- Cochran's Q
- Cohen's kappa
- Fisher's exact test
- Friedman two-way analysis of variance by ranks
- Kendall's W
- Kolmogorov-Smirnov test
- Kruskal-Wallis one-way analysis of variance by ranks
- Kuiper's test
- Mann-Whitney U or Wilcoxon rank sum test
- McNemar test (a special case of the chi-squared test)
- median test
- Siegel-Tukey test
- Spearman's rank correlation coefficient
- Wald-Wolfowitz runs test
- Wilcoxon signed-rank test
Nonparametric tests may have more statistical power than a parametric test when the assumptions underlying the parametric test are not satisfied.