library.nonpar Submodule

Module Summary

Interfaces for the NAG Mark 30.3 nonpar Chapter.

nonpar - Nonparametric Statistics

The functions in this module perform nonparametric statistical tests which are based on distribution-free methods of analysis. For convenience, the module contents are divided into five types of test: tests of location, tests of dispersion, tests of distribution, tests of association and correlation, and tests of randomness. There are also functions to fit linear regression models using the ranks of the observations.

The emphasis in this module is on testing; if you wish to compute nonparametric correlations you are referred to submodule correg, which contains several functions for that purpose.

There are a large number of nonparametric tests available. A selection of some of the more commonly used tests are included in this module.

Functionality Index

Regression using ranks

right-censored data: rank_regsn_censored()

uncensored data: rank_regsn()

Tests of association and correlation

Kendall’s coefficient of concordance: concordance_kendall()

Tests of dispersion

Mood’s and David’s tests on two samples of unequal size: test_mooddavid()

Tests of fit

${\chi }^2$ goodness-of-fit test: test_chisq()

$A^2$ and its probability of for a fully-unspecified Normal distribution: gofstat_anddar_normal()

$A^2$ and its probability of for an unspecified exponential distribution: gofstat_anddar_exp()

$A^2$ and its probability of for uniformly distributed data: gofstat_anddar_unif()

Anderson–Darling test statistic $A^2$: gofstat_anddar()

Kolmogorov–Smirnov one-sample distribution test

for a user-supplied distribution: test_ks_1sample_user()

for standard distributions: test_ks_1sample()

Kolmogorov–Smirnov two-sample distribution test: test_ks_2sample()

Tests of location

Cochran $Q$ test on cross-classified binary data: test_cochranq()

exact probabilities for Mann–Whitney $U$ statistic

no ties in pooled sample: prob_mwu_noties()

ties in pooled sample: prob_mwu_ties()

Friedman two-way analysis of variance on $k$ matched samples: test_friedman()

Kruskal–Wallis one-way analysis of variance on $k$ samples of unequal size: test_kruskal()

Mann–Whitney $U$ test on two samples of possibly unequal size: test_mwu()

Median test on two samples of unequal size: test_median()

sign test on two paired samples: test_sign()

Wilcoxon one sample signed rank test: test_wilcoxon()

Tests of randomness

Gaps test: randtest_gaps()

pairs (serial) test: randtest_pairs()

runs up or runs down test: randtest_runs()

triplets test: randtest_triplets()

For full information please refer to the NAG Library document

https://support.nag.com/numeric/nl/nagdoc_30.3/flhtml/g08/g08intro.html