## Wednesday, July 15, 2009

### Nonparametric tests for groups comparison - Independent samples - Differences in location

The aim of homogeneity test (or test for difference between groups) is to check if K (K >= 2) samples are drawn from the same population according to a variable of interest. In another words, we check if the probability distribution is the same in each sample.

The nonparametric tests make no assumptions about the distribution of the data. They are called also "distribution free" tests.

In this tutorial, we show how to implement nonparametric homogeneity tests for differences in location for K = 2 populations i.e. the distributions of the populations are the same excepting a shift in location (central tendency). The Kolmogorov-Smirnov test is the more general one. It checks all kind of differences between the cumulative distribution functions (CDF). Afterwards, we can implement other tests which characterize more deeply the difference. The Wilcoxon-Mann-Whitney test is certainly the most popular one. We will see in this tutorial that other tests can be also implemented.

Some the tests introduced here are usable when the number of groups is upper than 2 (K > 2).

Keywords: nonparametric test, Kolmogorov-Smirnov test, Wilcoxon-Mann-Whitney test, Van der Waerden test, Fisher-Yates-Terry-Hoeffding test, median test, location model
Components: FYTH 1-WAY ANOVA, K-S 2-SAMPLE TEST, MANN-WHITNEY COMPARISON, MEDIAN TEST, VAN DER WAERDEN 1-WAY ANOVA
Tutorial: en_Tanagra_Nonparametric_Test_MW_and_related.pdf
Dataset: machine_packs_cartons.xls
References:
R. Rakotomalala, « Comparaison de populations. Tests non paramétriques », Université Lyon 2 (in french).
Wikipedia, « Non-parametric statistics ».