# TIBCO Statistica® Nonparametric Statistics

The Nonparametric Statistics module features a selection of inferential and descriptive statistics including all common tests and some special application procedures. Available statistical procedures include the Wald-Wolfowitz runs test, Mann-Whitney U test (with exact probabilities [instead of the Z approximations] for small samples), Kolmogorov-Smirnov tests, Wilcoxon matched pairs test, Kruskal-Wallis ANOVA by ranks, Median test, Sign test, Friedman ANOVA by ranks, Cochran Q test, McNemar test, Kendall coefficient of concordance, Kendall tau (b, c), Spearman rank order R, Fisher's exact test, Chi-square tests, V-square statistic, Phi, Gamma, Sommer's d, contingency coefficients, and others.

Nonparametric methods were developed to be used in cases when the data scientist knows nothing about the parameters of the variable of interest in the population (hence the name nonparametric). In more technical terms, nonparametric methods do not rely on the estimation of parameters (such as the mean or the standard deviation) describing the distribution of the variable of interest in the population. Therefore, these methods are also sometimes called parameter-free methods or distribution-free methods.

Nonparametric methods are most appropriate when the sample sizes are small. When the data set is large it may not make sense to use these statistics due to the central limit theorem. In a nutshell, when the samples become large, then the sample means will follow the normal distribution even if the respective variable is not normally distributed in the population, or is not measured very well. Thus, parametric methods, which are usually much more sensitive are in most cases appropriate for large samples. However, the tests of significance of many of the nonparametric statistics are based on asymptotic (large sample) theory. Therefore, meaningful tests can often not be performed if the sample sizes become too small.

Note that specialized nonparametric tests and statistics are also part of other modules, e.g., Survival Analysis, Process Analysis, and others. All rank order tests can handle tied ranks and apply corrections for small n or tied ranks. The program can handle extremely large analysis designs. All tests are integrated with graphs that include various scatterplots, specialized box-and-whisker plots, line plots, histograms and many other 2D and 3D displays.