Nonparametric Statistics

Nonparametric statistical tests are distribution-independent tests that are used to analyse data for which an underlying distribution (such as the normal distribution) is not assumed. Non-parametric statistics have a number of advantages over parametric statistics. They can be quick and easy to use as they often use ranks or signs of differences rather than the values themselves. They can reduce the work of data collection because data can be ranks or simple scores rather than precise measurements. Sampling procedures do not assume homogeneity of variances, for example between locations or over time. There are fewer assumptions about, for example, the underlying distribution. But, there are possible disadvantages, particularly the failure to use a distribution if one is appropriate and the failure to use all of the available information.

statistiXL provides a diverse array of nonparametric tests. The sign test can be used to examine whether two populations have the same median, and for observations in pairs with one of each pair coming from each population. Various modifications of the sign test can be used for specific tests (e.g. trend, sign correlation, and a sign test for predicted patterns). The Friedman test for blocked data is equivalent to a sign test, but for more than 2 groups. The Mann-Whitney test (U statistic) is a nonparametric test that uses the ranks of two independent samples, from the highest to lowest (or lowest to highest), to calculate the U statistic; it is the nonparametric analog to the parametric two-sample t-test. The Wilcoxon's signed-rank test ranks the differences between pairs of data (or single data set of a sample) and compares the sum of positive and negative ranks with a critical U value; it is the nonparametric analog to the parametric paired t test. The Kruskal-Wallis test is a nonparametric test for the comparison of 3 or more treatment groups, which are independent; it is the nonparametric equivalent to analysis of variance (ANOVA). A common nonparametric correlation test is Spearman’s rho rank correlation coefficients; this is analogous to the parametric Pearson’s correlation coefficient. Mood's Median Test examines whether two or more samples come from a population having the same median. The Wald-Wolfowitz Runs test analyses a sequence of observations, or compares random samples which are mutually independent, for two or more outcomes e.g. two species of antelope, or three brands of automobile.

Results are presented in tabular form. Format varies for different nonparametric tests, but generally includes an optional descriptive statistics or ranks summary, and the appropriate statistic, degrees of freedom, and P value.

The help file for statistiXL provides an overview of nonparametric statistical test, and a comprehensive range of 14 examples, including sign tests, Mann-Whitney U test, Wilcoxon paired-sample test and test of symmetry about the median, median tests, Kruskal-Wallis test, Friedman’s test, Wald-Wolfowitz runs test, and Spearman rank correlation.