MannWhitneyWilcoxonTest Class

The Mann–Whitney U test (also called the Mann–Whitney–Wilcoxon (MWW), Wilcoxon rank-sum test, or Wilcoxon–Mann–Whitney test) is a non-parametric test of the null hypothesis that two populations are the same against an alternative hypothesis, especially that a particular population tends to have larger values than the other.

It has greater efficiency than the t-test on non-normal distributions, such as a mixture of normal distributions, and it is nearly as efficient as the t-test on normal distributions.

The following example comes from Richard Lowry's page at http://vassarstats.net/textbook/ch11a.html. As stated by Richard, this example deals with persons seeking treatment by claustrophobia. Those persons are randomly divided into two groups, and each group receive a different treatment for the disorder.

The hypothesis would be that treatment A would more effective than B. To check this hypothesis, we can use Mann-Whitney's Test to compare the medians of both groups.

// Claustrophobia test scores for people treated with treatment A
double[] sample1 = { 4.6, 4.7, 4.9, 5.1, 5.2, 5.5, 5.8, 6.1, 6.5, 6.5, 7.2 };

// Claustrophobia test scores for people treated with treatment B
double[] sample2 = { 5.2, 5.3, 5.4, 5.6, 6.2, 6.3, 6.8, 7.7, 8.0, 8.1 };

// Create a new Mann-Whitney-Wilcoxon's test to compare the two samples
MannWhitneyWilcoxonTest test = new MannWhitneyWilcoxonTest(sample1, sample2,
  TwoSampleHypothesis.FirstValueIsSmallerThanSecond);

double sum1 = test.RankSum1; //  96.5
double sum2 = test.RankSum2; // 134.5

double statistic1 = test.Statistic1; // 79.5
double statistic2 = test.Statistic2; // 30.5

double pvalue = test.PValue; // 0.043834132843420748

// Check if the test was significant
bool significant = test.Significant; // true

Reference