Mann-Whitney test

A nonparametric hypothesis test to determine whether two populations have the same population median (h). It tests the null hypothesis that the two population medians are equal (H0: h1 = h2). The alternative hypothesis can be left-tailed (h1 < h2), right-tailed (h1 > h2), or two-tailed (h1 ≠ h2). The Mann-Whitney test does not require the data to come from normally distributed populations, but it does make the following assumptions:

·  the populations of interest have the same shape

·  the populations are independent

For example, a consultant compares the payrolls of two companies to determine whether their median salaries differ. She takes random samples from both payrolls. The data are right-skewed, with many workers earning lower salaries and only a few executives earning high salaries. But because this skew applies to both companies, her data satisfies the "same shape" assumption.  Because the two populations are nonnormal, yet have the same shape, the consultant chooses the nonparametric Mann-Whitney test to compare the two samples.

The Mann-Whitney test uses the ranks of the sample data, instead of their specific values, to detect statistical significance.