Mann Whitney U Test Equation. The test statistic for the mann whitney u test is denoted u and is the smaller of u 1 and u 2 defined below. Your confusion may stem from the fact that you are calculating the probability of the u value falling within the interval when in fact you need the probability of it falling outside the interval.
Where r 1 sum of the ranks for group 1 and r 2 sum of the ranks for group 2. For any mann whitney u test the theoretical range of u is from 0 complete separation between groups h 0 most likely false and h 1 most likely true to n 1 n 2 little evidence in support of h 1. And using the same notation the mann whitney paper defines u 1 as.
S x y 1 if y x 1 2 if y x 0 if y x.
The mann whitney test uses a normal approximation method to determine the p value of the test. In every test u 1 u 2 is always equal to n 1 n 2. So for example one might compare the speed at which two different groups of people can run 100 metres where one group has trained for six weeks and the other has not. In this case you want 2 times p u geq 23.
