U-Test Mann-Whitney

Comparison of central tendencies of two independent samples.

Requirements:

Dependent variable must be ordinal scaled (rank order scaled). Distribution free.

Idea:

The values of both samples are brought in one rank order. For H0 it is expected that 'x<y' occurrs as frequently as 'y<x'.

Measure:

U measures how often a y-value is smaller than an x-value. Definition: if y<x, z=1, if x<y, z=0. .

Calculation of U:

= sum of ranks for sample 1.

For large sample sizes (n₁ or n₂ > 10) U is approximately normal distributed with:

and

Test:

If there are tied ranks, the standard deviation of U is corrected as follows:

Whereas

t_i = Number of subjects sharing rank i

k = Number of tied ranks