Wilcoxon Test

Comparison of central tendencies of two dependent samples.

Requirements:

Dependent variable must be interval scaled because differences are taken for the test. Distribution is free.

Idea:

Dependency of the two sample data is considered by taking the differences of paired values. The calculation of differences requires at least interval scaled data. In a next step the differences are brought into rank order. Under H0 the sum of positive differences should approximately equal the sum of negative differences. Zero-Differences are not considered in the test.

Measure:

T = Sum of ranks of less frequent sign.

Approximation with Normal Distribution:

For large sample sizes (n = Number of pairs > 25) T is approximately normal distributed with

and

Test:

If there are tied ranks, is corrected as follows:

Whereas

t_i = Number of subjects sharing rank i

k = Number of tied ranks