As powerful as parametric tests. Use for true interval data. No assumption about normality , homogeneity of variance , or the form of the underlying distribution. Probably the most powerful of all nonparametric statistics. But you must be sure that your data is at least interval in nature.
Null hypothesis is that the population medians are equal .
Another way to look at this is that under the null, each subject would have produced the two scores regardless of the treatment condition or order . Another way to look at this, is that if you figured the difference scores for each pair, the difference is just as likely to be positive as negative . Let us say we do a study with 7 pairs of scores . This psychologist knows that termperament is, to some extent, inherited. Therefore, he obtains 7 sets of identical twins and randomly assigns one of each pair to receive infant stimulation.