Nonparametric tests may be, and often are, more powerful in detecting population differences when certain assumptions are not satisfied.
All tests involving ranked data, i.e. data that can be put in order, are nonparametric.
The Wilcoxon Mann-Whitney Test is one of the most powerful of the nonparametric tests for comparing two populations. The Wilcoxon Mann-Whitney test does not require the assumption that the differences between the two samples are normally distributed . This test can also be applied when the observations in a sample of data are ranks, that is, ordinal data rather than direct measurements. It often involves the use of matched pairs, for example, before and after data, in which case it tests for a median difference of zero. The Wilcoxon Signed Ranks test does not require the assumption that the population is normally distributed.