Non-parametric methods (distribution free methods)

Statistical methods to analyze data from populations which do not assume a particular population distribution. Mann-Whitney U test, Kruskal-Wallis test and Wilcoxon's (T) test are examples. Such tests do not assume a distribution of the data specified by certain parameters (such as mean or variance). For example, one of the assumptions of the Student's t-test and ANOVA is normal distribution of the data. If this is not valid, a non-parametric equivalent must be used. If a wrong choice of test has been made, it does not matter very much if the sample size is large (a non-parametric test can be used where a parametric test might have been used but a parametric test can only be used when the assumptions are met). For a small sample size, non-parametric tests tend to give a larger P value. In general, parametric tests are more robust, more complicated to compute and have greater power efficiency. Parametric tests compare parameters such as the mean in t-test and variance in F-test as opposed to non-parametric tests which compare distributions.