Kolmogorov-Smirnov test

The Kolmogorov-Smirnov one-sample test for normality is based on the maximum difference between the sample cumulative distribution and the hypothesized cumulative distribution. If the D statistic is significant, then the hypothesis that the respective distribution is normal should be rejected. For many software programs, the probability values that are reported are based on those tabulated by Massey (1951); those probability values are valid when the mean and standard deviation of the normal distribution are known a-priori and not estimated from the data. However, usually those parameters are computed from the actual data. In that case, the test for normality involves a complex conditional hypothesis ("how likely is it to obtain a D statistic of this magnitude or greater, contingent upon the mean and standard deviation computed from the data"), and the Lilliefors probabilities should be interpreted (Lilliefors, 1967). Note that in recent years, the Shapiro-Wilks' W test has become the preferred test of normality because of its good power properties as compared to a wide range of alternative tests.

A non-parametric test applicable to continuous frequency distributions. It has greater power than the G-statistics or test for goodness of fit especially when the sample size is small. It can be used to compare two independent groups. The test is based on differences between two cumulative relative frequency distributions (it compares the distributions not the parameters).