Kolmogorov Smirnov Vs Shapiro Wilk. Kolmogorov smirnov a shapiro wilk. I ll compare the kolmogorov smirnov test a popular test for goodness of fit with the shapiro wilks test that miller preferred.
Briefly stated the shapiro wilk test is a specific test for normality whereas the method used by kolmogorov smirnov test is more general but less powerful meaning it correctly rejects the null hypothesis of normality less often. If the sample size is larger than 50 we use the kolmogorov smirnov test. Shapiro wilk has the best power for a given significance followed closely by anderson darling when comparing the shapiro wilk kolmogorov smirnov.
Some statisticians claim the latter is worse due to its lower statistical power.
The anderson darling test stephens 1974 is used to test if a sample of data comes from a specific distribution it is a modification of the kolmogorov smirnov k s test and gives more weight to the tails of the distribution than does the k s test. The k s test is distribution free in the sense that the critical values do. Like so the shapiro wilk serves the exact same purpose as the kolmogorov smirnov test. Some statisticians claim the latter is worse due to its lower statistical power.
