Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more. 
Home Statistical Tests Comparing Distributions ShapiroWilk Test  
See also: Normal Distribution, Test for Normality, KolmogorovSmirnov OneSample Test  
ShapiroWilk TestThe ShapiroWilk test is a test for normal distribution exhibiting high power, leading to good results even with a small number of observations. In contrast to other comparison tests the ShapiroWilk test is only applicable to check for normality. The basis idea behind the ShapiroWilk test is to estimate the variance of the sample in two ways: (1) the regression line in the QQPlot allows to estimate the variance, and (2) the variance of the sample can also be regarded as an estimator of the population variance. Both estimated values should approximately equal in the case of a normal distribution and thus should result in a quotient of close to 1.0. If the quotient is significantly lower than 1.0 then the null hypothesis (of having a normal distribution) should be rejected.
In order to calculate the statistic W one has to perform the following procedure:


Home Statistical Tests Comparing Distributions ShapiroWilk Test 