The use of U-statistics for testing normality against nonsymmetric alternatives

We propose a class of tests for normality and investigate a subclass of these tests for testing against nonsymmetric alternatives. Attention is devoted to a convenient linear combination of the order statistics divided by the sample standard deviation and to a second statistic. The null distribution of the first statistic is for most purposes satisfactorily approximated by a normal distribution if the sample size is 20 or greater, and the same is true of the second statistic for sample sizes of 50 or greater. Monte Carlo critical points are also provided. A Monte Carlo power study shows that the two statistics have good power properties relative to the sample skewness coefficient.