A Test for Normality in the Presence of Outliers

The Jarque-Bera test is a test based on the coefficients of skewness (S) and kurtosis (K) for testing whether the given random sample is from a normal population. When the random sample of size n contains m outliers, we use the remaining n-m observations to compute two statistics S* and K* which mimic the statistics S and K. The statistics S* and K* are next transformed to z1 and z2 which are uncorrelated and having standard normal distributions when the original population is normal. We show that the acceptance region given by a circle in the (z1, z2) plane is suitable for testing the normality assumption.