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Skewness-Kurtosis All Normality Test (All Departures From Normality)
The Skewness-Kurtosis All test for normality is one of three general normality tests designed to detect all departures from normality. It is comparable in power to the other two tests. The normal distribution has a skewness of zero and kurtosis of three. The test is based on the difference between the data's skewness and zero and the data's kurtosis and three.
The test rejects the hypothesis of normality when the p-value is less than or equal to 0.05. Failing the normality test allows you to state with 95% confidence the data does not fit the normal distribution. Passing the normality test only allows you to state no significant departure from normality was found.
It is the default test because it is not affected by ties like both the Anderson-Darling and Shapiro-Wilks tests.