A test for normality of the distribution of a range of values. Based on the assumption that normally distributed values will have a sample skewness and sample kurtosis very close to zero.


Return Value

Type: TestRes

A TestRes with the K statistic, which is Chi-Square distributed with 2 degrees of freedom under the null, and the P-value for the alternative that the data has skewness and kurtosis not equal to zero against the null that skewness and kurtosis are near zero. A normal distribution always has skewness and kurtosis that converge to zero as sample size goes to infinity.

Notes: Contrary to popular belief, tests for normality should usually not be used to deterimine whether T-tests are valid. If the sample size is large, T-tests are valid regardless of the distribution due to the central limit theorem. If the sample size is small, a test for normality will likely not be very powerful, and a priori knowledge or simple inspection of the data is often a better idea.

References: D'Agostino, Ralph B., Albert Belanger, and Ralph B. D'Agostino, Jr. "A Suggestion for Using Powerful and Informative Tests of Normality", The American Statistician, Vol. 44, No. 4. (Nov., 1990), pp. 316-321.