D'Agostino's K-squared test

In statistics, D’Agostino’s K2 test, named for Ralph D'Agostino, is a goodness-of-fit measure of departure from normality, that is the test aims to establish whether or not the given sample comes from a normally distributed population. The test is based on transformations of the sample kurtosis and skewness, and has power only against the alternatives that the distribution is skewed and/or kurtic. In statistics, D’Agostino’s K2 test, named for Ralph D'Agostino, is a goodness-of-fit measure of departure from normality, that is the test aims to establish whether or not the given sample comes from a normally distributed population. The test is based on transformations of the sample kurtosis and skewness, and has power only against the alternatives that the distribution is skewed and/or kurtic. In the following, { xi } denotes a sample of n observations, g1 and g2 are the sample skewness and kurtosis, mj’s are the j-th sample central moments, and x ¯ {displaystyle {ar {x}}} is the sample mean. Frequently in the literature related to normality testing, the skewness and kurtosis are denoted as √β1 and β2 respectively. Such notation can be inconvenient since, for example, √β1 can be a negative quantity.