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 gauge the compatibility of given data with the null hypothesis that the data is a realization of independent, identically distributed Gaussian random variables.
In order to remedy this situation, it has been suggested to transform the quantities g1 and g2 in a way that makes their distribution as close to standard normal as possible.
In particular, D'Agostino & Pearson (1973) suggested the following transformation for sample skewness: where constants α and δ are computed as and where μ2 = μ2(g1) is the variance of g1, and γ2 = γ2(g1) is the kurtosis — the expressions given in the previous section.
Similarly, Anscombe & Glynn (1983) suggested a transformation for g2, which works reasonably well for sample sizes of 20 or greater: where and μ1 = μ1(g2), μ2 = μ2(g2), γ1 = γ1(g2) are the quantities computed by Pearson.
Statistics Z1 and Z2 can be combined to produce an omnibus test, able to detect deviations from normality due to either skewness or kurtosis (D'Agostino, Belanger & D'Agostino 1990): If the null hypothesis of normality is true, then K2 is approximately χ2-distributed with 2 degrees of freedom.