SKEWNESS IN COMMINGLED DISTRIBUTIONS

A likelihood ratio test is given for distinguishing skewness from commingled distributions, using a power transform to remove skewness appropriately for each of the alternatives tested. The alternative hypotheses postulate that the transformed data are from 1 normal or a mixture of 2 or 3 normal homoscedastic distributions. Since each mixture has unique asymmetry, skewness is estimated simultaneously with the means, proportions and variance of components. Commingling cannot be rigorously proven in this way, as some other transform may provide a better approximation to normality. The error of asserting admixture whenever there is skewness is avoided, and estimates of admixture parameters provide a basis for more conclusive tests in relatives or other populations. Two examples are given, one in which adjustment for skewness left evidence of commingling. [The distributions of 2 blood clotting factors in humans.sbd.Stuart factor (factor X) and Christmas factor (factor IX).sbd.suggestive of major gene action were analyzed.].