Statistical treatment of reference values in laboratory medicine: testing the goodness-of-fit of an observed distribution to the Gaussian distribution.

During the preparation of an IFCC-recommendation on the statistical treatment of reference values, five tests of the goodness-of-fit of an empirical distribution to the Gaussian distribution were computerized and studied by Monte Carlo simulations: tests based on the coefficients of skewness and kurtosis, the Anderson-Darling's test, the Cramér-von Mises' test, and the Kolmogorov-Smirnov's test. Approximations for test probabilities were developed for all these tests. Based on the simulation results it is recommended to use the combination of the two coefficient-based tests for monitoring the transformation of an empirical distribution to Gaussian shape and to use the Anderson-Darling's test as an all-round test for Gaussianity.