Detecting Departures from Normality: A Monte Carlo Simulation of a New Omnibus Test Based on Moments.

The assumption of normality underlies much of the standard statistical methodology. Knowing how to determine whether a sample of measurements is from a normally distributed population is crucial both in the development of statistical theory and in practice. W. Ware and J. Ferron have developed a new test statistic, modeled after the K-squared test of R. D'Agostino and E. Pearson (1973), the g-squared test statistic. This statistic has been used to estimate critical values for sample sizes up to 100, but a more extensive derivation and validation of the critical values are required, and the power of g-squared against a wide range of alternative distributions requires study. Monte Carlo simulations were performed to investigate these areas. The main advantage of g-squared is its conceptual and computational simplicity. The power study shows that g-squared is sensitive to a wide range of alternative distributions, especially peaked distributions, having absolute power for many distributions with a large "n." G-squared could be valuable for testing univariate normality in statistical routines, but it does have some weaknesses. One of its main disadvantages is its low power with small sample sizes except for peaked distributions. While g- squared can tell you about a departure from normality, it can not tell if the departure is due to a single outlier. It is recommended that when testing for departures from normality, g-squared should be used as a supplemental quantitative measure of normality to the information obtained from histograms, box plots, stem and leaf diagrams, and normality plots. (Contains 7 figures, 12 tables, and 28 references.) (SLD)