POWER COMPARISON OF TESTS FOR NORMALITY AND RECOMMENDED TEST ORDERS FOR MANUFACTURING ORGANIZATIONS
Keywords:
normality testing, statistical process control, power comparison, type II error, quality engineeringAbstract
Manufacturing organizations are increasingly concerned with statistical analysis as a tool for understanding and improving processes. With the release of a new statistical package, QESuite, designed for manufacturers, it is important to directly compare the included normality tests to guide the standards of manufacturing organizations. A common metric of the usefulness of a normality test is its power, the test’s ability to identify data that do not follow the normal distribution correctly. Through Monte Carlo simulation, the power of 6 normality tests: Anderson-Darling, Jarque-Bera, Kolmogorov-Smirnov, Lilliefors (corrected KS), Shapiro-Wilk (Royston), and Ryan-Joiner; was evaluated at multiple sample sizes with different original distributions. The sample size of the data being tested greatly impacted the power of all the tests studied. As the sample size increased, the power of almost all the tests studied approached 1.0 (100%). The underlying distribution also showed an effect, with the power being higher for all tests when evaluating asymmetrical distributions than symmetric distributions. When the power was averaged across all distributions and the average ranks of each test across sample sizes were calculated, the following general order of highest power to lowest is recommended: Shapiro-Wilk (Royston), Lilliefors, Ryan-Joiner, Anderson-Darling, Jarque-Bera, Kolmogorov-Smirnov.
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