POWER COMPARISON OF TESTS FOR NORMALITY AND RECOMMENDED TEST ORDERS FOR MANUFACTURING ORGANIZATIONS
DOI:
https://doi.org/10.37255/jme.v19i2pp040-056Keywords:
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.
Downloads
References
Amedie, W., Awaj, Y., and Singh, A., “Quality Improvement Using Statistical Process Control Tools in Glass Bottles Manufacturing Company,” International Journal for Quality Research, vol. 7, no. 1, pp. 107-126, 2013.
Black, K., “Business statistics: for contemporary decision making,” John Wiley & Sons, 2023.
Ghasemi, A., and Zahediasl, S., “Normality tests for statistical analysis: a guide for non-statisticians,” International Journal of Endocrinol Metab, vol. 10, no. 2, pp. 486-9, 2012. doi: 10.5812/ijem.3505.
He, Q., and Wang, J., “Statistics pattern analysis: A new process monitoring framework and its application to semiconductor batch processes,” AIChE Journal, vol. 57, no. 1, pp. 107-121, 2011. https://doi.org/10.1002/aic.12345.
Jarque, C. M., and Bera, A. K., “A Test for Normality of Observations and Regression Residuals,” International Statistical Review, vol. 55, pp. 163-172, 1987. http://doi.org/10.2307/1403192.
Lee, C., Jeong, J., and Park, S., “Comprehensive comparison of normality tests: Empirical study using many different types of data,” Journal of the Korean Data & Information Science Society, vol. 27, no. 5, pp. 1399-1412, 2016. https://doi.org/10.7465/jkdi.2016.27.5.1399.
Lieber, R. L., “Statistical significance and statistical power in hypothesis testing,” Journal of Orthopaedic Research, vol. 8, no. 2, pp. 304-309, 1990. https://doi.org/10.1002/jor.1100080221.
Lilliefors, H., “On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown,” Journal of the American Statistical Association, vol. 62, no. 318, pp. 399-402, 1967. https://doi.org/10.2307/2283970.
Razali, N., and Yap, B., “Power Comparisons of Shapiro-Wilk, Kolmogorov-Smirnov, Lilliefors and Anderson-Darling Tests,” Journal of Statistical Modeling and Analytics, vol. 2, 2011.
Thode, H. J., “Testing for normality,” Marcel Dekker, 2002.
Wijekularathna, D., Manage, A., and Scariano, S., “Power analysis of several normality tests: A Monte Carlo simulation study,” Communications in Statistics - Simulation and Computation, vol. 51, no. 3, pp. 757-773, 2022. https://doi.org/10.1080/03610918.2019.1658780.
Yazici, B., and Asma, S., “A comparison of various tests of normality,” Journal of Statistical Computation and Simulation, vol. 77, pp. 175-183, 2007. https://doi.org/10.1080/10629360600678310.
Downloads
Published
Issue
Section
How to Cite
