A Power Comparison of Goodness-of-fit Tests for Normality Based on the Likelihood Ratio and the Non-likelihood Ratio

Rinnakorn Chaichatschwal; Kamon Budsaba

A Power Comparison of Goodness-of-fit Tests for Normality Based on the Likelihood Ratio and the Non-likelihood Ratio

Authors

Rinnakorn Chaichatschwal Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Phathum Thani, 12121, Thailand.
Kamon Budsaba Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University, Phathum Thani, 12121, Thailand.

Keywords:

Anderson-Darling, Goodness-of-fit, Shapiro-Francia, Shapiro-Wilk

Abstract

The goal of the study is to select the best goodness-of-fit test among six tests; the Z_A statistic, the Z_C statistic, the Z_K statistic, the Anderson-Darling ( A² ) statistic, the Shapiro-Wilk (W ) statistic and the Shapiro-Francia statistic ( W' ). The tests were compared when the normal parameters are unknown and sample sizes are 10, 30, 50, 70 and 100 each with 0.05 level of significance. With 1,000 Monte Carlo replications, the probability of type I error of all six statistics can be controlled for all sample sizes under study. Both sample sizes and types of the distribution affect the power of the test.

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How to Cite

Chaichatschwal, R., & Budsaba, K. (2015). A Power Comparison of Goodness-of-fit Tests for Normality Based on the Likelihood Ratio and the Non-likelihood Ratio. Thailand Statistician, 5, 57–68. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/34350