Document Type



Master of Science (MS)



First Advisor's Name

BM Golam Kibria

First Advisor's Committee Title

Committee Co-Chair

Second Advisor's Name

Florence George

Second Advisor's Committee Title

Committee Co-Chair

Third Advisor's Name

Wensong Wu

Third Advisor's Committee Title

Committee Member


Normality test, Goodness-of-fit, Power, Type I error, Shapiro-Wilk, Kolmogorov

Date of Defense



The importance of checking the normality assumption in most statistical procedures especially parametric tests cannot be over emphasized as the validity of the inferences drawn from such procedures usually depend on the validity of this assumption. Numerous methods have been proposed by different authors over the years, some popular and frequently used, others, not so much. This study addresses the performance of eighteen of the available tests for different sample sizes, significance levels, and for a number of symmetric and asymmetric distributions by conducting a Monte-Carlo simulation. The results showed that considerable power is not achieved for symmetric distributions when sample size is less than one hundred and for such distributions, the kurtosis test is most powerful provided the distribution is leptokurtic or platykurtic. The Shapiro-Wilk test remains the most powerful test for asymmetric distributions. We conclude that different tests are suitable under different characteristics of alternative distributions.





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