Subscribe Now Subscribe Today
Research Article

Type I Error Rate and Power of Three Normality Tests

Mehmet Mendes and Akin Pala
Facebook Twitter Digg Reddit Linkedin StumbleUpon E-mail

In this study, Shapiro-Wilks, Lilliefors and Kolmogorov-Smirnov tests were compared for Type I error and for power of the tests. The simulation was run 100, 000 times for different situations and for different types of departures from normality. For all different sample sizes and distributions, Shapiro-Wilks gave the most powerful results, followed by the Lilliefors test. Kolmogorov-Smirnov test results were the weakest among all three tests. All three test were most powerful when ran on data with exponential distribution.

Related Articles in ASCI
Similar Articles in this Journal
Search in Google Scholar
View Citation
Report Citation

  How to cite this article:

Mehmet Mendes and Akin Pala , 2003. Type I Error Rate and Power of Three Normality Tests. Information Technology Journal, 2: 135-139.

DOI: 10.3923/itj.2003.135.139


1:  Anonymous, 1994. Fortran Subroutines for Mathematical Application. Vol. 1-2, Visual Numerics, Inc., Houston, USA.

2:  Lilliefors, H.W., 1967. On the Kolmogorov-Smirnov test for normality with mean and variance unknown. J. Am. Stat. Assoc., 62: 399-402.

3:  Lin, C.C. and G.S. Mudholkar, 1980. A simple test for normality against asymetric. Alternatives Biometrika, 67: 455-455.

4:  Shapiro, S.S. and M.B. Wilk, 1965. An analysis of variance test for normality (Complete samples). Biometrika, 52: 591-611.
CrossRef  |  Direct Link  |  

5:  Shapiro, S.S., M.B. Wilk and H.J. Chan, 1968. A comparative study of various tests for normality. JASA, 63: 324-324.

6:  Ohta, H. and I. Arizono, 1989. A test for normality based on kullback-leibler information. Am. Stat., 43: 20-22.

7:  Hannu, O., 1983. New tests for normality. Biometrika, 70: 297-299.
CrossRef  |  

©  2021 Science Alert. All Rights Reserved