Statistical Analysis of Strength of W/S Test of Normality Against Non-normal Distribution Using Monte Carlo Simulation
American Journal of Theoretical and Applied Statistics
Volume 6, Issue 5-1, September 2017, Pages: 62-65
Received: Feb. 24, 2017; Accepted: Mar. 1, 2017; Published: Jul. 11, 2017
Views 1566      Downloads 67
Authors
Ukponmwan H. Nosakhare, Department of General Studies, Mathematics and Computer Science Unit, Petroleum Training Institute, Warri, Nigeria
Ajibade F. Bright, Department of General Studies, Mathematics and Computer Science Unit, Petroleum Training Institute, Warri, Nigeria
Article Tools
Follow on us
Abstract
Among the test of normality in existence is the W/S which has standard table as the interval for critical region with both lower and upper bound. The test is suitable for sample size ranging from 3 as displayed in the W/S Critical table. But the sensitivity of the test can be determined by computation of power of the test which would show how sensitive the test is to non-normal distribution. The paper addressed the sensitivity of the test using some selected distributions which are from asymmetric and symmetric in nature. Monte Carlo Simulation technique was used with 100 replicates for sample sizes of 5 to 100 with regular interval of 5. Distributions considered include; Weibull, Chi-Square, t and Cauchy distributions. The result shows inconsistency of the test as it has weak power for distribution used except Cauchy distribution. The findings shows that the test should be used with caution has it has weak or low power which could lead to statistical error, thereby call for proper modification of the test to improve its power.
Keywords
Range, Standard Deviation, Descriptive Statistics, Simulation, Power-of-Test
To cite this article
Ukponmwan H. Nosakhare, Ajibade F. Bright, Statistical Analysis of Strength of W/S Test of Normality Against Non-normal Distribution Using Monte Carlo Simulation, American Journal of Theoretical and Applied Statistics. Special Issue: Statistical Distributions and Modeling in Applied Mathematics. Vol. 6, No. 5-1, 2017, pp. 62-65. doi: 10.11648/j.ajtas.s.2017060501.19
Copyright
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
References
[1]
Anderson, T. W., and Darling, D. A. (1952). ‘‘Asymptotic theory of certain goodness-of fit criteria based on stochastic processes.’’ The Annals of Mathematical Statistics 23(2): 193-212.http://www.cithep.caltech.edu/~fcp/statistics/hypothesisTest/PoissonConsistency/AndersonDarling1952.pdf.
[2]
Douglas G. B. and Edith S. (2002): A test of normality with high uniform power. Journal of Computational Statistics and Data Analysis 40 (2002) 435 – 445. www.elsevier.com/locate/csda.
[3]
Eze F. C (2002): “Introduction to Analysis of Variance”. Vol. 1, Pg. 3. Lano Publishers, Obiagu Road, Enugu State, Nigeria.
[4]
Jarque, Carlos M. and Bera, Anil K. (1980): "Efficient tests for normality, homoscedasticity and serial independence of regression residuals". Economics Letters 6 (3): 255–259. doi:10.1016/0165-1765(80)90024-5.
[5]
Jarque, Carlos M. and Bera, Anil K. (1981): "Efficient tests for normality, homoscedasticity and serial independence of regression residuals: Monte Carlo evidence". Economics Letters 7 (4): 313–318. doi: 10.1016/0165-1765(81)900235-5.
[6]
Jarque, Carlos M. and Bera, Anil K. (1987): "A test for normality of observations and regression residuals". International Statistical Review 55 (2): 163–172. JSTOR 1403192.
[7]
Nor-Aishah H. and Shamsul R. A (2007): Robust Jacque-Bera Test of Normality. Proceedings of The 9th Islamic Countries Conference on Statistical Sciences 2007. ICCS-IX 12-14 Dec 2007
[8]
Mardia, K. V. (1980). ‘‘Tests of univariate and multivariate normality.’’ In Handbook of Statistics 1: Analysis of Variance, edited by Krishnaiah, P. R. 279-320. Amsterdam. North-Holland Publishing.
[9]
Ryan, T. A. and Joiner B. L. (1976): Normal Probability Plots and Tests for Normality, Technical Report, Statistics Department, the Pennsylvania State University.
[10]
Sarkadi, K. (1981), On the consistency of some goodness of fit tests, Proc. Sixth Conf. Probab. Theory, Brasov, 1979, Ed. Acad. R. S. Romania, Bucuresti, 195–204.
[11]
Yap B. W. and Sim C. H. (2011): Comparisons of various types of normality tests. Journal of Statistical Computation and Simulation 81:12, 2141-2155, DOI: 10.1080/00949655.2010.520163.
ADDRESS
Science Publishing Group
1 Rockefeller Plaza,
10th and 11th Floors,
New York, NY 10020
U.S.A.
Tel: (001)347-983-5186