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.
| Published in |
American Journal of Theoretical and Applied Statistics (Volume 6, Issue 5-1)
This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics |
| DOI | 10.11648/j.ajtas.s.2017060501.19 |
| Page(s) | 62-65 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2017. Published by Science Publishing Group |
Range, Standard Deviation, Descriptive Statistics, Simulation, Power-of-Test
| [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. |
APA Style
Ukponmwan H. Nosakhare, Ajibade F. Bright. (2017). 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, 6(5-1), 62-65. https://doi.org/10.11648/j.ajtas.s.2017060501.19
ACS Style
Ukponmwan H. Nosakhare; Ajibade F. Bright. Statistical Analysis of Strength of W/S Test of Normality Against Non-normal Distribution Using Monte Carlo Simulation. Am. J. Theor. Appl. Stat. 2017, 6(5-1), 62-65. doi: 10.11648/j.ajtas.s.2017060501.19
Share This Article
Twitter
Linked In
Facebook
Copy
Download@article{10.11648/j.ajtas.s.2017060501.19,
author = {Ukponmwan H. Nosakhare and Ajibade F. Bright},
title = {Statistical Analysis of Strength of W/S Test of Normality Against Non-normal Distribution Using Monte Carlo Simulation},
journal = {American Journal of Theoretical and Applied Statistics},
volume = {6},
number = {5-1},
pages = {62-65},
doi = {10.11648/j.ajtas.s.2017060501.19},
url = {https://doi.org/10.11648/j.ajtas.s.2017060501.19},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2017060501.19},
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.},
year = {2017}
}
TY - JOUR T1 - Statistical Analysis of Strength of W/S Test of Normality Against Non-normal Distribution Using Monte Carlo Simulation AU - Ukponmwan H. Nosakhare AU - Ajibade F. Bright Y1 - 2017/07/11 PY - 2017 N1 - https://doi.org/10.11648/j.ajtas.s.2017060501.19 DO - 10.11648/j.ajtas.s.2017060501.19 T2 - American Journal of Theoretical and Applied Statistics JF - American Journal of Theoretical and Applied Statistics JO - American Journal of Theoretical and Applied Statistics SP - 62 EP - 65 PB - Science Publishing Group SN - 2326-9006 UR - https://doi.org/10.11648/j.ajtas.s.2017060501.19 AB - 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. VL - 6 IS - 5-1 ER -
Email: