American Journal of Theoretical and Applied Statistics

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Statistical Analysis of Strength of W/S Test of Normality Against Non-normal Distribution Using Monte Carlo Simulation

Received: Feb. 24, 2017    Accepted: Mar. 01, 2017    Published: Jul. 11, 2017
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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.

DOI 10.11648/j.ajtas.s.2017060501.19
Published in American Journal of Theoretical and Applied Statistics ( Volume 6, Issue 5-1, September 2017 )

This article belongs to the Special Issue Statistical Distributions and Modeling in Applied Mathematics

Page(s) 62-65
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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), 2024. Published by Science Publishing Group

Keywords

Range, Standard Deviation, Descriptive Statistics, Simulation, Power-of-Test

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.
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    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

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    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

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    AMA 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

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  • @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://download.sciencepg.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}
    }
    

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Author Information
  • Department of General Studies, Mathematics and Computer Science Unit, Petroleum Training Institute, Warri, Nigeria

  • Department of General Studies, Mathematics and Computer Science Unit, Petroleum Training Institute, Warri, Nigeria

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