A New Non-parametric Test Procedure for the Median of an Asymmetrical Population

Mohammad Ibrahim Ahmmad Soliman Gaafar

doi:doi:10.11648/j.ajtas.20160506.17

| Peer-Reviewed

A New Non-parametric Test Procedure for the Median of an Asymmetrical Population

Mohammad Ibrahim Ahmmad Soliman Gaafar

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 6)

Received: 11 October 2016 Accepted: 25 October 2016 Published: 17 November 2016

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This paper proposes and investigates the performance of a new non-parametric test procedure for the median of a non-normal population when the symmetry assumption is suspected. The new test procedure uses the Yeo-Johnson family of power transformations and the Shapiro-Wilk test of normality to modify the classical normal scores test. Under skewed models, simulation results show that the proposed test procedure is superior to all competitor tests under consideration in terms of preserving the empirical size of the test at its nominal level and also having higher empirical powers.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 6)
DOI	10.11648/j.ajtas.20160506.17
Page(s)	376-386
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), 2024. Published by Science Publishing Group

Keywords

Power Transformations, Non-parametric Procedures, The Normal Scores Test, The Wilcoxon Signed Ranks Test, The Sign Test, The Shapiro-Wilk Test

References

[1]	Baklizi, A. (2005). A Continuously Adaptive Rank Test for Shift in Location. Australian and New Zealand Journal of Statistics, 47, 203-209.
[2]	Box, G. E. P. and Cox, D. R. (1964). Analysis of Transformations. Journal of the Royal Statitical Society, Ser. B, 26, 211-252.
[3]	Doksum, K. A. and Wong, C. W. (1983). Statistical Tests Based on Transformed Data. Journal of the American Statistical Association, 78, 411-417.
[4]	Fraser, D. A. S. (1957b). Most Powerful Rank-Type Tests. Annals of Mathematical Statistics, 28, 1040-1043.
[5]	Freidlin, B., Miao, W., and Gastwirth, J. L. (2003). On The Use of the Shapiro-Wilk Test in Two-Stage Adaptive Inference for Paired Data from Moderate to Very Heavy Tailed Distributions. Biometrical Journal, 45, 887-900.
[6]	Gastwirth, J. L .(1966). On Robust Procedures. Journal of the American Statistical Association, 61, 929-948.
[7]	Halawa, A. M. (1989). Testing for Location after Transformation to Normality. Ph.D. thesis (unpublished), Oregon State University, Oregon, U.S.A.
[8]	Halawa, A. M. (2001). A Test of the Median after the Two-domain Transformation. Journal of the Faculty of Commerce for Scientific Research, 38 (1), 29-41.
[9]	Harter, H. L. (1961). Expected Values of Normal Order Statistics. Biometrika, 48, 1 and 2, 151–165.
[10]	Hollander, M., Wolfe, D. A., and Chicken, E. (2014). Nonparametric Statistical Methods. New York: John Wiley & Sons.
[11]	John, J. A. and Draper, N. R. (1980). An Alternative Family of Transformations. Applied Statistics, 29, 190–197.
[12]	Randles, R. H. and Wolfe, D. A. (1979). Introduction to the Theory of Nonparametric Statistics. New York: John Wiley & Sons.
[13]	Randles, R. H., Fligner, M., Policello, G., and Wolfe, D. (1980). An Asymptotically Distribution-Free Test for Symmetry versus Asymmetry. Journal of the American Statistics Association 75 (369), 168–172.
[14]	Royston, J. P. (1982). An Extension of Shapiro and Wilk’s Test for Normality to Large Samples. Applied Statistics, 31, 115–124.
[15]	Shapiro, S. S. and Wilk, M. B. (1965). An Analysis of Variance Test for Normality (Complete Samples). Biometrika, 52, 591–611.
[16]	Van Zwet, W. R. (1964). Convex Transformations of Random Variables. Amsterdam, Mathematisch Centrum.
[17]	Yeo, I. K. and Johnson, R. A. (2000). A New Family of Power Transformations to Improve Normality and Symmetry. Biometrika, 87, 954–959.

Cite This Article

Plain Text BibTeX RIS

APA Style

Mohammad Ibrahim Ahmmad Soliman Gaafar. (2016). A New Non-parametric Test Procedure for the Median of an Asymmetrical Population. American Journal of Theoretical and Applied Statistics, 5(6), 376-386. https://doi.org/10.11648/j.ajtas.20160506.17

Copy | Download

ACS Style

Mohammad Ibrahim Ahmmad Soliman Gaafar. A New Non-parametric Test Procedure for the Median of an Asymmetrical Population. Am. J. Theor. Appl. Stat. 2016, 5(6), 376-386. doi: 10.11648/j.ajtas.20160506.17

Copy | Download

AMA Style

Mohammad Ibrahim Ahmmad Soliman Gaafar. A New Non-parametric Test Procedure for the Median of an Asymmetrical Population. Am J Theor Appl Stat. 2016;5(6):376-386. doi: 10.11648/j.ajtas.20160506.17

Copy | Download

@article{10.11648/j.ajtas.20160506.17,
  author = {Mohammad Ibrahim Ahmmad Soliman Gaafar},
  title = {A New Non-parametric Test Procedure for the Median of an Asymmetrical Population},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {6},
  pages = {376-386},
  doi = {10.11648/j.ajtas.20160506.17},
  url = {https://doi.org/10.11648/j.ajtas.20160506.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160506.17},
  abstract = {This paper proposes and investigates the performance of a new non-parametric test procedure for the median of a non-normal population when the symmetry assumption is suspected. The new test procedure uses the Yeo-Johnson family of power transformations and the Shapiro-Wilk test of normality to modify the classical normal scores test. Under skewed models, simulation results show that the proposed test procedure is superior to all competitor tests under consideration in terms of preserving the empirical size of the test at its nominal level and also having higher empirical powers.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - A New Non-parametric Test Procedure for the Median of an Asymmetrical Population
AU  - Mohammad Ibrahim Ahmmad Soliman Gaafar
Y1  - 2016/11/17
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160506.17
DO  - 10.11648/j.ajtas.20160506.17
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  - 376
EP  - 386
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160506.17
AB  - This paper proposes and investigates the performance of a new non-parametric test procedure for the median of a non-normal population when the symmetry assumption is suspected. The new test procedure uses the Yeo-Johnson family of power transformations and the Shapiro-Wilk test of normality to modify the classical normal scores test. Under skewed models, simulation results show that the proposed test procedure is superior to all competitor tests under consideration in terms of preserving the empirical size of the test at its nominal level and also having higher empirical powers.
VL  - 5
IS  - 6
ER  -

Copy | Download

Author Information

Mohammad Ibrahim Ahmmad Soliman Gaafar

Department of Statistics, Faculty of Commerce, Alexandria University, Alexandria, Egypt

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Mohammad Ibrahim Ahmmad Soliman Gaafar. (2016). A New Non-parametric Test Procedure for the Median of an Asymmetrical Population. American Journal of Theoretical and Applied Statistics, 5(6), 376-386. https://doi.org/10.11648/j.ajtas.20160506.17

Copy | Download

ACS Style

Mohammad Ibrahim Ahmmad Soliman Gaafar. A New Non-parametric Test Procedure for the Median of an Asymmetrical Population. Am. J. Theor. Appl. Stat. 2016, 5(6), 376-386. doi: 10.11648/j.ajtas.20160506.17

Copy | Download

AMA Style

Mohammad Ibrahim Ahmmad Soliman Gaafar. A New Non-parametric Test Procedure for the Median of an Asymmetrical Population. Am J Theor Appl Stat. 2016;5(6):376-386. doi: 10.11648/j.ajtas.20160506.17

Copy | Download

@article{10.11648/j.ajtas.20160506.17,
  author = {Mohammad Ibrahim Ahmmad Soliman Gaafar},
  title = {A New Non-parametric Test Procedure for the Median of an Asymmetrical Population},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {6},
  pages = {376-386},
  doi = {10.11648/j.ajtas.20160506.17},
  url = {https://doi.org/10.11648/j.ajtas.20160506.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20160506.17},
  abstract = {This paper proposes and investigates the performance of a new non-parametric test procedure for the median of a non-normal population when the symmetry assumption is suspected. The new test procedure uses the Yeo-Johnson family of power transformations and the Shapiro-Wilk test of normality to modify the classical normal scores test. Under skewed models, simulation results show that the proposed test procedure is superior to all competitor tests under consideration in terms of preserving the empirical size of the test at its nominal level and also having higher empirical powers.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - A New Non-parametric Test Procedure for the Median of an Asymmetrical Population
AU  - Mohammad Ibrahim Ahmmad Soliman Gaafar
Y1  - 2016/11/17
PY  - 2016
N1  - https://doi.org/10.11648/j.ajtas.20160506.17
DO  - 10.11648/j.ajtas.20160506.17
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  - 376
EP  - 386
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20160506.17
AB  - This paper proposes and investigates the performance of a new non-parametric test procedure for the median of a non-normal population when the symmetry assumption is suspected. The new test procedure uses the Yeo-Johnson family of power transformations and the Shapiro-Wilk test of normality to modify the classical normal scores test. Under skewed models, simulation results show that the proposed test procedure is superior to all competitor tests under consideration in terms of preserving the empirical size of the test at its nominal level and also having higher empirical powers.
VL  - 5
IS  - 6
ER  -

Copy | Download