Published

2014-01-01

On the Performance Evaluation of Different Measures of Association

Evaluación de diferentes medidas de asociación

DOI:

https://doi.org/10.15446/rce.v37n1.44353

Keywords:

Measures of association, Non-Normality, Non-Parametric methods, Normality, Parametric methods, Power. (en)
medidas de asociación, no normalidad, métodos no paramétricos, métodos paramétricos, potencia (es)

Downloads

Authors

  • Muhammad Riaz King Fahad University of Petroleum and Minerals
  • Shahzad Munir Quaid-i-Azam University
  • Zahid Asghar Quaid-i-Azam University

In this article our objective is to evaluate the performance of different measures of associations for hypothesis testing purposes. We have considered different measures of association (including some commonly used) in this study, one of which is parametric and others are non-parametric including three proposed modifications. Performance of these tests are compared under different symmetric, skewed and contaminated probability distributions that include Normal, Cauchy, Uniform, Laplace, Lognormal, Exponential, Weibull, Gamma, t, Chi-square, Half Normal, Mixed Weibull and Mixed Normal. Performances of these tests are measured in terms of power. We have suggested appropriate tests which may perform better under different situations based on their efficiency grading(s). It is expected that researchers will find these results useful in decision making.

En este articulo el objetivo es evaluar el desempeño de diferentes medidas de asociación para pruebas de hipótesis. Se consideran diferentes medidas, algunas paramétricas y otras no paramétricas, así como tres modificaciones propuestas por los autores. El desempeño de estas pruebas se evalúa considerando distribuciones simétricas, sesgadas y contaminadas incluyendo la distribución normal, Cauchy, uniforme, Laplace, lognormal, exponencial, Weibull, Gamma, t, Chi-cuadrado, medio normal, Weibull mezclada y normal mezclada. El desempeño se evalúa en términos de la potencia de los
tests. Se sugieren tests apropiados que tienen un mejor desempeño bajo diferentes niveles de eficiencia. Se espera que los investigadores encuentren

estos resultados útiles en la toma de decisiones.

https://doi.org/10.15446/rce.v37n1.44353

On the Performance Evaluation of Different Measures of Association

Evaluación de diferentes medidas de asociación

MUHAMMAD RIAZ1, SHAHZAD MUNIR2, ZAHID ASGHAR3

1King Fahad University of Petroleum and Minerals, Department of Mathematics and Statistics, Dhahran, Saudi Arabia. Professor. Email: riaz76qau@yahoo.com
2Quaid-i-Azam University, Department of Statistics, Islamabad, Pakistan. Professor. Email: farhan.saif@qau.edu.pk
3Quaid-i-Azam University, Department of Statistics, Islamabad, Pakistan. Professor. Email: g.zahid@gmail.com

Abstract

In this article our objective is to evaluate the performance of different measures of associations for hypothesis testing purposes. We have considered different measures of association (including some commonly used) in this study, one of which is parametric and others are non-parametric including three proposed modifications. Performance of these tests are compared under different symmetric, skewed and contaminated probability distributions that include Normal, Cauchy, Uniform, Laplace, Lognormal, Exponential, Weibull, Gamma, t, Chi-square, Half Normal, Mixed Weibull and Mixed Normal. Performances of these tests are measured in terms of power. We have suggested appropriate tests which may perform better under different situations based on their efficiency grading(s). It is expected that researchers will find these results useful in decision making.

Key words: Measures of association, Non-Normality, Non-Parametric methods, Normality, Parametric methods, Power.

Resumen

En este articulo el objetivo es evaluar el desempeño de diferentes medidas de asociación para pruebas de hipótesis. Se consideran diferentes medidas, algunas paramétricas y otras no paramétricas, así como tres modificaciones propuestas por los autores. El desempeño de estas pruebas se evalúa considerando distribuciones simétricas, sesgadas y contaminadas incluyendo la distribución normal, Cauchy, uniforme, Laplace, lognormal, exponencial, Weibull, Gamma, t, Chi-cuadrado, medio normal, Weibull mezclada y normal mezclada. El desempeño se evalúa en términos de la potencia de los tests. Se sugieren tests apropiados que tienen un mejor desempeño bajo diferentes niveles de eficiencia. Se espera que los investigadores encuentren estos resultados útiles en la toma de decisiones.

Palabras clave: medidas de asociación, no normalidad, métodos no paramétricos, métodos paramétricos, potencia.

Texto completo disponible en PDF

References

1. Daniel, W. W. (1990), Applied Nonparametric Statistics, Duxbury Classic Series, New York.

2. Gauthier, T. D. (2001), 'Detecting the trends using the Spearman's rank correlation coefficient', Environmental Forensics 2, 359-362.

3. Kendall, M. G. (1938), 'A new measure of rank correlation', Biometrika 5, 81-93.

4. Mahoney, M. & Magel, R. (1996), 'Estimation of the power of the Kruskal-Wallis test', Biometrical Journal 38, 613-630.

5. Maturi, T. A. & Elsayigh, A. (2010), 'A comparison of correlation coefficients via a three-step bootstrap approach', Journal of Mathematics Research 2, 3-10.

6. Mudelsee, M. (2003), 'Estimating Pearson's correlation coefficient with bootstrap confidence interval from serially dependent time series', Mathematical Geology 35, 651-665.

7. Munir, S., Asghar, Z. & Riaz, M. (2011), 'Performance evaluation of different tests for location parameters', Communications in Statistics-Simulation and Computation 40(6), 839-853.

8. Spearman, C. (1904), 'The proof and measurement of association between two things', American Journal of Psychology 15, 73-101.

9. Walker, D. A. (2003), 'JMASM9: converting Kendall's tau for correlational or meta-analytic analyses', Journal of Modern Applied Statistical Methods 2, 525-530.

10. Yitzhaki, S. (2003), 'Gini mean difference: a superior measure of variability for non normal distribution', Metron-International Journal of Statistics LXI, 285-316.

11. Zimmerman, D. W. (1994), 'A note on modified rank correlation', Journal of Educational and Behavioral Statistics 19, 357-362.

[Recibido en agosto de 2012. Aceptado en noviembre de 2013]

Este artículo se puede citar en LaTeX utilizando la siguiente referencia bibliográfica de BibTeX:

@ARTICLE{RCEv37n1a01,
    AUTHOR  = {Riaz, Muhammad and Munir, Shahzad and Asghar, Zahid},
    TITLE   = {{On the Performance Evaluation of Different Measures of Association}},
    JOURNAL = {Revista Colombiana de Estadística},
    YEAR    = {2014},
    volume  = {37},
    number  = {1},
    pages   = {1-24}
}

References

Daniel, W. W. (1990), Applied Nonparametric Statistics, Duxbury Classic Series, New York.

Gauthier, T. D. (2001), ‘Detecting the trends using the Spearman’s rank correlation coefficient’, Environmental Forensics 2, 359–362.

Kendall, M. G. (1938), ‘A new measure of rank correlation’, Biometrika 5, 81–93.

Mahoney, M. & Magel, R. (1996), ‘Estimation of the power of the Kruskal-Wallis test’, Biometrical Journal 38, 613–630.

Maturi, T. A. & Elsayigh, A. (2010), ‘A comparison of correlation coefficients via a three-step bootstrap approach’, Journal of Mathematics Research 2, 3–10.

Mudelsee, M. (2003), ‘Estimating Pearson’s correlation coefficient with bootstrap confidence interval from serially dependent time series’, Mathematical Geology 35, 651–665.

Munir, S., Asghar, Z. & Riaz, M. (2011), ‘Performance evaluation of different tests for location parameters’, Communications in Statistics-Simulation and Computation 40(6), 839–853.

Spearman, C. (1904), ‘The proof and measurement of association between two things’, American Journal of Psychology 15, 73–101.

Walker, D. A. (2003), ‘JMASM9: Converting Kendall’s tau for correlational or meta-analytic analyses’, Journal of Modern Applied Statistical Methods 2, 525–530.

Yitzhaki, S. (2003), ‘Gini mean difference: A superior measure of variability for non normal distribution’, Metron-International Journal of Statistics LXI, 285–316.

Zimmerman, D. W. (1994), ‘A note on modified rank correlation’, Journal of Educational and Behavioral Statistics 19, 357–362.

How to Cite

APA

Riaz, M., Munir, S. and Asghar, Z. (2014). On the Performance Evaluation of Different Measures of Association. Revista Colombiana de Estadística, 37(1), 1–24. https://doi.org/10.15446/rce.v37n1.44353

ACM

[1]
Riaz, M., Munir, S. and Asghar, Z. 2014. On the Performance Evaluation of Different Measures of Association. Revista Colombiana de Estadística. 37, 1 (Jan. 2014), 1–24. DOI:https://doi.org/10.15446/rce.v37n1.44353.

ACS

(1)
Riaz, M.; Munir, S.; Asghar, Z. On the Performance Evaluation of Different Measures of Association. Rev. colomb. estad. 2014, 37, 1-24.

ABNT

RIAZ, M.; MUNIR, S.; ASGHAR, Z. On the Performance Evaluation of Different Measures of Association. Revista Colombiana de Estadística, [S. l.], v. 37, n. 1, p. 1–24, 2014. DOI: 10.15446/rce.v37n1.44353. Disponível em: https://revistas.unal.edu.co/index.php/estad/article/view/44353. Acesso em: 28 mar. 2025.

Chicago

Riaz, Muhammad, Shahzad Munir, and Zahid Asghar. 2014. “On the Performance Evaluation of Different Measures of Association”. Revista Colombiana De Estadística 37 (1):1-24. https://doi.org/10.15446/rce.v37n1.44353.

Harvard

Riaz, M., Munir, S. and Asghar, Z. (2014) “On the Performance Evaluation of Different Measures of Association”, Revista Colombiana de Estadística, 37(1), pp. 1–24. doi: 10.15446/rce.v37n1.44353.

IEEE

[1]
M. Riaz, S. Munir, and Z. Asghar, “On the Performance Evaluation of Different Measures of Association”, Rev. colomb. estad., vol. 37, no. 1, pp. 1–24, Jan. 2014.

MLA

Riaz, M., S. Munir, and Z. Asghar. “On the Performance Evaluation of Different Measures of Association”. Revista Colombiana de Estadística, vol. 37, no. 1, Jan. 2014, pp. 1-24, doi:10.15446/rce.v37n1.44353.

Turabian

Riaz, Muhammad, Shahzad Munir, and Zahid Asghar. “On the Performance Evaluation of Different Measures of Association”. Revista Colombiana de Estadística 37, no. 1 (January 1, 2014): 1–24. Accessed March 28, 2025. https://revistas.unal.edu.co/index.php/estad/article/view/44353.

Vancouver

1.
Riaz M, Munir S, Asghar Z. On the Performance Evaluation of Different Measures of Association. Rev. colomb. estad. [Internet]. 2014 Jan. 1 [cited 2025 Mar. 28];37(1):1-24. Available from: https://revistas.unal.edu.co/index.php/estad/article/view/44353

Download Citation

CrossRef Cited-by

CrossRef citations5

1. Rana A. Bakoban. (2017). Estimation for coefficient of variation of an extension of the exponential distribution under type-II censoring scheme. Open Physics, 15(1), p.566. https://doi.org/10.1515/phys-2017-0065.

2. Edoardo Saccenti. (2023). Metabolomics. , p.59. https://doi.org/10.1007/978-3-031-39094-4_3.

3. Liliana López-Kleine, Cristian González-Prieto. (2016). Challenges Analyzing RNA-Seq Gene Expression Data. Open Journal of Statistics, 06(04), p.628. https://doi.org/10.4236/ojs.2016.64053.

4. Muhammad Muzzamil Hussain Khattak, Muhammad Asif Khan, Sameer Ud Din, Muhammad Zaheer Khan, Muhammad Faisal Habib. (2023). Examining equity of walking accessibility to green spaces: A case study of Islamabad. Ain Shams Engineering Journal, 14(12), p.102556. https://doi.org/10.1016/j.asej.2023.102556.

5. René Lehmann, Bodo Vogt. (2024). Improving Likert scale big data analysis in psychometric health economics: reliability of the new compositional data approach. Brain Informatics, 11(1) https://doi.org/10.1186/s40708-024-00232-z.

Dimensions

PlumX

Plum Print visual indicator of research metrics
  • Citations
  • CrossRef - Citation Indexes: 4
  • Scopus - Citation Indexes: 4
  • Usage
  • SciELO - Full Text Views: 2154
  • SciELO - Abstract Views: 1628
  • Captures
  • Mendeley - Readers: 3
  • Social Media
  • Facebook - Shares, Likes & Comments: 289
-
see details

Article abstract page views

746

Downloads

License

Copyright (c) 2014 Revista Colombiana de Estadística

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).