On the Performance Evaluation of Different Measures of Association

• MUHAMMAD RIAZ ^[2] ; SHAHZAD MUNIR ^[1] ; ZAHID ASGHAR ^[1]
  1. [1] Quaid-i-Azam University

     Quaid-i-Azam University

     Pakistán

     
  2. [2] King Fahad University of Petroleum and Minerals Department of Mathematics and Statistics
• Localización: Revista Colombiana de Estadística, ISSN-e 2389-8976, ISSN 0120-1751, Vol. 37, Nº. 1, 2014, págs. 1-24
• Idioma: inglés
• DOI: 10.15446/rce.v37n1.44353
• Títulos paralelos:
  • Evaluación de diferentes medidas de asociación
• Enlaces
  • Texto completo
• Resumen
  • español

    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.

  • English

    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.

• Referencias bibliográficas
  • Daniel, W. W.. (1990). Applied Nonparametric Statistics. Duxbury Classic Series.
  • Gauthier, T. D.. (2001). 'Detecting the trends using the Spearman's rank correlation coefficient'. Environmental Forensics. 2....
  • 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...
  • Mudelsee, M.. (2003). 'Estimating Pearson's correlation coefficient with bootstrap confidence interval from serially dependent time...
  • Munir, S.,Asghar, Z.,Riaz, M.. (2011). 'Performance evaluation of different tests for location parameters'. Communications in Statistics-Simulation...
  • 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...
  • Yitzhaki, S.. (2003). 'Gini mean difference: a superior measure of variability for non normal distribution'. Metron-International...
  • Zimmerman, D. W.. (1994). 'A note on modified rank correlation'. Journal of Educational and Behavioral Statistics. 19. 357-362