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Ahmed Alsayed
Giancarlo Manzi

Author(s) and WSEAS

Ahmed Alsayed
Giancarlo Manzi

WSEAS Transactions on Computers

Print ISSN: 1109-2750
E-ISSN: 2224-2872

Volume 18, 2019

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

A Comparison of Monotonic Correlation Measures with Outliers

AUTHORS: Ahmed Alsayed, Giancarlo Manzi

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ABSTRACT: This paper aims at examining the performance of a recently proposed measure of dependence – the Monotonic Dependence Coefficient – MDC - with respect to classical monotonic correlation measures like Pearson’s r, Spearman’s ߩ ,and Kendall’s τ, using simulated outlier contaminated and non-contaminated data sets as well as a contaminated real dataset, considering three different cases. This comparison aims at checking how and when these coefficients detect dependence relationships between two variables when outliers are present. Several scenarios are created with multiple values for the dependence measures, outlier contamination fractions and data patterns. The basic simulated dataset is generated from a bivariate standard normal distribution. Using values generated from the exponential, power-transformed, lognormal, and Weibull distributions, added to the basic generated dataset, we transform the contaminated data, allowing for multiple patterns. The main findings tend to favour the Spearman’s ߩ coefficient for most of the simulated scenarios, especially when the outlier contamination is taken into account, whereas MDC performs better than ߩ in noncontaminated data. However, in the real data scenario Spearman’s ߩ outperforms the other measures in two out of three cases, whereas MDC performs better in the other case.

KEYWORDS: Outliers; Correlation Coefficient; Monotonic Dependence; Monte Carlo Simulation; Environmental Quality; Economic Growth.


[ 1] Kendall MG. The Advanced Theory of Statistics, vol. 1, fourth ed. London: Charles Griffin & Company, 1948.

[2] Fredricks GA, Nelsen RB. On the relationship between Spearman’s rho and Kendall’s tau for pairs of continuous random variables. J Stat Plan Inference. 2007; 137: 2143-2150.

[3] Ferrari PA, Raffinetti E. A Different Approach to Dependence Analysis. Multivar Behav Res, 2015; 50(2): 248-264.

[4] Raffinetti, E, Ferrari, PA. New Perspectives for the MDC Index in Social Research Fields. In Morlini, I., Minerva, T., Vichi, M. (Eds.): Advances in Statistical Models for Data Analysis, Zurich, Switzerland: Springer Verlag: 211-219, 2015.

[5] Bishara AJ, Hittner JB. Reducing bias and error in the correlation coefficient due to nonnormality. Educ Psychol Meas, 2015; 75(5): 785-804.

[6] Bliss CI. Statistics in Biology. New York (NY): McGraw-Hill; 1967.

[7] Rousseeuw PJ, Leroy AM. Robust Regression and Outlier Detection. New York (NY): John Wiley & Sons; 1987.

[8] Abdullah MB. On a Robust Correlation Coefficient. The Statistician, 1990; 39: 455-460.

[9] Osborne JW, Overbay A. The Power of Outliers (and Why Researchers Should Always Check Them). Practical Assessment, Research and Evaluation, 2004; 9(6): 1-8.

[10] Barnett V, Lewis T. Outliers in statistical data. 3rd edition, 1994, Chichester (UK): John Wiley & Sons.

[11] Grubbs FE. Procedures for detecting outlying observations in samples. Technometrics, 1969, 11:1 - 21.

[12] Iglewicz B, Hoaglin D. How to detect and handle outliers. 1993, Milwaukee (WI): ASQC Quality Press.

[13] Vale, C., & Maurelli, V. (1983). Simulating multivariate non-normal distributions. Psychometrika, 48(3), 465–471.

[14] Al Sayed, A. R., Isa, Z., & Kun, S. S. (2018). Outliers Detection Methods in Panel Data Regression: An Application to Environment Science. International Journal of Ecological Economics & Statistics, 39(1), 73-86.

[15] Al Sayed, A. R., & Sek, S. K. (2013). Environmental Kuznets curve: evidences from developed and developing economies. Applied Mathematical Sciences, 7(22), 1081–1092.

[16] Rousseeuw, P. J., and B. C. van Zomeren. 1990. Unmasking multivariate outliers and leverage points. Journal of the American Statistical Association 85: 633–639.

WSEAS Transactions on Computers, ISSN / E-ISSN: 1109-2750 / 2224-2872, Volume 18, 2019, Art. #29, pp. 223-230

Copyright © 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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