Differences Between Pearson’s Product Moment Correlation Coefficient and An Absolute Value Correlation Coefficient in the Presence of Outliers

  • Norafefah Mohamad Sobri 6Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Kelantan, Bukit Ilmu, Machang, Kelantan, Malaysia
  • Prof Dr. Habshah Midi Faculty of Sciences, University Putra Malaysia
  • Nurul Bariyah Ibrahim Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Kelantan, Bukit Ilmu, Machang, Kelantan, Malaysia
  • Nor Azima Ismail Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Kelantan, Bukit Ilmu, Machang, Kelantan, Malaysia
  • Wan Faizah Wan Yaacob Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Kelantan, Bukit Ilmu, Machang, Kelantan, Malaysia
  • Mohd Azry Abdul Malik Faculty of Computer and Mathematical Sciences, Universiti Teknologi MARA Kelantan, Bukit Ilmu, Machang, Kelantan, Malaysia
Keywords: Absolute Value Correlation Coefficient, contaminated, Pearson’s Correlation Coefficient, outliers

Abstract

The correlation coefficient is one of the most commonly used statistical measures in all branches of statistics. The empirical evidence shows that this correlation coefficient is sufficiently non-robust against outliers. The aim of this study is to compare the performance of the estimator of correlation coefficient. In this study, Pilot-plant data was considered at first stage. Second stage of this study, the simulation data were generated based on normal and uniform distribution at its four contaminated form. The methods of analysis used in this study were Pearson’s correlation coefficient and An Absolute Value correlation coefficient. It can be conclude that an Absolute Value correlation coefficient performs well and more robust compared to Pearson’s correlation coefficient in existence of outliers. Then we investigated the bias, standard error (SE) and root mean square error (RMSE) to judge their performance. The result shows that an Absolute Value performs better than Pearson’s correlation coefficient. In general An Absolute Value correlation coefficient appears to be a good estimator because it has the lowest values of bias, standard error and RMSE.

Published
2016-06-10