A Comparison of the Pearson, Spearman Rank and Kendall Tau Correlation Coefficients Using Quantitative Variables

Abstract

In all fields and branches of sciences especially statistics, the correlation coefficient is one of the most often used statistical measures. This study has been carried out for comparing the performances of the Pearson (), Spearman's Rank (), and Kendall’s Tau () correlation coefficients under three sample sizes based on the data of quantitative variables of cotton. Descriptive statistics showed the presence of genetic variability for the cotton studied traits in this study. The quantity, significance, and direction of the correlation calculated by  differed in some cases from the other methods under the three sample sizes, opposite is true for  and . The highest number of positive correlations among studied traits were by  under N = 30 observations, and by   and  under N = 20 observations. The studied correlation methods performances by Root Mean Square Error (RMSE) revealed that  and  appear to be a good estimator of correlation because they have the lowest values of RMSE. The highest values of RMSE were observed by  and   under N=10 and N=20, and by   under N=30. The results of PCA could be useful and appropriate in this study, in which the PCA1 had highly positively correlated with the three studied methods for N=10 observations, and with  and  for N=20 observations.