Empirical Power Comparism of Three Correlation Coefficients

Abstract

A Comparison of Pearson's moment (r), Kendall's (t) and the Spearman's rank (r2) correlations was made to find out when they may be suitable for use, particularly when the assumptions that support their use are violated. Bi-variate Samples of size n = 5, 10, 15, 20, 25, 30, 40, 50 and 100 from the normal and exponential distributions with population correlation values of p = 0, 0.25, 0.5, 0.75 and 0.9 (chosen to represent positive correlation between 0 and 1) were used. The power function for a = 0.01 and 0.05 was calculated for the tests. For the normal distribution, the Pearson's moment correlation coefficient was discovered to be the more powerful. However, in the exponential distribution, the power of the Pearson's moment correlation coefficient was lower than those of the non-parametric correlation coefficients, except for small sample sizes i.e, n≤15.