Intrinsically Ties Adjusted Tau (C-Tat) Correlation Coefficient
OYEKA CYPRIL ANENE · American Journal of Theoretical and Applied Statistics · 2013
This paper proposes a method for correcting and adjusting the usual or regular estimates of Tau correlation coefficients for the possibility of ties within and between observations in the population being correlated. The index here called C-Tat for ‘ties adjusted Tau correlation coefficient’ is formulated to intrinsically and structurally adjust and correct the estimated Tau correlation coefficient for the possible presence of tied observations in the sampled populations and for the fact that the estimates obtained are often dependent on, that is, vary depending on which of the two populations under study has its assigned ranks arranged in their natural order and which has its assigned ranks arranged in their natural order and which has its assigned ranks tagged along. The proposed method is illustrated with some sample data and shown to yield more reliable and efficient estimates of tau correlation coefficients than the usual method which is able to give the same estimates only if there are no tied observations what-so-ever in the sampled populations.