Ties Adjusted Rank Correlation Coefficient

Abstract

This paper proposes, develops and presents a method that may be used to adjust and correct sample estimates of the usual spearman rank correlation coefficient for the possible presence of tied observation in the sampled populations. Without these adjustments the sums of squares of ranks in the denominator of the usual expression for the estimation of spearman rank correlation coefficients are often over estimated if there are ties in the populations and no effort is made to correct and adjust for them especially if these ties are not few, resulting in inefficient, unreliable and often misleading estimates. The proposed method is shows to be easily modified and applied to estimate ties adjusted spearman partial rank correlation coefficient between any two populations holding observations from a third population at constant levels with all the populations adjusted for the possible presence of tied observations. The usual statistical tests for significance are also easily modified using the ties adjusted rank correlation coefficients in place of the unadjusted and usual rank correlation coefficients. The proposed method is illustrated with some sample data and shows to produce more efficient estimates than the usual ties unadjusted uncorrected spearman rank correlation coefficients.