Confidence Intervals for Partial Rank Correlations

Abstract

A partial rank correlation coefficient T⁽ⁿ⁾ _XY|Z , based on comparing pairs for which the values of the conditioning variable follow each other in a numerical ordering, is studied. Simulation results show that it is possible to obtain reasonably good confidence intervals by estimating σ ²/(1 − τ ² _XY|Z ). The advantage of using the coefficient T⁽ⁿ⁾ _XY|Z is that it is always clear what this coefficient measures, in contrast to, for example, Pearson's, Spearman's, or Kendall's partial correlation coefficients, which can give values far from 0 even in cases of conditional independence. The main disadvantage is that the asymptotic efficiency relative to the sample partial correlation coefficient (in the case of trivariate normal variables) is never higher than .33. Coefficients like T⁽ⁿ⁾ _XY|Z have been studied by Goodman and by Quade.

Key Words:

• Asymptotic distribution
• Confidence intervals
• Partial correlation
• Rank correlation