Kendall's tau is a non-parametric correlation coefficient best described as?

• A. Pearson correlation
• B. Spearman's rho
• C. Phi coefficient
• D. Kendall's tau

Answer: (D)

Kendall's tau is a non-parametric measure of association that uses the ranks of the data and focuses on how two variables move together. For each pair of observations, you determine if the pair is concordant (the order of the two variables agrees) or discordant (the order disagrees). Tau is essentially the difference between the probability of concordance and the probability of discordance, yielding a value from -1 to 1. A value near 1 means strong positive association in ranks, near -1 indicates strong negative association, and around 0 means little to no association. Because it relies on ranks rather than raw scores, it doesn’t assume normality or linearity and is suitable for ordinal data or non-normal distributions. There are adjustments for ties (tau-b and tau-c) to improve accuracy when data contain tied ranks. This contrasts with Pearson correlation, which assumes a linear relationship and normally distributed data, and with the Phi coefficient, which is used for binary data. Spearman's rho is another rank-based non-parametric measure, computed differently from Kendall's tau.