The rank correlation coefficient (Rs) is used to measure what?

• A. The linear correlation between two variables
• B. The correlation between the rankings of two distributions
• C. The variance of the residuals
• D. The covariance of X and Y

Answer: (B)

Rank correlation tests how well the orderings of two sets of data agree. It converts the data to ranks and then measures the association between those ranks, so it captures monotonic relationships rather than just straight-line (linear) relationships. This makes it ideal when the data are ordinal or when the relationship isn’t perfectly linear or when outliers would distort a linear fit. A perfect positive ranking agreement gives a value of 1, a perfect inverse ranking gives -1, and no consistent ordering gives around 0. So Rs is specifically about the correlation between the rankings of two distributions, not the actual values, not the variance of residuals, and not the covariance of X and Y.