Question

When is using Spearman's rank correlation coefficient preferred over Pearson's correlation coefficient?

a) is generally a bad idea because ranks convey less information
b) may produce a better measure of correlation if one variable is highly skewed
c) both of the above
d) none of the above

Answer 1

The use of Spearman's rank correlation coefficient is preferred over Pearson's when dealing with highly skewed variables or when parametric assumptions are not met. It measures the strength of a monotonic relationship using ranked data. Correlation is weakest when the coefficient is closest to 0.

Step-by-step explanation:

Spearman's rank correlation coefficient is preferred over Pearson's correlation coefficient in certain circumstances, notably when one variable is highly skewed. This indicates that option (b) 'may produce a better measure of correlation if one variable is highly skewed' is the correct answer.

Spearman's rank correlation is designed to be used when the data do not meet the assumptions necessary for the Pearson's correlation coefficient, which requires that both variables have a normal distribution and a linear relationship. When the data are ranked rather than using the raw data, Spearman's helps to measure the strength of a monotonic relationship where data are non-parametric. In other cases where there are significant outliers or the measurements are on an ordinal scale, Spearman's can be more appropriate.

It's worth noting that the correlation coefficient indicates the weakest relationship when it is closest to 0, which would make option (a) the correct choice for the second part of the question.