When is rank correlation more precise than simple correlation coefficient?
Rank correlation is more precise than simple correlation coefficient in two main situations.
First, when the data contains extreme values. Spearman's correlation coefficient is not affected by extreme values, making it better than Karl Pearson's correlation coefficient in such cases. Thus, if the data contains some extreme values, rank correlation proves to be very useful.
Second, when there is a non-linear relationship between variables where the direction is clear. In such cases, Spearman's rank correlation coefficient can be effectively used to estimate the correlation. However, generally rank correlation is not as accurate as the ordinary method because all the information concerning the data is not utilised.
Explanation
The textbook explicitly mentions two situations where Spearman's rank correlation is better than Karl Pearson's simple correlation coefficient: (1) when data contains extreme values, as rank correlation is not affected by them, and (2) when there is a non-linear relationship with clear direction. The context also notes that generally rank correlation is less accurate than the ordinary method since it doesn't utilise all information about the data.