Question

Why does the rank correlation coefficient differ from the Pearsonian correlation coefficient? 

Answer 1

Generally, all the properties of Karl Pearson’s coefficient of correlation are similar to that of the rank correlation coefficient. However, the rank correlation coefficient is generally lower or equal to Karl Pearson’s coefficient. The rank correlation coefficient is generally preferred to measure the correlation between the two qualitative variables. These variable attributes are given the ranks on the basis of preferences. The difference between the two coefficients is due to the fact that the rank correlation coefficient uses ranks instead of the full set of observations that leads to some loss of information. If the precisely measured data are available, then both the coefficients will be identical. Secondly, if extreme values are present in the data, then the rank correlation coefficient is more precise and reliable and consequently, its value differs from that of Karl Pearson’s coefficient.