Q.Write a short note on: Rank correlation.

Rank correlation measures the closeness of relationship between two variables ranked in order rather than measured exactly, and is especially useful for qualitative data such as beauty, honesty or intelligence. It is computed by Spearman's coefficient, which lies between minus one and plus one. This is an AP Intermediate 2nd-year Economics (statistics) topic.

Meaning: Rank correlation is a method of measuring the degree of association between two variables when their values are given, or can be arranged, in the form of ranks or orders of merit rather than precise numerical measurements. It was developed by the statistician Charles Edward Spearman, and so the measure is called Spearman's rank-correlation coefficient.

Formula: Spearman's rank-correlation coefficient (usually denoted R) is calculated as follows: R equals one minus the quantity six times the sum of the squares of the differences between the ranks of the two variables, divided by n multiplied by (n squared minus one), where the difference for each pair is the rank of the first variable minus the rank of the second, and n is the number of pairs of observations.

Features and uses:

1. Its value lies between minus one and plus one — plus one meaning perfect positive rank agreement, minus one meaning perfect negative (reverse) agreement, and zero meaning no rank correlation.
2. It is especially useful for qualitative data such as beauty, intelligence, honesty or efficiency, which cannot be measured numerically but can be ranked. …