Rank correlation

Let us suppose that a group of n individuals is arranged in order of merit or proficiency in possession of two characteristics A and B. these ranks in two characteristics will, in general, be different. For example, if we consider the relation between intelligence and beauty, it is not necessary that a beautiful individual is intelligent also. Let (x_{i},y_{i}); i=1,2,………,n be the ranks of the ith individual in two characteristics A and B respectively. Pearson coefficient of correlation between the ranks x_{i}’s and y_{i} ‘s is called the rank correlation coefficient between A and B for that group of individuals.

Assuming that no two individuals are bracketed equal in either classification, each of the variables X and Y takes the values 1,2,………..,n

Hence,

In general x_{i} ≠ y_{i} . Let d_{i} =x_{i} -y_{i}

Squaring and summin over I form 1 to n, we get

Dividing both side by n, we get

Where is the rank correlation coefficient between A and B.

Which is the spearman’s formula for the rank correlation coefficient.

Sub Category