Rank Correlation Coefficient

Spearman’s Rank Correlation Coefficient

Spearman's correlation coefficient, (ρ - Rho), measures the strength of association between two ranked variables. Data which are arranged in numerical order, usually from largest to smallest and numbered 1,2,3____ are said to be in ranks or ranked data.

These ranks prove useful at certain times when two or more values of one variable are the same. The coefficient of correlation for such type of data is given by Spearman rank difference correlation coefficient.

This measure is useful in dealing with qualitative characteristics, such as intelligence, beauty, morality, colour, etc.

✒️ The numerical value of the correlation coefficient, ρ ranges between -1 and +1

✒️ ρ   > 0 implies positive agreement among ranks 

✒️ ρ  < 0 implies negative agreement

✒️ ρ = 0 implies no agreement 

✒️ Closer   ρ  is to 1, better is the agreement while   ρ  closer to -1 indicates strong agreement in the reverse direction.

The Formula is,

ρ = 1 − 6∑D²/N(N²-1)

D= Difference in ranks

N= No. of pairs of observations