. Rank Correlation . . Spearman’s Rank Correlation Coefficient In , Charles Edward Spearman, a British psychologist found out the method of ascertaining the coefficient of correlation by ranks.
This method is based on rank. This measure is useful in dealing with qualitative characteristics, such as intelligence, beauty, morality, character, etc. It cannot be measured quantitatively, as in the case of Pearson’s coefficient of correlation. Rank correlation is applicable only to individual observations.
The result we get from this method is only an approximate one, because under ranking method original value are not taken into account. The formula for Spearman’s rank correlation which is denoted by ρ (pronounced as row) is t = – N N h (or) t = N N where d = The difference of two ranks = R Y and N = Number of paired observations. Rank coefficient of correlation value lies between – and + . Symbolically, – ≤ ρ ≤+ .
When we come across spearman’s rank correlation, we may find two types of problem (i) When ranks are given (ii) When ranks are not given Example . The following are the ranks obtained by students in Statistics and Mathematics Statistics Mathematics Find the rank correlation coefficient. Let R X is considered for the ranks of Statistics and R Y is considered for the ranks of mathematics. - - R X R Y d = R Y d - - - - d