Rank Correlation:
When the variables under consideration are not capable of quantitative measurement but can be arranged in serial order (ranks), we find correlation between the ranks of two series. This happens when we deal with qualitative characteristics such as honesty, beauty, etc. This method is called Spearman’s Rank Difference Method or Ranking Method and the correlation coefficient so obtained is called Rank Correlation Coefficient and is denoted by rs. This method was developed by Charles Edward Spearman, a British Psychologist in 1904. Spearman’s rank correlation coefficient is also used when the measurements are given for both the series. However, Spearman’s rank correlation coefficient rs is nothing but Karl Pearson’s correlation coefficient between the ranks, it can be interpreted in the same way as the Karl Pearson’s correlation coefficient.
Case1: When ranks are different in the two series, then
where, rs =coefficient of rank correlation
Sum of squares of the differences in ranks (D = Rx −Ry, Rx, Ry denotes rank in x and y data.) while N = Number of Pairs
Case 2: When there is a tie i.e., if any two or more individuals have equal ranks then the formula (1) for calculating rank correlation coefficient breaks down we use the following formula:
Where m is the number of times an item is repeated. The correction factor 1/12 (m3 − m) is to be added for each repeated value in both the series.
Computation of Rank Correlation Coefficient:
Steps (when ranks are given).
1. Compute D = Rx −Ry, the difference of ranks in the two series.
2. Compute D2 and get ΣD2.
3. Use the formula (8.1) or (8.2) as the case may be .
Steps (when ranks are not given).
1. Convert the given values into ranks separately for both series;
2. Compute D, the difference of ranks.
3. Compute D2 and get ΣD2.
4. Use the formula (8.1) or (8.2) as the case may be .