Glossary term
Spearman Rank Correlation: Meaning and Definition
Reviewed and approved by Dr. Anamika ShrivastavaPublished Last updated
Spearman's rank correlation measures how closely two rankings of the same items agree. It is used when data are ranks or cannot be measured directly. Its value is one minus six times the sum of squared rank differences divided by n times n squared minus one.
In more detail
Spearman’s coefficient converts values to ranks and applies the correlation idea to them. It suits ordered qualities, like judges’ scores, and data with extreme values. Tied items share the average of their ranks, and a small correction is added for each tie.
Example
Two judges rank six singers 1 to 6 and 2, 1, 4, 3, 6, 5. The sum of squared rank differences is 6, so the coefficient is 1 − 36 ÷ 210 = 0.83.
Key points
- rs = 1 − 6Σd² ÷ n(n² − 1).
- Lies between −1 and +1.
- Tied ranks need a correction of (m³ − m) ÷ 12.
Common mistake
Forgetting to rank both variables the same way, from highest or from lowest.
Related terms
Where it is explained
This term is explained in Class 11 Statistics Chapter 6: Correlation.