Table of Contents
What Is Spearman's Rank Correlation?
Spearman's rank correlation coefficient (denoted rho or r_s) is a non-parametric measure of the strength and direction of the monotonic relationship between two variables. Unlike Pearson's correlation, it does not assume linearity or normality; it only requires that the relationship be monotonic (consistently increasing or decreasing).
Spearman's correlation works by converting the raw data to ranks and then computing the Pearson correlation on those ranks. This makes it robust to outliers and suitable for ordinal data, ranked preferences, and any situation where the relationship may be monotonic but not necessarily linear.
Formula
Where d_i is the difference between the ranks of corresponding x and y values, and n is the number of pairs.
Interpretation
| |r_s| Range | Strength |
|---|---|
| 0.00 - 0.19 | Very weak |
| 0.20 - 0.39 | Weak |
| 0.40 - 0.59 | Moderate |
| 0.60 - 0.79 | Strong |
| 0.80 - 1.00 | Very strong |
Frequently Asked Questions
When should I use Spearman instead of Pearson?
Use Spearman when: (1) the data is ordinal, (2) the relationship is monotonic but not linear, (3) the data contains outliers, (4) the assumptions of normality are violated, or (5) you are working with ranked data such as survey responses or competition rankings.
How do I handle tied ranks?
When two or more values are equal (tied), assign each the average of the ranks they would have received. For example, if two values tie for ranks 3 and 4, both receive rank 3.5. With many ties, a correction factor should be applied to the formula for accurate results.