Spearman Rank Correlation Calculator
Calculate the Spearman rank correlation coefficient from two paired data sets.
Measures monotonic relationships without requiring a normal distribution.
Spearman Rank Correlation
The Spearman rank correlation coefficient (ρ or r_s) measures the strength and direction of a monotonic relationship between two variables. Unlike Pearson’s correlation, it works on ranks rather than raw values — making it robust to outliers and usable with ordinal data.
Steps to compute Spearman’s r:
- Rank each variable separately (lowest value = rank 1)
- Assign average ranks to ties
- Compute Pearson correlation on the two sets of ranks
Simple formula (no ties):
r_s = 1 − 6Σdᵢ² / (n(n²−1))
Where dᵢ = rank(xᵢ) − rank(yᵢ) and n = number of pairs.
This calculator uses the Pearson-on-ranks method, which handles ties correctly.
Interpreting the result:
| r_s | Interpretation |
|---|---|
| 0.9 – 1.0 | Very strong positive monotonic relationship |
| 0.7 – 0.9 | Strong positive |
| 0.5 – 0.7 | Moderate positive |
| 0.3 – 0.5 | Weak positive |
| −0.3 – 0.3 | Negligible relationship |
| −0.5 – −0.3 | Weak negative |
| −0.7 – −0.5 | Moderate negative |
| Below −0.7 | Strong to very strong negative |
Monotonic vs linear:
Spearman detects if Y consistently increases (or decreases) as X increases — the relationship does not need to be linear. Pearson requires a linear relationship and normally distributed data. For non-normal data or ordinal scales, Spearman is the safer choice.
p-value interpretation:
The p-value tests whether the correlation is significantly different from zero. Small p-value (< 0.05) = statistically significant correlation. Requires at least 4 pairs for a meaningful test.
Enter data as comma-separated numbers. Both lists must have the same length.