Spearman's Correlation Calculator
Enter paired observations to evaluate Spearman's ρ, which measures monotonic association using ranked data.
Spearman's ρ
1.0000
Very strong monotonic relationship.
| x | Rank(x) | y | Rank(y) |
|---|---|---|---|
| 1 | 1.00 | 3 | 1.00 |
| 2 | 2.00 | 4 | 2.00 |
| 3 | 3.00 | 7 | 3.00 |
| 4 | 4.00 | 9 | 4.00 |
| 5 | 5.00 | 11 | 5.00 |
How to Use This Calculator
- Enter paired x and y values, one pair per line.
- Ensure both lists have the same number of entries.
- Review Spearman's rho and the ranks table.
- Use rho to gauge monotonic relationships, even when data are non-linear.
Formula
Assign ranks to x and y (averaging ties).
Compute Pearson's correlation between the ranked variables.
ρ = covariance(rank(x), rank(y)) / [σ(rank(x)) · σ(rank(y))]
This rank-based method assesses monotonic association, resisting influence from scale or non-linear transformations.
Full Description
Spearman's correlation coefficient measures the degree to which two variables move together monotonically. It handles ordinal data and monotonic but non-linear relationships where Pearson's correlation may fail.
By ranking data first, Spearman's rho mitigates the impact of outliers and uneven scales.
Frequently Asked Questions
Does Spearman's rho detect linear relationships?
Yes. Perfect linear relationships produce |ρ| = 1, provided there are no ties or rank issues.
How are ties handled?
The calculator assigns average ranks to tied values, which is standard practice for Spearman's rho.
Can rho be used with ordinal data?
Yes. Spearman's rho is well-suited for ordinal variables where ranks are meaningful.
Is rho sensitive to outliers?
Less than Pearson's r, but extreme values still affect rankings. Inspect data visually when outliers are present.