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.
How we build and check this calculator
This calculator runs entirely in your browser, so the numbers you enter stay on your device. The math behind it is written by hand and tested against worked examples and standard references before the page goes live.
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