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Facts and limits of this method
| What it measures | Monotonic association — consistently rising or falling, not necessarily linear |
|---|---|
| Method | Pearson correlation computed on ranks rather than values |
| Tie handling | Tied values receive the average of the ranks they span |
| Robustness | An extreme value becomes just the highest rank, so it cannot dominate |
| p-value | Exact, via the t-distribution with n−2 degrees of freedom |
| Minimum rows | 3, and meaningfully around 20 |
When it misleads you
- Ranks discard magnitude completely. A jump from 88 to 260 in the sample data becomes a step of one rank, exactly like a jump from 44 to 45. That is what makes Spearman robust and also what makes it unable to tell you how big anything is.
- It detects monotonic relationships only. A U-shaped relationship gives a rho near zero just as Pearson does — robustness against outliers is not robustness against curvature that changes direction.
- Heavy ties weaken it. If a column has many repeated values, large blocks of rows share an averaged rank and the coefficient loses resolution; with a column of only three distinct values Spearman is close to meaningless.
- A high rho does not imply a proportional relationship. It says the order matches, which permits any monotonic shape, including ones where a small change in one column corresponds to an enormous change in the other.
How it is calculated
Each column is converted to ranks: the smallest value gets rank 1, the next rank 2, and so on. The Pearson correlation is then computed on those two rank columns, which is the definition of Spearman rho.
Tied values receive the average of the ranks they occupy. If three rows share the same value at positions 4, 5 and 6, all three get rank 5. This matters: assigning them 4, 5 and 6 in arbitrary order would inject a fake ordering and systematically inflate the coefficient.
Robustness follows directly from the ranking. In the sample data one salary of 260 sits among values in the forties to eighties — under Pearson it dominates the whole calculation, while under Spearman it is simply rank 14, contributing exactly as much as any other row.
The p-value is derived the same way as for Pearson, through a t statistic with n−2 degrees of freedom and the exact incomplete beta function. On very small samples this is an approximation for rho, and the result is best read as indicative rather than definitive.
Questions and answers
When should I choose Spearman over Pearson?
When your scatter plot shows a consistently rising or falling relationship that is not straight, when the data contains outliers you do not want to remove, or when the columns are rankings or ratings rather than measurements.
Why is my Spearman so different from my Pearson?
Usually one of two reasons: an outlier is inflating Pearson, or the relationship is curved. Compare them on the scatter plot — the disagreement between the two coefficients is itself diagnostic.
How are tied values handled?
They receive the average rank of the positions they span. This is the standard method and it prevents the arbitrary ordering of equal values from creating a correlation that is not there.
Can Spearman be used on ratings like 1 to 5?
Yes, and it is the right choice for them — Pearson assumes the distance from 1 to 2 equals the distance from 4 to 5, which is exactly the assumption a rating scale does not justify. Watch out for heavy ties, though.
Is anything uploaded?
No. Ranking and correlation both happen in your browser.