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Spearman Rank Correlation Calculator

Compute Spearman’s ρ from two paired lists, with tie-aware ranking, a t-statistic and an approximate p-value.

X values

Y values (same order)

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How it works

ρ = Pearson correlation of the ranks (= 1 − 6Σd² ÷ n(n²−1) when there are no ties)

Spearman’s correlation measures whether Y tends to rise (or fall) as X rises, without assuming a straight line — it is Pearson’s r computed on ranks. Tied values receive their average rank, which is why the Pearson-on-ranks form is used here rather than the shortcut formula.

Worked example

The default IQ vs weekly TV-hours data gives ρ = −0.176: a very weak negative relationship that is not significant.

Frequently asked questions

When should I prefer Spearman over Pearson?

For ordinal data, curved-but-monotonic relationships, or when outliers would dominate Pearson’s r.

How accurate is the p-value?

It uses the t approximation with n−2 degrees of freedom, fine for n ≥ 10. For tiny samples use an exact table.

Related calculators

Pearson Correlation Coefficient (r) Calculator

Compute Pearson’s r between two paired lists, with r², the covariance and a plain-language reading of how strongly the variables move together.

Correlation Coefficient Calculator

Compute the Pearson correlation coefficient r between two lists of numbers, with r-squared and a plain-language reading of the relationship.

R-Squared Calculator

Compute the coefficient of determination R² between two data sets — the share of variance explained — along with the Pearson correlation r.

For education — check assumptions (sample size, distribution) before using statistics in real decisions.