Spearman Rank Correlation Calculator
Calculate Spearman's rank correlation coefficient (rho) from paired data. Unlike Pearson's r, Spearman's rho measures the strength of a monotonic (not necessarily linear) relationship and is robust to outliers and non-normal distributions.
Spearman's rank correlation coefficient is a non-parametric measure of the strength and direction of association between two variables. It works by first converting the raw data to ranks, then computing the Pearson correlation on the ranks. The formula simplifies to rho = 1 - (6 * sum of d-squared) / (n * (n-squared - 1)), where d is the difference between paired ranks.
Spearman's rho ranges from -1 (perfect inverse monotonic relationship) to +1 (perfect direct monotonic relationship). A value of 0 indicates no monotonic association. Because it operates on ranks, it is resistant to outliers and does not require the data to be normally distributed.
This calculator also computes Pearson's r for comparison. When the two coefficients differ substantially, it suggests the relationship is monotonic but not linear. For example, an exponential growth pattern would show a high Spearman rho but a lower Pearson r.