Correlation Calculator

About the Correlation Calculator

A correlation coefficient measures how closely two variables follow a straight line, on a scale from -1 (a perfect downhill line) through 0 (no straight line relationship) to +1 (a perfect uphill line). Pearson's r is the covariance of the two lists divided by the product of their standard deviations. Spearman's rho is the same calculation applied to the ranks of the values, with tied values sharing the average of their ranks, so it detects any steadily rising or falling relationship, curved or not, and is much less affected by outliers. The p-value comes from the t statistic r times the square root of n minus 2, divided by the square root of 1 minus r squared, with n minus 2 degrees of freedom. The confidence interval uses Fisher's z transformation, the inverse hyperbolic tangent of r, which has an approximately normal spread. The calculator's example is the first set of Anscombe's quartet, eleven pairs with r = 0.8164, t = 4.2415 with 9 degrees of freedom, p = 0.00217 and a 95% interval of 0.424 to 0.951. Spearman's rho for the same data is 0.8182. The best fit line, about y = 0.5x + 3, comes from least squares. Anscombe's other three sets give almost exactly the same r with very different shapes, which is why the scatter plot matters: r summarizes a straight line relationship and says nothing about curves or outliers. A significant correlation does not show that one variable causes the other.