Correlation tells you how strongly two variables move together, condensed to a single number. Pearson's r measures linear association and runs from -1 to 1: -1 marks a perfect negative line, 0 means no linear pattern, and 1 a perfect positive one. Students sizing up relationships before modeling and analysts screening metrics use it constantly.
Rank-based alternatives handle messy data well. Spearman's r and Kendall's tau detect monotone trends rather than strictly linear ones.
Pearson's r equals the covariance of x and y divided by the product of their standard deviations: r = Sxy / (Sx * Sy). For x = 1, 2, 3, 4, 5 and y = 2, 1, 4, 3, 5, both means are 3, the summed cross-deviations total 8, and both squared-deviation sums equal 10, so r = 8 / sqrt(10 * 10) = 0.8.
Spearman and Kendall first convert values to ranks. That damps the influence of outliers and suits curved but consistent relationships, where a straight-line summary would understate the pattern.
Paste paired observations into the Values (x,y) field, one pair per line. Then pick the Coefficient: Pearson's r, Spearman's r, or Kendall's tau. Set a Confidence level if you want an interval around the estimate.
Press Calculate and the result appears, with the confidence interval if requested. Read it in context: an r of 0.8 from 5 pairs is merely suggestive, while the same value across 500 observations is far stronger evidence of a genuine link, and small samples can overstate r badly.
Pearson's r runs from -1 to 1. The endpoints mark perfect linear relationships in the negative and positive directions, 0 means no linear pattern, and values between suggest partial but real association.
Use Spearman's r when data are ordinal, skewed, or contain outliers, since it ranks values first. It captures monotone trends that bend, such as diminishing returns, where Pearson's linearity assumption fails.
Kendall's tau is also rank-based and counts concordant versus discordant pairs. It has a clearer probability interpretation and behaves well on small samples or data with many tied ranks.
No, correlation measures association only, and a third variable or reverse causation can create the link. Even a strong r of 0.9 needs an experiment or design logic before causal claims are safe.
Sampling noise makes r wobble, especially with few pairs. A 95 percent interval around r = 0.5 from 12 pairs can stretch from near 0 to 0.85, so the interval honestly shows the uncertainty.