Enter paired X and Y data to compute the Pearson correlation coefficient r, measuring the strength and direction of a linear relationship, with a significance check.
| Item | Formula / Note | Source / Standard |
|---|---|---|
| Pearson r | r = Σ(x−x̄)(y−ȳ) ÷ √[Σ(x−x̄)² Σ(y−ȳ)²], −1 to 1 | Pearson 1896 |
| Strength interpretation | |r|<0.1 negligible, 0.1–0.3 weak, 0.3–0.5 moderate, 0.5–0.7 strong, >0.7 very strong | Cohen 1988 effect-size conventions |
| Linearity limitation | r captures only linear association; Anscombe's quartet shows identical r with wildly different data | Anscombe 1973, American Statistician |
| Correlation ≠ causation | Confounders create spurious correlation; causal claims need experiments or causal designs | Basic statistical-inference principle |