Correlation Calculator

This calculator computes the Pearson correlation coefficient r and its significance test purely from six summary sums — Number of Data Points (n), Σxy, Σx, Σy, Σx², and Σy² — rather than raw paired data, using r = (nΣxy − ΣxΣy) / √(|nΣx²−(Σx)²| × |nΣy²−(Σy)²|) (lines 12-17). Degrees of Freedom is the simplest output here: it's exactly n − 2 (line 21) and is completely unaffected by any of the five sum inputs — only Number of Data Points moves it. T-Statistic responds far more strongly to Σx than to any other input at the calculator's defaults, since Σx feeds directly into both the numerator and one of the two denominator terms of r, and the resulting t-statistic is itself a steep function of r near the calculator's default correlation strength.

The P-Value calculation branches on an exact condition — Degrees of Freedom at least 30 uses the plain normal approximation, otherwise a small-sample adjustment (adjustedZ = |t| × √(df/(df+1))) is applied first (lines 30-35) — and at the default 10 data points (df = 8), every calculation runs through that small-sample branch, which a reader wouldn't see unless Number of Data Points is set to 32 or more. Number of Data Points is never rounded to a whole number anywhere in this engine, despite conceptually representing a count of paired observations — a fractional value like 10.5 is used exactly as typed throughout every formula. This calculator does not compute a correlation from a raw list of (x, y) pairs — you have to supply the six sums yourself, so any arithmetic mistake in deriving those sums from your original data will silently produce a wrong but plausible-looking r.