StatReason

Point-Biserial Correlation Calculator

Measure the association between a naturally binary variable (such as pass/fail or treatment/control) and a numeric outcome, reported on the same familiar scale as an ordinary Pearson correlation.

What this answers

This calculator answers "how strongly does group membership relate to this numeric outcome?" using a correlation coefficient rather than only a mean difference and a significance test, useful when you want an association-strength framing for a naturally binary predictor.

How it is calculated

The point-biserial correlation is mathematically identical to a Pearson correlation computed after coding the binary group as 0 and 1: this calculator reuses that same underlying calculation rather than a separate formula, so the result, its t statistic, and its p-value are all exactly consistent with what a Pearson correlation on the coded data would give. Which group you code as 0 versus 1 only flips the sign of r, never its magnitude.

Worked example

For group 0 outcomes of 1, 2, and 3 and group 1 outcomes of 8, 9, and 10, the two groups are cleanly separated with no overlap, so the point-biserial correlation is very close to the maximum possible value, reflecting that knowing the group almost perfectly predicts which range the outcome falls in.

Assumption audit

Calculated from your data: each group's mean, the resulting r, and its t statistic and p-value, plus whether either group is empty (which blocks the calculation).
Evidence to review: whether the numeric outcome is roughly similarly distributed in shape within each group; like any Pearson-based correlation, this measure is most naturally interpreted as a linear association and is sensitive to outliers within either group.
You must verify: that the binary grouping variable is genuinely categorical (not an artificially dichotomized continuous variable, which discards information and can distort the correlation), and that observations are independent.

What this result does not mean

A strong point-biserial correlation shows the two groups differ consistently on the outcome, not that group membership causes the difference; any observational grouping carries the same confounding risks as a simple two-group mean comparison. It is mathematically equivalent information to an independent t-test's effect size, just expressed on a correlation scale.

Limitations

This calculator requires the group variable to already be coded as exactly 0 and 1; a variable with more than two categories needs a different method entirely, and a naturally continuous variable that was artificially split into two groups should generally be kept continuous and analyzed with a genuine Pearson or Spearman correlation instead.