Enter your continuous variable values for two groups (Group 0 and Group 1) to calculate the Point Biserial Correlation (r_pb). Paste or type comma-separated numbers for each group, choose your significance level and tail type, and get back the correlation coefficient, t-statistic, p-value, and a significance decision.
Point Biserial Correlation (r_pb)
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t-Statistic
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Degrees of Freedom
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p-Value
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Total N
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Result
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The point biserial correlation (r_pb) measures the strength and direction of the relationship between a dichotomous (binary) variable and a continuous (metric) variable. It is mathematically equivalent to the Pearson correlation when one variable is coded as 0 and 1. Values range from -1 to +1, where 0 means no relationship.
Use it when one variable is genuinely binary (e.g. pass/fail, male/female, treated/untreated) and the other is continuous (e.g. test score, weight, income). It is not appropriate when both variables are continuous — use Pearson's r instead.
A two-tailed test checks whether the correlation is significantly different from zero in either direction (positive or negative). A one-tailed test checks only one direction and is used when you have a directional hypothesis before collecting data. When in doubt, use two-tailed.
As a rule of thumb: |r_pb| < 0.1 is negligible, 0.1–0.3 is small, 0.3–0.5 is moderate, and > 0.5 is large. A positive value means Group 1 tends to have higher continuous variable scores; a negative value means Group 0 tends to score higher.
The most common significance level in social sciences is α = 0.05, meaning a 5% risk of a false positive. Use α = 0.01 for more rigorous research (e.g. medical studies) and α = 0.10 for exploratory work. The choice should be made before analyzing your data.
The continuous variable should be approximately normally distributed within each group, and the variances in both groups should be roughly equal (homoscedasticity). The dichotomous variable must have exactly two categories. The observations must be independent of each other.
The t-statistic is derived from r_pb using the formula: t = r_pb × √((n − 2) / (1 − r_pb²)), where n is the total sample size. This t-value is then compared to a t-distribution with n − 2 degrees of freedom to obtain the p-value.
Yes — when the binary variable is coded as 0 and 1, the point biserial correlation is algebraically identical to Pearson's product-moment correlation. The point biserial formula is simply a computationally convenient rearrangement for the binary-plus-continuous case.