Calculate the correlation between a binary and a continuous variable.
The point biserial correlation is mathematically a Pearson correlation with one variable coded 0 and 1. Its maximum magnitude depends on the group split, peaking when the groups are equal in size. A highly unbalanced split caps the achievable correlation regardless of how different the group means are, which matters when interpreting item discrimination in testing.
Point Biserial Correlation
r_pb = ((M₁ − M₀) ÷ s) √(pq)
r_pb = ((M₁ − M₀) ÷ s) √(pq) The point biserial correlation is mathematically a Pearson correlation with one variable coded 0 and 1. Its maximum magnitude depends on the group split, peaking when the groups are equal in size.
A highly unbalanced split caps the achievable correlation regardless of how different the group means are, which matters when interpreting item discrimination in testing.
This calculator takes 5 inputs: Mean of group 1, Mean of group 0, Overall standard deviation, Proportion in group 1, Sample size. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.