Point Biserial Correlation Calculator

Calculate the correlation between a binary and a continuous variable.

About Point Biserial Correlation Calculator

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.

Formula

Point Biserial Correlation

r_pb = ((M₁ − M₀) ÷ s) √(pq)

pq: Product of the group proportions, maximised at an even split

Worked example

With the default values below, Point Biserial Correlation Calculator returns Point Biserial Correlation of 0.454905. Change any input above and every figure here is recalculated in your browser.

Inputs used

Mean of group 1: 78
Mean of group 0: 65
Overall standard deviationminimum 0: 14
Proportion in group 1accepts 0.1–99.9 %: 40 %
Sample sizeminimum 3: 100

Results

Point Biserial Correlation: 0.454905
Difference in Means: 13.0000
T Statistic: 5.05686
Variance Explained: 20.6939%
Strength: Moderate

Step by step

1Values used
2Point Biserial Correlation
3Point Biserial Correlation= 0.454905
4Difference in Means= 13.0000
5T Statistic= 5.05686
6Variance Explained= 20.6939
7Strength= Moderate

Assumptions and limits

The result is derived only from the 5 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How is Point Biserial Correlation calculated?

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.

Why does Point Biserial Correlation matter?

A highly unbalanced split caps the achievable correlation regardless of how different the group means are, which matters when interpreting item discrimination in testing.

What values do I need to enter?

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.