Point-biserial correlation is used to measure the relationship between a binary variable, x, and a continuous variable, y.

Similar to the , the point-biserial correlation coefficient takes on a value between -1 and 1 where:

• -1 indicates a perfectly negative correlation between two variables
• 0 indicates no correlation between two variables
• 1 indicates a perfectly positive correlation between two variables

This tutorial explains how to calculate the point-biserial correlation between two variables in Python.

Example: Point-Biserial Correlation in Python

Suppose we have a binary variable, x, and a continuous variable, y:

x = [0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0]
y = [12, 14, 17, 17, 11, 22, 23, 11, 19, 8, 12]

We can use the function from the scipy.stats library to calculate the point-biserial correlation between the two variables.

Note that this function returns a correlation coefficient along with a corresponding p-value:

import scipy.stats as stats

#calculate point-biserial correlation
stats.pointbiserialr(x, y)

PointbiserialrResult(correlation=0.21816, pvalue=0.51928)

The point-biserial correlation coefficient is 0.21816 and the corresponding p-value is 0.51928.

Since the correlation coefficient is positive, this indicates that when the variable x takes on the value “1” that the variable y tends to take on higher values compared to when the variable x takes on the value “0.”

Since the p-value of this correlation is not less than .05, this correlation is not statistically significant. 

You can find the exact details of how this correlation is calculated in the scipy.stats.