*31*

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

Similar to the Pearson correlation coefficient, 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 pointbiserialr() 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 documentation.*