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 Excel.
Example: Point-Biserial Correlation in Excel
Suppose we have the following binary variable, x, and a continuous variable, y:
To calculate the point-biserial correlation between x and y, we can simply use the =CORREL() function as follows:
The point-biserial correlation between x and y is 0.218163.
Since this number 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.”
We can easily verify this by calculating the average value of y when x is 0 and when x is 1:
When x = 0, the average value of y is 14.2. When x = 1, the average value of y is 16.2. This confirms the fact that the point-biserial correlation between the two variables should be positive.
We can also use the following formulas to calculate the p-value for this correlation coefficient:
The p-value turns out to be 0.5193. Thus, although the correlation coefficient between the two variables is slightly positive it turns out to not be a statistically significant correlation.