**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 R.

**Example: Point-Biserial Correlation in R**

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

x <- c(0, 1, 1, 0, 0, 0, 1, 0, 1, 1, 0) y <- c(12, 14, 17, 17, 11, 22, 23, 11, 19, 8, 12)

We can use the built-in R function **cor.test() **to calculate the point-biserial correlation between the two variables:

#calculate point-biserial correlation cor.test(x, y) Pearson's product-moment correlation data: x and y t = 0.67064, df = 9, p-value = 0.5193 alternative hypothesis: true correlation is not equal to 0 95 percent confidence interval: -0.4391885 0.7233704 sample estimates: cor 0.2181635

From the output we can observe the following:

- The point-biserial correlation coefficient is
**0.218** - The corresponding p-value is
**0.5193**

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.”

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

Note that the output also provides a 95% confidence interval for the true correlation coefficient, which turns out to be:

**95% C.I. = (-0.439, 0.723)**

Since this confidence interval contains zero, this is further evidence that the correlation coefficient is not statistically significant.

*You can find the complete documentation for the cor.test() function here.*