How to calculate Point-Biserial Correlation in R?

Point-biserial correlation is a measure of the association between a binary variable and a continuous variable. To calculate point-biserial correlation in R, one can use the cor.test() function, which takes two vectors as its arguments and provides the point-biserial correlation coefficient and related p-values. The first argument should be the binary vector, and the second argument should be the continuous vector. The function also provides the confidence interval for the correlation coefficient.

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 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:

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. 

Note: You can find the complete documentation for the cor.test() function .

The following tutorials explain how to calculate other correlation coefficients in R: