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.
Note: You can find the complete documentation for the cor.test() function here.
The following tutorials explain how to calculate other correlation coefficients in R: