Point Biserial Correlation

A point-biserial correlation is used to measure the strength and direction of the association that exists between one continuous variable and one dichotomous variable. It is a special case of the Pearson’s product-moment correlation, which is applied when you have two continuous variables, whereas in this case one of the variables is measured on a dichotomous scale.

For example, you could use a point-biserial correlation to determine whether there is an association between salaries, measured in US dollars, and gender (i.e., your continuous variable would be “salary” and your dichotomous variable would be “gender”, which has two categories: “males” and “females”). Alternately, you could use a point-biserial correlation to determine whether there is an association between cholesterol concentration, measured in mmol/L, and smoking status (i.e., your continuous variable would be “cholesterol concentration”, a marker of heart disease, and your dichotomous variable would be “smoking status”, which has two categories: “smoker” and “non-smoker”).

ASSUMPTIONS OF POINT BISERIAL CORRELATION

Every statistical method has assumptions. Assumptions mean that your data must satisfy certain properties in order for statistical method results to be accurate.

The assumptions for Point-Biserial correlation include:

1) Continuous and Binary

2)Normally Distributed

3) No Outliers

4)Equal Variances

WHEN WE USE POINT BISERIAL CORRELATION

You should use Point-Biserial Correlation in the following scenario:

1)You want to know the relationship between two variables

2)Your variables of interest include one continuous and one binary variable

3)You have only two variables

Relationship

You are looking for a statistical test to look at how two variables are related. Other types of analyses include testing for a difference between two variables or predicting one variable using another variable (prediction).

One Continuous and One Binary

For this test, you should have one continuous and one binary variable. Continuous means that the variable can take on any reasonable value. Some good examples of continuous variables include age, weight, height, test scores, survey scores, yearly salary, etc.

Binary means that your variable is a category with only two possible values. Some good examples of binary variables include smoker(yes/no), sex(male/female) or any True/False or 0/1 variable.

If you have two continuous variables, you should use Pearson Correlation. And if you have at least one ordinal variable, you should use Spearman’s Rho or Kendall’s Tau instead.

Two Variables

POINT BISERIAL CORRELATION EXAMPLE :

Variable 1: Height.

Variable 2: Gender.

In this example, we are interested in the relationship between height and gender. To begin, we collect these data from a group of people.

GRAPHICAL REPRESENTATION OF POINT BISERIAL CORRELATION