Point-Biserial Correlation Calculator
The point-biserial correlation is used to measure the relationship between a continuous variable and a dichotomous (binary) variable. It's mathematically equivalent to the Pearson correlation when one variable has only two values (0 and 1).
When to Use
Use the point-biserial correlation when you want to examine the relationship between:
- A continuous variable (e.g., test scores, height, reaction time)
- A dichotomous variable with two distinct groups (e.g., male/female, pass/fail, treatment/control)
Example Applications
- Correlation between gender and test performance
- Relationship between treatment group (yes/no) and recovery time
- Association between pass/fail status and study hours
Requirements
- One continuous variable measured on an interval or ratio scale
- One dichotomous variable with exactly two categories
- Independence of observations
Interpretation
- rpb = 0: No relationship between the variables
- rpb = +1: Perfect positive relationship
- rpb = -1: Perfect negative relationship
- |rpb| > 0.5: Strong relationship
- |rpb| between 0.3-0.5: Moderate relationship
- |rpb| < 0.3: Weak relationship
Equation
rpb = (M₁ - M₂) / SD × √(p × q)
Where M₁ and M₂ are the means of the two groups, SD is the overall standard deviation, p is the proportion of cases in group 1, and q is the proportion of cases in group 2 (q = 1 - p).
Coefficient of Determination (r²)
The squared correlation (r²) represents the proportion of variance in the continuous variable that can be explained by the dichotomous variable.
