Point-Biserial Correlation

Point-biserial correlation is a correlation coefficient measuring the strength and direction of association between a continuous variable and a binary variable, equal to Pearson's r with the binary variable coded 0/1.

점이연 상관계수는 연속형 변수와 이분형 변수 사이 연관의 강도와 방향을 나타내는 상관계수로, 이분형 변수를 0과 1로 코딩해 구한 피어슨 상관계수와 같다.

How do I measure the correlation between a continuous score and a two-category variable?

연속형 점수와 두 범주로 된 변수 사이의 상관은 어떻게 구하나요?

The point-biserial correlation quantifies how strongly a continuous variable differs between the two categories of a dichotomous variable, on the familiar −1 to +1 scale. Its significance test is mathematically equivalent to the pooled-variance independent-samples t-test, so it is often reported as an effect size for a two-group comparison.

When to use Point-Biserial Correlation

• One continuous variable and one naturally dichotomous variable, such as treatment versus control
• Expressing a two-group mean difference as a correlation-type effect size
• Item analysis, correlating a correct/incorrect item with a total score

When to use something else

• The binary variable is an artificial split of an underlying continuous trait: use the biserial correlation
• Ordinal or strongly non-normal continuous variable: use the Mann-Whitney U test with a rank-biserial correlation

Assumptions and requirements

• Exactly two categories in the binary variable
• Continuous variable approximately normal within each category, with similar variances
• Independent observations

What the analysis reports

• Point-biserial r, positive when the second category in sorted order has the higher mean
• Two-sided p-value
• Box plot of the continuous variable by category

How to report it

There was a significant point-biserial correlation between [binary variable] and [continuous variable], r_pb([df]) = [value], p = [value].

Related methods

• Pearson Correlation Analysis
• Independent Samples t test
• Spearman Rank Correlation

Run Point-Biserial Correlation on Quorant