Point-Biserial Correlation

Q: Is point-biserial correlation free on StatRyx?

Yes. You can run it without an account (3 free analyses), and a free account adds 10 more — a one-time allowance, no payment needed. Every result includes the APA 7 write-up. Paid plans (Student from $9/month) add more analyses and Word, PDF and Excel export.

Q: How is rpb different from Pearson r?

When one variable is binary (0/1), Pearson r and rpb are mathematically identical. The name 'point-biserial' simply signals that one variable is a natural dichotomy, helping readers understand the design.

Q: How do I report a point-biserial correlation in APA 7?

State the coding of the binary variable, then rpb with its degrees of freedom (n − 2) and p: "Gender (0 = female, 1 = male) was positively correlated with salary, rpb(198) = .34, p < .001."

Q: What is the difference between point-biserial and biserial correlation?

Point-biserial is for a truly binary variable (e.g., passed/failed, treatment/control). The biserial correlation assumes the binary variable was cut from an underlying continuous one (e.g., anxious vs not anxious from a scale) and estimates the correlation with that continuum. It is always larger than rpb.

Q: How do I convert rpb to Cohen's d?

For equal group sizes, d = 2r / √(1 − r²). For example, rpb = .30 corresponds to d ≈ 0.63.

Measure the relationship between a continuous variable and a naturally binary (dichotomous) variable.

Point-Biserial Correlation (rpb) measures the association between a continuous variable and a genuinely dichotomous (binary) variable — one that has exactly two naturally occurring categories, such as sex (male/female), disease status (present/absent), or pass/fail. It is mathematically equivalent to Pearson's r applied to a 0/1 coded binary variable, and its square (rpb²) equals eta-squared from the corresponding independent samples t-test.

Because it is equivalent to the independent t-test, StatRyx reports the t-statistic and p-value alongside rpb, and notes this equivalence. rpb ranges from −1 to +1 with the same interpretation as Pearson's r.

The point-biserial correlation (rpb) measures the relationship between a binary variable (coded 0/1) and a continuous one. It is mathematically identical to Pearson's r computed on the 0/1 codes, and it carries the same information as an independent t-test: the two tests give the same p-value. Its sign shows which group scores higher, and its size reads like r: .10 small, .30 medium, .50 large.

When to use the Point-Biserial Correlation

You want to express the group difference from an independent t-test as a correlation coefficient
You are building a correlation matrix that includes both continuous and binary variables
You want to evaluate item discrimination in a test (correlating binary item responses with a continuous total score)
You want a correlation-scale effect size for a two-group difference
You need item–total correlations for right/wrong test items

When not to use it

The binary variable is artificially dichotomised (was originally continuous) — use Pearson correlation on the original continuous scale instead
Both variables are continuous — use Pearson or Spearman correlation instead
Group sizes are extremely unequal (e.g., 95% vs 5%) — use Report Cohen's d from a t-test, which is less affected by the group split instead

Worked example

Variable	Binary Group	M (Group 0)	M (Group 1)	rpb	p
Sex – Salary	Female/Male	52,400	62,800	.34	< .001

How to report it (APA 7)

A point-biserial correlation indicated a significant positive association between sex (0 = female, 1 = male) and salary, rpb = .34, t(198) = 5.12, p < .001, rpb² = .12.

Frequently asked questions

Is point-biserial correlation free on StatRyx?