## Quick Reference

A measure of the association between a binary variable, *X*, taking values 0 and 1, and a continuous random variable, *Y*. If it is assumed that for each value of *X* the distribution of *Y* is normal, with different means but the same variance, then an appropriate measure is the point biserial correlation coefficient. This is estimated from a sample as *r** _{pb}* (-1≤

*r*

*≤1), given by , where*

_{pb}*y*

*̄*

_{1}and

*ȳ*

_{0}are the mean

*Y*-values corresponding to the two values of

*X*, is the sample variance (using the

*n*−1 divisor) of the combined set of

*n*

*Y*-values, and

*p*is the proportion of

*X*values equal to 1.

If it can be assumed that *X* is a dichotomous representation of an underlying continuous random variable, *W*, with *W* and *Y* having a bivariate normal distribution, then an appropriate measure is the biserial correlation coefficient. This is estimated as *r** _{b}*, given by where and

*h*is the value defined by P(

*Z*≥

*h*)=

*p*, for a standard normal variable

*Z*.

*Subjects:*
Probability and Statistics.

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