The sampling distribution of d′

Abstract

The distribution of sample d̂′s, although mathematically intractable, can be tabulated readily by computer. Such tabulations reveal a number of interesting properties of this distribution, including: (1) sample d̂′s are biased, with an expected value that can be higher or lower than the true value, depending on the sample size, the true value itself, and the convention adopted for handling cases in which the sample d̂′ is undefined; (2) the variance of d̂′ also depends on the convention adopted for handling cases in which the sample d̂′ is undefined and is in some cases poorly approximated by the standard approximation formula, (3) the standard formula for a confidence interval for d̂′ is quite accurate with at least 50-100 trials per condition, but more accurate intervals can be obtained by direct computation with smaller samples.