The sampling distribution of d'

The distribution of sample (d) over cap's, although mathematically intractable, can be tabulated readily by computer. Such tabulations reveal a number of interesting properties of this distribution, including: (1) sample di'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 (d) over cap's undefined; (2) the variance of (d) over cap' also depends on the convention adopted for handling cases in which the sample (d) over cap' is undefined and is in some cases poorly approximated by the standard approximation formula, (3) the standard formula for a confidence interval for (d) over cap' is quite accurate with at least 50-100 trials per condition, but more accurate intervals can be obtained by direct computation with smaller samples.