The optimal correction for estimating extreme discriminability

Discriminability measures such asd’ and logd become infinite when performance is extremely accurate and no errors are recorded. Different arbitrary corrections can be applied to produce finite values, but how well do these values estimate true performance? To answer this question, we directly calculated the effects of a range of different corrections on the sampling distributions of\(\hat d'\) and log\(\hat d\). Many arbitrary corrections produced better estimates of discriminability than did the intuitively plausible technique of rerunning problem conditions. We concluded that when it is not possible to run more trials and when other techniques are not appropriate, the best correction overall is to add a correction constant between 0.25 and 0.5 to all response counts, regardless of their value.