Recovering the variance of d' from hit and false alarm statistics

Sometimes the reports of primary studies that are potentially analyzable within the signal detection theory framework do not report sample statistics for its main indexes, especially the sample variance of d'. We describe a procedure for estimating the variance of d' from other sample statistics (specifically, the mean and variance of the observed rates of hit and false alarm). The procedure acknowledges that individuals can be heterogeneous in their sensitivity and/or decision criteria, and it does not adopt unjustifiable or needlessly complex assumptions. In two simulation studies reported here, we show that the procedure produces certain biases, but, when used in meta-analysis, it produces very reasonable results. Specifically, the weighted estimate of the mean sensitivity is very accurate, and the coverage of the confidence interval is very close to the nominal confidence level. We applied the procedure to 20 experimental groups or conditions from seven articles (employing recognition memory or attention tasks) that reported statistics for both the hit and false alarm rates, as well as for d'. In most of these studies the assumption of homogeneity was untenable. The variances estimated by our method, based on the hit and false alarm rates, approximate reasonably to the variances in d' reported in those articles. The method is useful for estimating unreported variances of d', so that the associated studies can be retained for meta-analyses.