Estimating the expected value and variance of SDT indexes with heterogeneous individuals

Several methods of calculating the variance of the more popular parametric indexes of signal detection theory (SDT) have been proposed. Miller's exact method and Gourevitch and Galanter's approximate method have proved appropriate for most practical situations using yes-no detection paradigms. Those methods, specifically developed for single-point estimates, are also useful for a sample of estimates that share their parametric values of sensitivity and bias, δ and C, respectively. However, sometimes it has been observed that the empirical variances of the estimates, σˆd′2 and σˆc2, exceeds by several factors the expected values calculated by the above methods. These discrepancies can be due to a number of reasons, perhaps the most likely one being that the sample of observers or participants is not actually homogeneous. We present further developments of those two methods for calculating the variance of the indexes, d′ and c, when the samples are heterogeneous in sensitivity and/or bias. Simulation studies show that our formulas provide reasonably accurate estimates of the variance of d′ and c.