Estimating population or group sensitivity and its precision from a set of individual d'

A commonly used method of estimating population sensitivity is the so-called averaged d' method. In this method, the arithmetic mean of a set of individual d' is usually taken as a population sensitivity estimator. This practice ignores the fact that the individual d' itself is an estimator with an inherent variance. For observations with different levels of precision, the arithmetic mean is not the best estimator of a population parameter. It may lead to an estimate with a large variation. Another fact, which is often ignored, is that the variance of individual d' involves both between- and within-subject variations in a random effects model when population sensitivity and its level of precision are estimated. Failing to account for both components of variance leads to an underestimate of variation and an overestimate of precision for the estimator. In this paper a lognormal distribution rather than a normal distribution is assumed for individual sensitivity. An iterative weighting procedure is proposed for estimating population sensitivity on the log scale on the basis of a random effects model. An ordinary weighting procedure is proposed for estimating group sensitivity on the log scale on the basis of a fixed effects model. The levels of precision of population and group sensitivity estimators are also given. Numerical examples illustrate the estimation procedures.