The variance of d′ estimates obtained in yes—no and two-interval forced choice procedures

Abstract

In studies of detection and discrimination, data are often obtained in the form of a 2 x 2 matrix and then converted to an estimate of d' based on the assumptions that the underlying decision distributions are Gaussian and equal in variance. The statistical properties of the estimate of d', d' are well understood for data obtained using the yes-no procedure, but less effort has been devoted to the more commonly used two-interval forced choice (2IFC) procedure. The variance associated with d' is a function of true d' in both procedures, but for small values of true d' the variance of d' obtained using the 2IFC procedure is predicted to be less than the variance of d' obtained using yes-no; for large values of true d', the variance of d' obtained using the 2IFC procedure is predicted to be greater than the variance of d' from yes-no. These results follow from standard assumptions about the relationship between the two procedures. The present paper reviews the statistical properties of d' obtained using the two standard procedures and compares estimates of the variance of d' as a function of true d' with the variance observed in values of d' obtained with a 2IFC procedure.