I have been asked by a journal editor to provide the splithalf reliability for an aggregate dependent variable, d', which is a Signal Detection parameter that captures perceptual sensitivity. However, d' cannot be calculated on a trial-by-trial level, because d' is inherently an aggregate measure (see calculation information below). My question is as follows: Is it possible to calculate the splithalf reliability for an aggregate measure such as d', given that there is no trial-level data that can be used for usual splithalf reliability calculations? It sounds as if the editor is asking for a bivariate correlation between d' from the fist and second halves of the task, but that does not correspond to my understanding of what splithalf reliability is meant to meausure.
Calculation information: d' is calculated by 1) calculating the rate of hits (when a signal [i.e., target] stimulus is correctly identified), 2) calculating the rate of false alarms (when a non-signal [i.e., non-target] stimulus is incorrectly identified as a signal stimulus), 3) z-transforming both values (generating the inverse of the Cumulative Normal Distribution Function for hits and false alarms, separately), and 4) calculating z-transformed(Hits) - z-transformed(False alarms).