Likelihood ratio, optimal decision rules, and relationship between proportion correct and d' in the dual-pair AB-versus-BA identification paradigm

The equal-variance Gaussian signal detection theory (SDT) decision model for the dual-pair (4IAX) change-detection paradigm has been described in earlier publications. In this research article, we consider the equal-variance Gaussian SDT model for the related 4IAX AB-versus-BA identification paradigm. The likelihood ratios, optimal decision rules, receiver-operating characteristics (ROCs), and relationships between d' and proportion correct (PC) are analyzed for two special cases: that of statistically independent observations, which typically applies in constant-stimuli experiments, and that of highly correlated observations, which typically applies in experiments where stimuli are roved widely across trials or pairs. A surprising outcome of this analysis is that, although these two situations lead to different optimal decision rules, the predicted ROCs and PC responses for these two cases are not substantially different and are either identical to or similar to those observed in the basic yes-no paradigm. Supplemental materials for this study can be downloaded from app.psychonomic-journals.org/content/supplemental.