The paired A–Not A design within signal detection theory: Description, differentiation, power analysis and application

Signal detection theory gives a framework for determining how well participants can discriminate between two types of stimuli. This article first examines similarities and differences of forced-choice and A–Not A designs (also known as the yes-no or one-interval). Then it focuses on the latter, in which participants have to classify stimuli, presented to them one at a time, as belonging to one of two possible response categories. The A–Not A task can be, on a first level, replicated or non-replicated, and the sub-design for each can be, on a second level, either a monadic, a mixed, or a paired design. These combinations are explained, and the present article then focuses on the both the non-replicated and replicated paired A–Not A task. Data structure, descriptive statistics, inference statistics, and effect sizes are explained in general and based on example data (Düvel et al., 2020). Documents for the data analysis are given in an extensive online supplement. Furthermore, the important question of statistical power and required sample size is addressed, and several means for the calculation are explained. The authors suggest a standardized procedure for planning, conducting, and evaluating a study employing an A–Not A design.