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

Abstract

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.

“Sentio Ergo Est”: Unmasking the Emotional Realities of Misperception

“…207-208; for the coding script, see https://osf.io/h2u9s). Mean uncorrected sensitivity ( 𝐴 𝑆𝑡𝑖𝑚𝑢𝑙𝑢𝑠−𝑡𝑦𝑝𝑒 𝑟𝑒𝑠𝑝𝑜𝑛𝑠𝑒𝑠 ) (see Düvel & Kopiez, 2022; see also https://www.cns.nyu.edu/~david/handouts/sdt/sdt.html) in these studies was .625 (SD = .071) 1 . An a-priori power analyses conducted in G-power (Faul et al, 2009; see also https://clincalc.com/stats/samplesize.aspx) with trial contour sequence estimations (Baker et al, 2021; see https://shiny.york.ac.uk/powercontours/), showed that for the number of trials in the current experiment (k (1) blurs = 100; k (6) overall = 200; see Main Experiment: Results: Psychophysiological Framework and Analyses; see also Cacioppo et al, 2007;pp.…”

Development of an adaptive test of musical scene analysis abilities for normal-hearing and hearing-impaired listeners

“…To account for these processes with respect to individual differences among test-takers, we designed a straightforward and simple 'yes-no' task (also known as the 'A-not A' task; see Düvel & Kopiez, 2022) that required participants to decide whether a single target instrument (or lead singingvocals) was part of a two-second mixture of instruments. In a calibration phase, two online experiments were conducted in order to establish item characteristics that could be used as predictors in an explanatory IRT model.…”