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**Monotonicity of rank order probabilities in signal detection models of simultaneous detection and identification.**
*(English)*
Zbl 1479.91290

Summary: We examine different models of recognition memory in a simultaneous detection and identification task, which features multiple simultaneously presented test stimuli. A common finding from eyewitness identification research investigating such tasks is that the more confident decision makers are about detecting the presence of a target, the higher the probability that they also correctly identify it. We demonstrate that for members of the signal detection theory (SDT) model framework, predicting such a relationship is – contrary to previous assertions – not entailed by a monotonic diagnosticity ratio. Instead, it can be shown that this prediction follows if latent memory signals’ rank order probabilities exhibit monotonicity under changes in the response criterion. For a selection of common SDT models, we prove that this monotonicity property holds in situations in which two test stimuli are presented simultaneously. Threshold models such as the two-high-threshold model (2HTM), however, do not necessarily possess this feature. Leveraging this fact, we show that in the presence of lures which resemble a target, the 2HTM is unable to make the same predictions as many reasonable SDT models with monotonic rank order probabilities. This enables us to construct a critical, distribution-free test between these models. An empirical investigation implementing this test reveals a clear failure of the 2HTM to account for the qualitative response patterns, which are consistent with the predictions of SDT models with monotonic rank order probabilities.

### Keywords:

signal detection theory; simultaneous detection and identification; rank order probabilities; recognition memory; threshold models; similar lures
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\textit{C. G. Meyer-Grant} and \textit{K. C. Klauer}, J. Math. Psychol. 105, Article ID 102615, 24 p. (2021; Zbl 1479.91290)

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