Signal detection models for the same–different task

• Signal detection models for the same–different task are presented.
• The models apply to the full four by two same–different table.
• The approach allows one to consider models that recognize bias and other effects.
• Two basic three-parameter signal detection models are presented.
• It is shown how to fit the models with standard software for nonlinear mixed models.

Signal detection models for the same–different task are presented. In contrast to the standard approach that only considers the proportion correct, the models apply to the full four by two same–different table. The approach allows one to consider models that recognize bias and other effects. Two basic signal detection models, associated with different decision rules, are presented. A version of the covert decisions rule is introduced that directly allows for same–different bias, in contrast to earlier versions. It is shown how to fit the models with standard software for nonlinear mixed models. The models are applied to data from a recent same–different study.