Extending Systems Factorial Technology to Errored Responses

Systems factorial technology (SFT) is a theoretically derived methodology that allows for strong inferences to be made about underlying processing architectures (e.g., whether processing occurs in a pooled, coactive fashion or in serial or in parallel). Measures of mental architecture using SFT have been restricted to the use of error-free response times (RTs). In this article, through formal proofs and demonstrations, we extended the measure of architecture, the survivor interaction contrast (SIC), to RTs conditioned on whether they are correct or incorrect. We show that so long as an ordering relation (between stimulus conditions of different difficulty) is preserved, we learn that the canonical SIC predictions result when exhaustive processing is necessary and sufficient for a response. We further prove that this ordering relation holds for the popular Wiener diffusion model for both correct and error RTs but fails under some classes of a Poisson counter model, which affords a strong potential experimental test of the latter class versus the others. Our exploration also serves to point to the importance of detailed studies of how errors are made in perceptual and cognitive tasks.