Reprint of “Survivor interaction contrast wiggle predictions of parallel and serial models for an arbitrary number of processes”

• We explore the precise behavior of the serial exhaustive SIC function for n=2n=2.
• We provide a generalization of the SIC function to an arbitrary number of processes.
• We analyze the generalized SIC for both parallel and serial models with minimum and maximum time stopping rules.
• We demonstrate application of the theorems to data from a short-term memory search task.

The Survivor Interaction Contrast (SIC) is a distribution-free measure for assessing the fundamental properties of human information processing such as architecture (i.e., serial or parallel) and stopping rule (i.e., minimum time or maximum time). Despite its demonstrated utility, there are some vital gaps in our knowledge: first, the shape of the serial maximum time SIC is theoretically unclear, although the one 0-crossing negative-to-positive signature has been found repeatedly in the simulations. Second, the theories of SIC have been restricted to two-process cases, which restrict the applications to a limited class of models and data sets. In this paper, we first prove that in the two-process case, a mild condition known as strictly log-concavity is sufficient as a guarantor of a single 0-crossing of the serial maximum time SIC. We then extend the definition of SIC to an arbitrary number of processes, and develop implicated methodology of SIC in its generalized form, again in a distribution-free manner, for both parallel and serial models in conjunction with both the minimum time and maximum time stopping rules. We conclude the paper by demonstrating application of the theorems to data from a short-term memory search task.