One important endeavor in the perceptual sciences involves measuring how effectively multiple sources of information are utilized. Such measures of efficiency—known here as “capacity”—typically make use of reaction-time (RT) data. Many modeling approaches make parametric assumptions regarding the form of the RT distribution, such as diffusion models (Ratcliff, 1978) and the Linear Ballistic Accumulator (Brown & Heathcote, 2008). On the other hand, non-parametric approaches are perhaps most notably exemplified by the theory driven methodology for systems identification known as “Systems Factorial Technology” (SFT). SFT typically implements the double factorial paradigm (DFP) to examine components of information processing besides capacity, including architecture (e.g., parallel vs. serial), decision rule (OR vs. AND), and independence (cf. Little et al., 2017; Townsend & Nozawa, 1995).

Consider a prototypical example using visual detection. The DFP presents participants with one of four trial-types: two dots (double-target), one dot to the left (A) or right (B) of the center of a screen (single-target), and no targets (target-absence); target salience (brightness) is manipulated at two levels (High vs. Low) along with target-presence versus absence. In an OR detection design, correct detection occurs when a dot is present in location A, B, or both locations (i.e., the double-target) (“yes”), while correct rejection occurs on target-absent (“no”) trials. AND detection dictates that the correct response is “yes” if and only if both targets are present, and “no” otherwise.

This report examines the ramifications of computing the capacity coefficient, C(t), for AND designs. This is particularly important considering findings reported by Howard et al. (2021) showing compelling evidence for cognitive resource expenditure for target-absent trials; absent information was typically assumed to not utilize processing resources (e.g., Townsend & Nozawa, 1995). To that end, Howard et al. proposed a 4-alternative identification AND design with a modified capacity measure, CID(t). While this endeavor represents a viable alternative to AND detection designs in certain cases, the new measure risks underestimating a system’s true capacity. I therefore suggest an approach for AND detection designs that compute capacity bounds using parallel independent predictions from target-absent trials.