Perspectives on the 2 × 2 Matrix: Solving Semantically Distinct Problems Based on a Shared Structure of Binary Contingencies - Neth, Hansjörg; Gradwohl, Nico; Streeb, Dirk; Keim, Daniel A.; Gaissmaier, Wolfgang (Frontiers in Psychology, 2021)
Cognition is both empowered and limited by representations. The matrix lens model addresses tasks that are based on frequency counts, binary contingencies, and conditional probabilities in a general fashion. By analyzing and explicating a wide variety of problems, our model links semantically distinct domains and provides a new perspective on representational accounts of cognition that recognizes representational isomorphs as opportunities, rather than as problems. The definitions of many scientific measures, theoretical debates on biases in Bayesian reasoning, and the facilitation effects observed when presenting problems in alternative representation formats, are clarified by a unifying framework that is anchored in the shared structural construct of a 2×2 matrix. Our model’s key explanatory mechanism is the adoption of particular perspectives on a 2×2 matrix that categorizes the frequency counts of cases by some condition, treatment, risk, or outcome factor. By the selective steps of filtering, framing, and focusing on specific aspects, the measures used in various semantic domains negotiate distinct trade-offs between abstraction and specialization. As a consequence, the transparent communication of such measures must explicate the perspectives encapsulated in their derivation. A better understanding of the role of perspectives in the scientific process yields both theoretical insights and practical applications.