On selective influences, marginal selectivity, and Bell/CHSH inequalities

TL;DR

This paper explores the connection between Bell/CHSH inequalities in quantum physics and marginal selectivity in psychology, emphasizing the importance of data compliance for interpreting influences in binary response experiments.

Contribution

It clarifies the conditions under which violations of inequalities indicate genuine influences, linking quantum physics concepts to psychological experimental analysis.

Findings

Violations of marginal selectivity affect interpretability of influences.

Bell/CHSH inequalities relate to psychological data on binary responses.

Data compliance with inequalities is crucial for valid conclusions.

Abstract

The Bell/CHSH inequalities of quantum physics are identical with the inequalities derived in mathematical psychology for the problem of selective influences in cases involving two bi- nary experimental factors and two binary random variables recorded in response to them. The following points are made regarding cognitive science applications: (1) compliance of data with these inequalities is informative only if the data satisfy the requirement known as marginal selectivity; (2) both violations of marginal selectivity and violations of the Bell/CHSH inequalities are interpretable as indicating that at least one of the two responses is influenced by both experimental factors.