title: On contextuality in behavioural data.
abstract: Dzhafarovet al.(Dzhafarovet al.2016Phil. Trans. R. Soc. A374, 20150099. (doi:10.1098/rsta.2015.0099)) reviewed several behavioural datasets imitating the formal design of the quantum-mechanical contextuality experiments. The conclusion was that none of these datasets exhibited contextuality if understood in the generalized sense proposed by Dzhafarovet al.(2015Found. Phys.7, 762-782. (doi:10.1007/s10701-015-9882-9)), while the traditional definition of contextuality does not apply to these data because they violate the condition of consistent connectedness (also known as marginal selectivity, no-signalling condition, no-disturbance principle, etc.). In this paper, we clarify the relationship between (in)consistent connectedness and (non)contextuality, as well as between the traditional and extended definitions of (non)contextuality, using as an example the Clauser-Horn-Shimony-Holt inequalities originally designed for detecting contextuality in entangled particles.
authors.affiliation: Department of Psychological Sciences, Purdue University, West Lafayette, IN, USA ehtibar@purdue.edu.
authors.forename: Ehtibar N
authors.identifier: http://orcid.org/0000-0003-1909-7706
authors.initials: EN
authors.lastname: Dzhafarov
authors.affiliation: Department of Mathematical Information Technology, University of Jyväskylä, Jyväskylä, Finland.
authors.forename: Janne V
authors.initials: JV
authors.lastname: Kujala
authors.affiliation: Department of Psychological Sciences, Purdue University, West Lafayette, IN, USA.
authors.forename: Víctor H
authors.initials: VH
authors.lastname: Cervantes
authors.affiliation: Department of Psychological Sciences, Purdue University, West Lafayette, IN, USA.
authors.forename: Ru
authors.initials: R
authors.lastname: Zhang
authors.affiliation: Department of Psychology and Neuroscience, University of Colorado, Boulder, CO, USA.
authors.forename: Matt
authors.initials: M
authors.lastname: Jones
keywords: consistent connectedness; contextuality; cyclic systems