  Dzhafarov, Zhang, and Kujala (Phil. Trans. Roy. Soc. A 374, 20150099)
reviewed several behavioral data sets imitating the formal design of the
quantum-mechanical contextuality experiments. The conclusion was that none of
these data sets exhibited contextuality if understood in the generalized sense
proposed in Dzhafarov, Kujala, and Larsson (Found. Phys. 7, 762-782, 2015),
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-signaling 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 (CHSH) inequalities originally designed for detecting
contextuality in entangled particles.
