University of Turku, Finland, jvk@iki.fi
(joint work with Ehtibar N. Dzhafarov)
The Contextuality-by-Default approach to determining and measuring the (non)contextuality of a system of random variables requires that every random variable in the system be represented by an equivalent set of dichotomous random variables. We present general principles that justify the use of dichotomizations and determine their choice. We primarily focus on two types of random variables most often encountered in practice: categorical and real-valued ones (including continuous random variables, underrepresented in the contextuality literature). A categorical variable (one with a finite number of unordered values) is represented by all of its possible dichotomizations. If the values of a random variable are real numbers, then they are dichotomized by intervals above and below a variable cut point.