Measures of association in contingency space analysis

• The operant contingency value (OCV) has one variance term in the denominator.
• Phi and Yule’s QQ pool two and three variance terms, respectively.
• Yule’s QQ substantially overestimated both the OCV and phi with simulated data.
• The relationship between the OCV and phi was generally monotonic with empirical data.
• Unlike phi, the OCV was unaffected by discrepancies in diagonal cell frequencies.

Sequential recording of behavior and its consequences is a common strategy for identifying potential maintaining variables in the natural environment. Disagreement remains over a standard approach to detecting contingent relations in the resulting data as well as a suitable association metric. In operant research, contingency is defined as the difference between the probability of reinforcement given some behavior and the probability of reinforcement given the absence of that behavior. Joint occurrences of behavior and its reinforcing consequences can be summarized in a 2 by 2 contingency table for which a variety of association measures exist. We analyzed three such measures algebraically (operant contingency value [OCV], phi coefficient, and Yule’s QQ), compared their relative magnitudes in a simulation study, and examined their relationship when computed on the same set of sequential observation data. Based on these analyses, we concluded that the OCV is a more robust measure for accurately indexing both absolute and relative degrees of contingency during functional behavior assessment.