Comparing Two Methods of Quantifying Response-Stimulus Relations: Contingency Space Analysis and Yule's Q

Abstract

Yule’s Q (YQ) and Contingency Space Analysis (CSA) are two methods of quantifying response-stimulus relations that have not been compared previously. YQ is a statistic derived from the odds ratio and is a measure of the sequential association between two observed events. CSA involves a comparison of two transitional probabilities and provides a visual representation of contingencies in operant space. We identified two distinct points in contingency space for which the YQ statistic was the same and attempted to approximate these points using concurrent schedules of reinforcement. We evaluated the effects of each schedule on response patterns in mice via an A-B-A-B reversal design. Inspection of actual contingencies revealed much variability within each comparison phase. Indeed, actual probabilities of reinforcement did not match the intended probabilities and thus were not sufficiently distinct to produce differentiated responding. Subsequent regression analyses revealed unexpected variability in the relations between each contingency index and responding among subjects. Results also indicated high correspondence between YQ and each of two potential measures of contingency strength: a difference in transitional probabilities and a ratio of transitional probabilities.