Contingency spaces and measures in classical and instrumental conditioning

The contingency between conditional and unconditional stimuli in classical conditioning paradigms, and between responses and consequences in instrumental conditioning paradigms, is analyzed. The results are represented in two- and three-dimensional spaces in which points correspond to procedures, or procedures and outcomes. Traditional statistical and psychological measures of association are applied to data in classical conditioning. Root mean square contingency, Ø, is proposed as a measure of contingency characterizing classical conditioning effects at asymptote. In instrumental training procedures, traditional measures of association are inappropriate, since one degree of freedom-response probability-is yielded to the subject. Further analysis of instrumental contingencies yields a surprising result. The well established "Matching Law" in free-operant concurrent schedules subsumes the "Probability Matching" finding of mathematical learning theory, and both are equivalent to zero contingency between responses and consequences.