REINFORCEMENT THEORIES HOLD THAT AN EVENT REINFORCES THE TENDENCY FOR THE SAME EVENT TO RECUR. THE CONTAGIOUS POISSON PROCESS IS A MARKOV PROCESS WHICH HAS BEEN USED TO REPRESENT THE REINFORCEMENT OF EVENTS. STANDARD METHODS FOR ESTIMATING AND TESTING THE MODEL ARE GENERALLY INEFFICIENT AND USUALLY INCONSISTENT. NEW METHODS ARE PROPOSED FOR ESTIMATING THE PARAMETERS OF THE CONTAGIOUS POISSON PROCESS AND FOR TESTING THE MODEL AGAINST THE MORE RESTRICTED COMPOUND POISSON PROCESS. THE PROPOSED METHODS ARE MORE STATISTICALLY EFFICIENT THAN THOSE PREVIOUSLY USED, AND THEY MAKE LESS STRINGENT ASSUMPTIONS ABOUT THE DATA. SINCE THE COMPOUND POISSON IS A VERY RESTRICTIVE HYPOTHESIS, ITS COMPARISON WITH THE CONTAGIOUS POISSON PROCESS ONLY TESTS WHETHER THE RATE OF EVENT OCCURRENCE DOES OR DOES NOT INCREASE WITH TIME. WHETHER REINFORCEMENT DOES OR DOES NOT OCCUR IS NOT DETERMINED. ON BALANCE, THE CONTAGIOUS POISSON PROCESS IS A LIKELY FIRST APPROXIMATION OF REINFORCEMENT, EVEN WHEN MANY OF ITS ASSUMPTIONS APPEAR UNREALISTIC. AT LEAST IT SERVES AS A USEFUL BASELINE FOR DETERMINING WHETHER AND WHAT ELABORATIONS ARE NECESSARY. MATHEMATICAL EQUATIONS, NOTES, AND REFERENCES (CA. 25) ARE PROVIDED. (AUTHOR ABSTRACT MODIFIED)