Difference in power between or and according to sample size (in columns) and discrepancy function (in rows).

Difference in power between or and for detecting departures from the Poisson distribution at the 5% level and when the true distribution is a Polya distribution with maximum value equal to 5, with the sample size N equal to 20 or 50. Various discrepancy functions and test statistic functions are considered. The difference in power is positive, indicating more power for or . The magnitude of the difference can be quite substantial, ranging from 0.1 to 0.25. Similar results were obtained between and , with slightly greater power differences than between or and .