The sampling distribution of k

Abstract

Research on Herrnstein's single-schedule equation contains conflicting findings; some laboratories report variations in the k parameter with reinforcer value, and others report constancy. The reported variation in k typically occurs across very low reinforcer values, and constancy applies across higher values. Here, simulations were conducted assuming a wide range of reinforcer values, and the parameters of Herrnstein's equation were estimated for simulated responding. In the simulations, responses controlled by current reinforcement contingencies were added to other responses ('noise'), controlled by the experimental environment and by contingencies in effect at other times. Expected reinforcer rates were calculated by entering simulated responding into a reinforcement feedback function. These were then fitted using Herrnstein's hyperbola, and the sampling distributions of the two fitted parameters were studied. Both k and Re were underestimated by curve fitting when low-deprivation or reinforcer-quality conditions were simulated. Further simulations showed that k and Re were increasingly underestimated as the assumed noise level was increased, particularly when low-deprivation or reinforcer quality was assumed. It is concluded that reported variations in k from single schedules should not be taken to indicate that the asymptotic rate of responding depends on reinforcement parameters.