The estimation of the parameters of a negative binomial distribution with special reference to psychological data

As an analytical tool the negative binomial distribution may have wide applications in the psychological field. The estimation of its parameters is demonstrated to be often inefficient when fitting by the method of moments. This causes possibly true hypotheses to be rejected. Formulas for the efficiency of the moment method and solution of the likelihood equations are derived. Efficiency graphs and detailed tables for the function reduce the maximum-likelihood method to a minimum of computational labour. Practical applications of the ease and power of the M.L. procedure are given.The author wishes to express his gratitude to the South African Council for Scientific and Industrial Research for permission to publish this paper; to Mr. A. G. Arbous for supplying the data on absenteeism; to Mr. R. V. Sutton for the data on Two-hand Co-ordination errors; and last, but not least, to the staff of the Statistical Section who computed various tables under the expert guidance of Mr. J. S. Maritz.     

Task sets under reconstruction: effects of partially incorrect precues.

To perform a task that differs from a previously performed one, it is necessary to prepare for the new task as well as to disable the task set of the preceding task. In a series of three experiments we examined whether preparation for a task shift implies a direct update of the task set that is carried over from the preceding trial. To this end, in Experiments 1 and 2 we factorially varied the relation of the task in trial n, first, to the task in trial n - 1 (intertask relation) and, second, to the task that was precued for trial n (precue-to-task relation). Invalid precues resulted in substantial costs, which increased with longer precueing intervals. However, this increasing effect of the precue-to-task relation was not accompanied by a decreasing effect of the intertask relation. Furthermore, both effects had different qualitative properties. These findings suggest that two tasks can be represented concurrently but on two different levels of representation. In Experiment 3 we observed that the persistence of the effect of the intertask relation depends on the possibility that task repetitions can occur in trials in which a task shift is precued. This suggests that the persistence of the effect of the intertask relation is controlled in a context-sensitive way.