Abstract
An axiomatic model for tests of pure speed is developed, leading to the conclusion that such test scores may, under certain circumstances, be regarded as realizations of a Poisson process. This leads to further study of the situation in terms of strong true score theory with the assumption of a Poisson distribution of scores and true score equal to the parameter of the Poisson distribution. Important conclusions are that (1) the Spearman‐Brown formula holds in continuous time, (2) the raw moments of the distribution of true scores are obtainable from a knowledge of the factorial moments of observed scores over a population of examinees, and (3) under reasonable assumptions the distribution of observed scores over examinees ought to be negative binomial. An empirical example is given demonstrating the fit of the model to various predictions based on the model. In particular, the Poisson assumption can be tested independently of any assumption about the distribution of true or observed scores over examinees.
Published Version
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