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Stochastic Processes as True-Score Models for Highly Speeded Mental Tests

Moore, William E.
Publication Year:
Report Number:
ETS Research Bulletin
Document Type:
Page Count:
Subject/Key Words:
Erland Process, Kit of Reference Tests for Cognitive Factors, Mathematical Models, Poisson Process, Probability, Timed Tests, True Scores


The previous theoretical development of the Poisson progress as a strong model for the true-score theory of mental tests is discussed, and additional theoretical properties of the model from the standpoint of individual examinees are developed. The paper introduces the Erlang process as a family of test theory models and shows in the context of mental testing, that the Poisson process is a particular case of the Erlang process. Probability density functions mathematically define the parameters and lead to semantic interpretations of parameters in terms of tests and examinee characteristics. Experimental research gives the fit of observations to theoretically predicted functional forms for individual examinees. In particular experimental measurements determine observed-score distributions for individuals and give estimates of their true scores. The models apply to homogeneous, itemized tests of pure speed. The models were tested with tenth grade boys who responded to six highly speeded tests from the Kit of Reference Tests for Cognitive Factors. Three tests measured speed of clerical or perceptual skill, and three measured speed of computational skill in arithmetic. The Poisson process was applied with varying degrees of success to three of the six highly speeded tests while the Erlang process applied to one test. For two tests (Maze Tracing and Addition) the stochastic models had no application. (Author/CK)

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