Simple and Hierarchical Models for Stochastic Test Misgrading

The test misgrading is treated in this paper as a stochastic process. Three characteristic values, the expected number of misgradings, the expected inter-occurence time of misgradings, and the expected waiting for the nth misgrading, are discussed based on a simple Poisson model and a hierarchical Beta-Poisson model. Regular tests for classroom teaching and the Test of Written English (TWE) in the Test of English as a Foreign Language (TOEFL) are illustrated as examples in the model construction.


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