On the estimation of the proportion of masters in criterion-referenced testing

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J.A. Emrick's (1971) model is a latent class model of mastery testing that can be used to estimate the proportion of masters in a given population. A. Hamerle (1980), in a recent paper on this model, has proposed an estimator for the proportion of masters that is claimed to constitute a maximum likelihood approach. It is indicated that Hamerle is not quite correct in his presentation of Emrick's model and that his estimator is not maximum likelihood. An estimator is provided using the method of moments; this estimator appears to have the same shape as Hamerle's estimator, but should be interpreted differently since it is derived under the correct version of Emrick's model. An attractive property of the method of moments is that it also yields simple estimators for the present model if the two success parameters are unknown. It appears that these estimators can be used for tests consisting of three or more items. Results of extensive Monte Carlo studies indicate that the estimators possess excellent statistical properties.
Original languageEnglish
Place of PublicationEnschede, The Netherlands
PublisherUniversity of Twente
Publication statusPublished - 1981

Publication series

NameTwente Educational Memorandum
PublisherUniversity of Twente, Faculty of Educational Science and Technology


  • Mastery tests
  • Foreign countries
  • Maximum likelihood statistics
  • Criterion referenced tests
  • Monte Carlo methods
  • Estimation (Mathematics)
  • Mathematical model
  • Latent trait theory


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