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Reliability as a Function of the Number of Item Options Derived from the “Knowledge or Random Guessing” Model

Published online by Cambridge University Press:  01 January 2025

Robert G. MacCann
Robert G. MacCann*
Affiliation:
Measurement and Research Services, Board of Studies NSW, Sydney, Australia
*
Requests for reprints should be addressed to: Dr. Robert MacCann, Head, Measurement & Research Services, Board of Studies NSW, GPO Box 5300, Sydney, AUSTRALIA 2001 E-mail: maccann@boardofstudies.nsw.edu.au
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Abstract

For (0, 1) scored multiple-choice tests, a formula giving test reliability as a function of the number of item options is derived, assuming the “knowledge or random guessing model,” the parallelism of the new and old tests (apart from the guessing probability), and the assumptions of classical test theory. It is shown that the formula is a more general case of an equation by Lord, and reduces to Lord's equation if the items are effectively parallel. Further, the formula is shown to be closely related to another formula derived from Lord's randomly parallel tests model.

Keywords

guessing (tests)test reliabilitydistractorstest lengtherror of measurement
Type
Notes And Comments
Information
Psychometrika , Volume 69 , Issue 1 , March 2004 , pp. 147 - 157
Copyright
Copyright © 2004 The Psychometric Society

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