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Bayesian Checks on Cheating on Tests

Published online by Cambridge University Press:  01 January 2025

Wim J. van der Linden  and
Charles Lewis
Wim J. van der Linden*
Affiliation:
CTB/McGraw-Hill
Charles Lewis
Affiliation:
Fordham University
*
Correspondence should be sent to Wim J. van der Linden, CTB/McGraw-Hill, 20 Ryan Ranch Road, Monterey, CA 93940. Email: wim_vanderlinden@ctb.com
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Abstract

Posterior odds of cheating on achievement tests are presented as an alternative to p\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$p$$\end{document} values reported for statistical hypothesis testing for several of the probabilistic models in the literature on the detection of cheating. It is shown how to calculate their combinatorial expressions with the help of a reformulation of the simple recursive algorithm for the calculation of number-correct score distributions used throughout the testing industry. Using the odds avoids the arbitrary choice between statistical tests of answer copying that do and do not condition on the responses the test taker is suspected to have copied and allows the testing agency to account for existing circumstantial evidence of cheating through the specification of prior odds.

Keywords

answer copyingBayesian checkscheating on testserasure analysisgeneralized binomial distributionstatistical hypothesis testing
Type
Original Paper
Information
Psychometrika , Volume 80 , Issue 3 , September 2015 , pp. 689 - 706
Copyright
Copyright © 2014 The Psychometric Society

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