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A Statistical Test for Cheating

Lord, Frederic M.
Publication Year:
Report Number:
ETS Research Memorandum
Document Type:
Page Count:
Subject/Key Words:
Cheating, Statistical Analysis, Statistical Significance, Testing Problems


A statistical test for cheating is developed. The case of a single examinee who has taken parallel forms of the same selection test on three occasions, obtaining scores x, y, z, is used to illustrate the development. It is assumed that each score is normally distributed with the same known variance, that is, the variance of the errors of measurement. These scores are further assumed to be distributed independently, since each score differs from its mean (true) value only because of errors of measurement. Based on these assumptions, a significance test is presented to indicate evidence of cheating. Mathematical derivations for the test of significance are presented as well as a numerical example.

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