~ a loose collection of statistical and quantitative research material
for fun and enrichment ~

by roland b. stark

yellow brick road to stats heaven

Statistical Methods of
Detecting Copying on Multiple Choice Tests:
A Review and an Application


Researchers consistently elicit surprise and dismay when they report on the pervasiveness of academic dishonesty. Cheating on examinations, and in particular the practice of copying answers from other students, has spurred educators to devise statistical methods that can expose it. This paper surveys the main issues in the copy detection field, examining four methods in detail. I apply these techniques to data taken from a university examination, and I compare the four with respect to ease of calculation, prevalence of use, and rates of sensitivity and specificity. I also give an overview of other copy detection methods, discussing key issues to consider, limitations that apply, and factors that inhibit the adoption of these techniques. An appendix briefly touches on the detection of cheating by impersonation and by improper erasures.

Full text available for $5.95.

Word Cloud derived from frequencies of word use in the paper.

Cheating Paper - Word Cloud

copyright 2007-2012 by roland b. stark.

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The best thinking does not result in smoke after the flashing fire, but in light emerging from the smoke.


Statistics' real contribution to society is primarily moral, not technical.

Steve Vardeman and Max Morris

There are times when not being quantitative is a kind of false piety which can only make obscure and thus more difficult the choices we must make.

John Allan Paulos

I don't think it is necessary to know exactly what I mean.

Michel Foucault

You cannot have a democracy without a statistical system that is objective and accurate.

Janet Norwood

Many things in life just cry out not to be explained.

Anthony Lane

The researcher armed with a confidence interval, but deprived of the false respectability of statistical significance, must work harder to convince himself and others of the importance of his findings. This can only be good.

Michael Oakes

New statistical methodology is often applied promiscuously, more so if it is complicated, computer-based, and hard to check. The process of connecting it back to the basic principles of statistical inference comes later, but in the long run no methodology can survive if it flouts these principles.

Bradley Efron

Some people find "Call me Ishmael" unforgettable while others become giddy with anticipation reading "Let Uo be the unit vector and X1 through Xn independent variables with Y as the dependent variable" or "consider the symmetric matrix R. When it comes to the written word there may be no accounting for taste.

Malcolm Ree

While it may be premature in some cases and unreasonable in others to expect to form lawful relationships between social variables, we shall certainly never do so if we give up the attempt.

Michael Oakes

It is the mark of an instructed mind to rest satisfied with the degree of precision which the nature of the subject permits and not seek an exactness where only an approximation of the truth is possible.


If there were one approach that was clearly superior, then the Law of the Statistical Jungle would dictate that it would survive, and all of the other techniques would exist only as historical footnotes. The continued survival of all of them, and the constant introduction of new ones, indicates that no clearly superior solution exists; hence, the unfortunate need to think about what we're doing.

Geoffrey Norman and David Streiner