  Multiple-choice exams are frequently used as an efficient and objective
method to assess learning but they are more vulnerable to answer-copying than
tests based on open questions. Several statistical tests (known as indices in
the literature) have been proposed to detect cheating; however, to the best of
our knowledge they all lack mathematical support that guarantees optimality in
any sense. We partially fill this void by deriving the uniform most powerful
(UMP) under the assumption that the response distribution is known. In
practice, however, we must estimate a behavioral model that yields a response
distribution for each question. We calculate the empirical type-I and type-II
error rates for several indices that assume different behavioral models using
simulations based on real data from twelve nationwide multiple-choice exams
taken by 5th and 9th graders in Colombia. We find that the index with the
highest power among those studied, subject to the restriction of preserving the
type-I error, is one based on the work of Wollack (1997) and Linden and
Sotaridona (2006) and is superior to the indices studied and developed by
Wesolowsky (2000) and Frary, Tideman, and Watts (1977). We compare the results
of applying this index to all 12 exams and find that examination rooms with
stricter proctoring have a lower level of copying. Finally, a Bonferroni
correction to control for the false positive rate is proposed to detect massive
cheating.
