The Empirical Power and Type I Error Rates of the GBT and ω Indices in Detecting Answer Copying on Multiple-Choice Tests

Cengiz Zopluoglu, Ernest C. Davenport

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

Abstract

The generalized binomial test (GBT) and ω indices are the most recent methods suggested in the literature to detect answer copying behavior on multiple-choice tests. The ω index is one of the most studied indices, but there has not yet been a systematic simulation study for the GBT index. In addition, the effect of the ability levels of the examinees in answer copying pairs on the statistical properties of the GBT and ω indices have not been systematically addressed as yet. The current study simulated 500 answer copying pairs for each of 1,440 conditions (12 source ability level × 12 cheater ability level × 10 amount of copying) to study the empirical power and 10,000 pairs of independent response vectors for each of 144 conditions (12 source ability level × 12 cheater ability level) to study the empirical Type I error rates of the GBT and ω indices. Results indicate that neither GBT nor ω inflated the Type I error rates, and they are reliable to use in practice. The difference in statistical power of these two methods was very small, and GBT performs slightly better than does ω. The main effect for the amount of copying and the interaction effect between source ability level and the amount of copying are found to be very strong while all other main and interactions effects are negligible.

Original languageEnglish (US)
Pages (from-to)975-1000
Number of pages26
JournalEducational and Psychological Measurement
Volume72
Issue number6
DOIs
StatePublished - Dec 2012

Keywords

  • answer copying
  • cheating
  • generalized binomial test
  • item response theory
  • multiple-choice tests

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