Computation of the Response Similarity Index M4 in R under the Dichotomous and Nominal Item Response Models

Year 2019, Volume: 6 Issue: 5, 1 - 19, 30.12.2019

Cengiz Zopluoglu

https://doi.org/10.21449/ijate.527299

Cited By: 1

Abstract

Unusual response similarity
among test takers may occur in testing data and be an indicator of potential
test fraud (e.g., examinees copy responses from other examinees, send text
messages or pre-arranged signals among themselves for the correct response, item
pre-knowledge). One index to measure the degree of similarity between two
response vectors is M4 proposed by Maynes
(2014). M4 index is based on a generalized trinomial
distribution and it is computationally very demanding. There is currently no
accessible tool for practitioners who may want to use M4 in their research and
practice. The current paper introduces the M4 index and its computational
details for the dichotomous and nominal item response models, provides an R
function to compute the probability distribution for the generalized trinomial
distribution, and then demonstrates the computation of the M4 index under the
dichotomous and nominal item response models using R.

Keywords

response similarity, M4, test fraud, item response theory, test security

Computation of the Response Similarity Index M4 in R under the Dichotomous and Nominal Item Response Models

Abstract

Unusual response similarity among test takers may occur in testing data and be an indicator of potential test fraud (e.g., examinees copy responses from other examinees, send text messages or pre-arranged signals among themselves for the correct response, item pre-knowledge). One index to measure the degree of similarity between two response vectors is M4 proposed by Maynes (2014). M4 index is based on a generalized trinomial distribution and it is computationally very demanding. There is currently no accessible tool for practitioners who may want to use M4 in their research and practice. The current paper introduces the M4 index and its computational details for the dichotomous and nominal item response models, provides an R function to compute the probability distribution for the generalized trinomial distribution, and then demonstrates the computation of the M4 index under the dichotomous and nominal item response models using R.

Keywords

response similarity, M4, test fraud, item response theory, test security

References

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