A bivariate lognormal response-time model for the detection of collusion between test takers

A bivariate lognormal model for the distribution of the response times (RTs) on a test by a pair of test takers is presented. As the model has parameters for the item effects on the RTs, its correlation parameter automatically corrects for the spuriousness in the observed correlation between the RTs of different test takers due to variation in the time intensities of the items. This feature suggests using the model in a routine check of RT patterns for possible collusion between test takers using the maximum-likelihood estimate (MLE) of the correlation parameter or a statistical test of a hypothesis about it. Both the MLEs of the model parameters and a Lagrange multiplier test of a hypothesis for this purpose are derived. As in any type of statistical decision making, results from such procedures should be corroborated by evidence from other sources (e.g., results from a response-based analysis or observations during the test session). The effectiveness of the model in removing the spuriousness from correlated RTs is illustrated through the use of empirical RT data.