Using patterns of summed scores in paper-and-pencil tests and computer-adaptive tests to detect misfitting item score patterns

Two new methods have been proposed to determine unexpected sum scores on subtests (testlets) both for paper-and-pencil tests and computer adaptive tests. A method based on a conservative bound using the hypergeometric distribution, denoted rho, was compared with a method where the probability for each score combination was calculated using a highest density region (HDR). Furthermore, these methods were compared with the standardized log-likelihood statistic with and without a correction for the estimated latent trait value (denoted as l(z)* and l(z), respectively). Data were simulated on the basis of the one-parameter logistic model, and both parametric and nonparametric logistic regression was used to obtain estimates of the latent trait. Results showed that it is important to take the trait level into account when comparing subtest scores. In a nonparametric item response theory (IRT) context, on adapted version of the HDR method was a powerful alterative to rho. In a parametric IRT context, results showed that l(z)* had the highest power when the data were simulated conditionally on the estimated latent trait level.