This paper demonstrates that, after applying a simple modification to Li and Stout’s (Psychometrika 61(4):647–677, 1996) CSIBTEST statistic, an improved variant of the statistic could be realized. It is shown that this modified version of CSIBTEST has a more direct association with the SIBTEST statistic presented by Shealy and Stout (Psychometrika 58(2):159–194, 1993). In particular, the asymptotic sampling distributions and general interpretation of the effect size estimates are the same for SIBTEST and the new CSIBTEST. Given the more natural connection to SIBTEST, it is shown that Li and Stout’s hypothesis testing approach is insufficient for CSIBTEST; thus, an improved hypothesis testing procedure is required. Based on the presented arguments, a new chi-squared-based hypothesis testing approach is proposed for the modified CSIBTEST statistic. Positive results from a modest Monte Carlo simulation study strongly suggest the original CSIBTEST procedure and randomization hypothesis testing approach should be replaced by the modified statistic and hypothesis testing method.

This paper proposes a model-based family of detection and quantification statistics to evaluate response bias in item bundles of any size. Compensatory (CDRF) and non-compensatory (NCDRF) response bias measures are proposed, along with their sample realizations and large-sample variability when models are fitted using multiple-group estimation. Based on the underlying connection to item response theory estimation methodology, it is argued that these new statistics provide a powerful and flexible approach to studying response bias for categorical response data over and above methods that have previously appeared in the literature. To evaluate their practical utility, CDRF and NCDRF are compared to the closely related SIBTEST family of statistics and likelihood-based detection methods through a series of Monte Carlo simulations. Results indicate that the new statistics are more optimal effect size estimates of marginal response bias than the SIBTEST family, are competitive with a selection of likelihood-based methods when studying item-level bias, and are the most optimal when studying differential bundle and test bias.