In light of these conflicting findings, this study uses substantially different populations and design choices taken from the National Assessment of Educational Progress (NAEP) to further investigate the relationship between bias, the CV, and the number of strata, which has also been found to be an indicator of bias (Burke & Rust, 1995). It is found that the CV is a relatively weak indicator of bias, showing poor power properties. Suggestions are made to improve upon statistical suppression rules related to the CV and number of replicate strata.