A multitude of methods has been proposed to estimate the sampling variance of ratio estimates in complex samples (Wolter, 1985). Hansen and Tepping (1985) studied some of those variance estimators and found that a high coefficient of variation (CV) of the denominator of a ratio estimate is indicative of a biased estimate of the standard error of a ratio estimate. Using the same populations, Kovar (1985) and Kovar, Rao, and Wu (1988) repeated the research and showed that the relation between a high CV and bias in standard errors is weak. 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.