Experimental data may include values below the limit of detection or limit of quantitation. Such data are often substituted by a fixed value, such as half the limit of quantitation or even omitted entirely. Either approach can bias the results and, in the case of parallel line bioassay, lead to unnecessary assay failure. This article demonstrates that a better statistical technique, Tobit analysis, can account properly for values that are below the limit of quantitation. Specifically, this article focuses on the analysis of bioassay data. We apply Tobit analysis to simulated bioassay data and show that this method leads to a higher probability that an assay will correctly pass parallelism testing, when compared with the commonly used substitution method. We conclude that Tobit analysis should be the method of choice for the analysis of bioassays containing values below the limit of quantitation.