Quantitative polymerase chain reaction (PCR)-based tests are used in several different scientific fields to determine levels of a target DNA sequence of interest (the target molecule). The accuracy of quantitative PCR-based tests can be assessed by using the assay to determine the number of copies of the target molecule in a sample with a known concentration of the target molecule. For example, a sample with a known concentration of a target DNA sequence is serially diluted into replicate aliquots and these are tested to determine if the observed quantity of the target is close to the expected quantity (given the concentration in the original sample and the dilution). Statistical methods that are conventionally used to assess the accuracy of these assays do not take into account the variability in the number of target molecules in each aliquot from the original sample. We develop methods that take into account this extra variation and which determine the accuracy of quantitative PCR-based tests in estimating the number of target molecules based on a set of assays of serial dilutions from an original sample with a known concentration of target molecules. These methods are applied to data from an experiment to test the accuracy of a real-time PCR assay at low HIV-1 DNA copy levels.