UNLABELLED Relative potency bioassays are used to estimate the potency of a test biological product relative to a standard or reference product. It is established practice to assess the parallelism of the dose-response curves of the products prior to calculating relative potency. This paper provides a review of parallelism testing for bioassays. In particular three common methods for parallelism testing are reviewed: two significance tests (the F-test, the χ(2)-test) and an equivalence test. Simulation is used to compare these methods. We compare the sensitivity and specificity and receiver operating characteristic curves, and find that both the χ(2)-test and the equivalence test outperform the F-test on average, unless the assay-to-assay variation is considerable. No single method is optimal in all situations. We describe how bioassay scientists and statisticians can work together to determine the best approach for each bioassay, taking into account its properties and the context in which it is applied. LAY ABSTRACT Bioassays are experiments that use living organisms, tissues, or cells to measure the concentration of a pharmaceutical. Typically the response of the living matter to a test sample with an unknown concentration of a pharmaceutical is compared to the response to a standard reference sample with a known concentration. An important step in the analysis of bioassays is checking that the test sample is responding like a diluted copy of the reference sample; this is known as testing for parallelism. There are three statistical methods commonly used to test for parallelism: the F-test, the χ(2)-test, and the equivalence test. This paper compares the three methods using computer simulations. We conclude that different methods are best in different situations, and we provide guidelines to help bioassay scientists and statisticians decide which method to use.