Abstract Philosophical considerations in the interpretation of probability can confuse the meaning of interval estimates. Most techniques for calculating interval estimates for the median effective dose (LC50) have been developed under a Neyman-Pearson probability structure, which requires interpretation in terms of asymptotic mathematics. Fiducial probability, designed to allow the inductive use of a single experiment, fails to resolve this major difficulty in interpretation. In the evaluation of LC50 estimators, care should be exercised to ensure correct identification of random variables, consistent partitioning of sources of variability and proper choice of criteria for comparing estimators. Despite the difficulties raised by these issues, the calculation of interval estimates in short-term toxicity testing remains an important benchmark in assessing the potentially harmful effects of chemical compounds in the environment.