Statistical hypothesis testing formulations for U.S. environmental regulatory standards for ozone

Environmental regulatory standards are intended to protect human health and environmental welfare. Current standards are based on scientific and policy considerations but appear to lack rigorous statistical foundations and may have unintended regulatory consequences. We examine current and proposed U.S. environmental regulatory standards for ozone from the standpoint of their formulation and performance within a statistical hypothesis testing framework. We illustrate that the standards can be regarded as representing constraints on a percentile of the ozone distribution, where the percentile involved depends on the defined length of ozone season and the constraint is stricter in regions with greater variability. A hypothesis testing framework allows consideration of error rates (probability of false declaration of violation and compliance) and we show that the existing statistics on which the standards are based can be improved upon in terms of bias and variance. Our analyses also raise issues relating to network design and the possibilities of defining a regionally based standard that acknowledges and accounts for spatial and temporal variability in the ozone distribution.