The Sequential Probability Ratio Test: An efficient alternative to exact binomial testing for Clean Water Act 303(d) evaluation

• Type of Material: Article
• Authors: Connie Chen, Carnegie Mellon University; Matthew Gribble, Emory University; Jay Bartroff, University of Southern California; Steven M. Bay, Southern California Coastal Water Research Project; Larry Goldstein, University of Southern California
• Language: English
• Date: 2017-05-01
• Publisher: Elsevier
• Publication Version: Author Accepted Manuscript (After Peer Review)
• Copyright Statement: © 2017 Elsevier Ltd
• License: Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International
• Final Published Version (URL): http://dx.doi.org/10.1016/j.jenvman.2017.01.039
• Title of Journal or Parent Work: Journal of Environmental Management
• ISSN: 0301-4797
• Volume: 192
• Start Page: 89
• End Page: 93
• Grant/Funding Information: M. Gribble was supported during this project by T32 training grant support from the National Institute for Environmental Health Sciences (T32ES013678) and the HERCULES Exposome Research Center funded by the National Institute for Environmental Health Sciences (P30 ES019776).; J. Bartroff was supported in part by grant DMS-1310127 from the National Science Foundation and grant R01 GM068968 from the National Institutes of Health.
• Keywords: Study design; Sediment quality objectives; Environmental Sciences; QUALITY ASSESSMENT; Water quality; Science & Technology; Life Sciences & Biomedicine; Environmental Sciences & Ecology; IMPAIRMENT; Clean Water Act; Sequential probability ratio test; CALIFORNIA
• Research Categories: Statistics; Environmental Sciences; Mathematics

Abstract

The United States's Clean Water Act stipulates in section 303(d) that states must identify impaired water bodies for which total maximum daily loads (TMDLs) of pollution inputs into water bodies are developed. Decision-making procedures about how to list, or delist, water bodies as impaired, or not, per Clean Water Act 303(d) differ across states. In states such as California, whether or not a particular monitoring sample suggests that water quality is impaired can be regarded as a binary outcome variable, and California's current regulatory framework invokes a version of the exact binomial test to consolidate evidence across samples and assess whether the overall water body complies with the Clean Water Act. Here, we contrast the performance of California's exact binomial test with one potential alternative, the Sequential Probability Ratio Test (SPRT). The SPRT uses a sequential testing framework, testing samples as they become available and evaluating evidence as it emerges, rather than measuring all the samples and calculating a test statistic at the end of the data collection process. Through simulations and theoretical derivations, we demonstrate that the SPRT on average requires fewer samples to be measured to have comparable Type I an d Type II error rates as the current fixed-sample binomial test. Policymakers might consider efficient alternatives such as SPRT to current procedure.