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Response to Comment on “Comment on ‘An Alternative Minimum Level Definition for Analytical Quantification’ ” SIR: We appreciate the opportunity to respond to the comments of Rigo concerning the importance and estimation of the relationship between measurement variation and spike concentration, or average measurement response, as discussed in our earlier correspondence (2). We are pleased to see the continuing interest in this important subject. Specifically, we will discuss constant variance models versus models that allow measurement variation to increase with measured concentration, quantitation limits versus statistical limits for individual measurements, Rigo’s generalized model of measurement variation, and some generalities on the use of measurements to determine compliance with regulations. Rigo’s comments on air regulations are outside the scope of our original comment and outside our areas of expertise in water regulations. As such, we will not respond directly to those comments. We strongly disagree with the characterization by Rigo of our comments as relating only to “homoscedastic (constant) variance data sets”. Our comments were directed primarily toward objectively verifiable errors and omissions in the development of the Alternative Minimum Level (AML) as presented by Gibbons et al. (1). We also identified errors by Gibbons et al. (1) in the application of the method detection limit (MDL), limit of quantitation (LOQ), and the AML. Similar to Rigo, we believe that most measurement variation is comprised of “a low concentration region where uncertainty is essentially constant, a transition zone and then a region where the uncertainty increases with concentration....”. Rigo states that he is concerned about the characterization of individual measurements by some sort of prediction interval in the context of regulatory compliance. He is not concerned about the development of lower limits to quantitation (“It really doesn’t matter what the quantitation limit is”). We disagree. The development of appropriate lower limits to quantitation is an important consideration in determining how low reliable measurement can be made and regulatory limits may be set. Additionally, the relative standard deviations associated with such limits may generally be used as rough upper estimates for the amount of measurement variation that will be found at higher concentrations. Development of accurate prediction intervals for individual measurements may be of interest, but this will require what is almost certain to be prohibitively expensive amounts of data. Rigo presents a generalized model for the relationship between measurement variation and average measurement result which we further generalize as s ) xa + bxj c, where s is the standard deviation determined by multiple measurements on well-mixed splits from a single sample; xj is the average concentration measurement over well-mixed splits from a single sample; and a, b, c, and d are constants estimated such that deviations from the model are approximately normal in distribution. Such a model will be very flexible in describing particular observed data sets. However, such flexibility may also allow estimated curves to diverge toward d
10.1021/es9920011 Not subject to U.S. Copyright. Publ. 1999 Am. Chem. Soc. Published on Web 03/04/1999
idiosyncratic departures from the true underlying relationship between standard deviation and average measurement result. Ideally, any estimated relationship between standard deviation and average measurement result will exhibit consistency across a range of analytes and analytical techniques. To this end, we are engaged in a data gathering at EPA that will, hopefully, provide a significant advance toward implementing such models in practical applications. We plan to submit the results of this work to this Journal when there are findings to report. While the model presented by Rigo is interesting, we suggest that rigorous evaluation in application to a number of both large and small datasets is required before attempting to use Rigo’s model under operational conditions. The example presented by Rigo (Figure la,b) is insufficient to convince us that his procedure has practical utility. Finally, Rigo mentions avoiding false positives and a concern for whether or not a measurement is likely to indicate compliance with a regulation or not. We are not familiar with how permit limits are expressed for stack emissions, but wastewater permit limits are expressed in terms of measurement results, as opposed to expressing the limit in terms of true concentration. If a measured concentration exceeds the wastewater permit limit, then the discharger is not in compliance with their permit. There are no “false positives”. Limits are developed based a number of factors, that include law, policy, science, technology, and public comments. Where science and technology do not provide clear differentiation between desirable and undesirable actions, law and policy strongly influence where the burden of proof lies between environmental protection and economic activity. For some limits, law or policy indicates that the government must demonstrate that guidelines are economically and technically achievable by the regulated industry. Such is the case with some technology based effluent guidelines. At the other extreme, law or policy may indicate that the government will require the discharger to demonstrate that they are unlikely to harm human health or the environment. Such is the case with water quality based effluent limits. In all cases, limits are developed based on a balance between public policy and individual rights.
Acknowledgments These comments reflect the personal opinions of the authors and not the policy of the U.S. Environmental Protection Agency.
Literature Cited (1) Gibbons, R. D.; Coleman, D. E.; Maddalone, R. F. Environ. Sci. Technol. 1997, 31, 2071-2077. (2) Kahn, H. D.; Telliard, W. A., White, C. E. Environ. Sci. Technol. 1998, 32, 2346-2348.
Henry D. Kahn,* William A. Telliard, and Charles E. White Engineering and Analysis Division (4303) Office of Science and Technology Office of Water U.S. Environmental Protection Agency Washington, DC 20460 ES9920011
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