Risk Analysis, Vol. 33, No. 3, 2013 DOI: 10.1111/risa.12021 Response Response to Mark Powell’s Comments Peyton M. Ferrier and Jean C. Buzby In his recent comments on “The Economic Ef- ficiency of Sampling Size: The Case of Beef Trim,” Mark Powell (2013) expresses concerns over the va- lidity of our findings stemming mainly from the spec- ification of our benefit function. (1) Specifically, Dr. Powell believes, first that we incorrectly specified the prevalence rate; second that this error causes our benefit function to overstate the damages associated with any given prevalence rate; and, third, that there are other errors with our model. We disagree and ex- plain our reasoning in this response. Before addressing Dr. Powell’s specific concerns, we reiterate that our article’s purpose was to address the choice of sampling size in the testing of food for health and other risks. Within official statements de- scribing the USDA’s Food Safety and Inspection Ser- vice (FSIS) sampling protocol, it is asserted that the sampling size of food safety tests represents a specific statistical significance level for a given set of condi- tions about the world. Specifically, FSIS guidelines for beef trim sampling state: “60 selected portions are needed to have 95% confidence that contami- nation will be detected when the percentage of po- tential portions (that could have been selected) that are contaminated is equal to 5%.” (2) These guide- lines do not justify why the 95% significance level is the appropriate statistical criterion for the test’s significance (β ) nor why 5% is deemed an accept- able conjectured prevalence rate (p) around which to design a test. As various interest groups and pol- icymakers have noted, specifying lower levels of β and p necessitates a larger sample size n. While im- proving risk outcomes, increasing sample sizes also increases the costs of testing. Our article applies cost- benefit analysis to the selection of a test’s β -level or, equivalently, its sample size, to account for this tradeoff. First, in addressing the comments, please note that our definition of the prevalence rate (p) differs from Dr. Powell’s presentation of it. We define the prevalence rate as “the rate at which samples in a contaminated lot contain Escherichia coli O157:H7.” We specifically chose this definition to parallel the notion of p representing the “percentage of poten- tial portions (that could have been selected)” defini- tion used in the FSIS draft guidelines. In contrast, Dr. Powell’s comments characterize our prevalence rate as: “p = prevalence rate of E. coli O157:H7 within contaminated lots.” Whereas our definition specifi- cally refers to the presence of E. coli O157:H7 on potential samples, Dr. Powell’s focus is on the distri- bution of the pathogen throughout the entire surface area of the carcass. Dr. Powell then notes that the likelihood that a sampled piece of beef trim contains E. coli O157:H7 (given some distribution of the pathogen on car- casses) depends on the surface area of the sampled trim. We do not deny this but feel that it is beside the point. We have tacitly assumed that the sampling process, including the size and surface areas of “po- tential portions,” are roughly equivalent across tests. If one allows for significant deviation from that as- sumption, one introduces an entirely new line of in- quiry into the appropriate design of tests. We feel that consideration of the prevalence rate under our definition is appropriate given the particular policy question we aim to address (i.e., the choice of sam- pling size) and given the existing FSIS guidelines jus- tifying the sample size. In reference to Dr. Powell’s assertion that our specification of the prevalence rate constitutes a fundamental error, we disagree and feel his argument is primarily semantic. He redefines our prevalence rate and then asserts that we are incorrect owing to the disagreement. Second, Dr. Powell believes that our definition of the prevalence rate leads to our overestimating the damages of the pathogen within our benefit func- tion. This function is the averted health damage 353 0272-4332/13/0100-0353$22.00/1 Published 2013. This article is a U.S. government work and is in the public domain for the USA.