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Statistical Considerations in Environmental Microbial Forensics

Abstract

In environmental microbial forensics, as in other pursuits, statistical calculations are sometimes inappropriately applied, giving rise to the appearance of support for a particular conclusion or failing to support an innately obvious conclusion. This is a reflection of issues related to dealing with sample sizes, the methodologies involved, and the difficulty of communicating uncertainties. In this brief review, we attempt to illustrate ways to minimize such problems. In doing so, we consider one of the most common applications of environmental microbial forensics—the use of genotyping in food and water and disease investigations. We explore three important questions. (i) Do hypothesis tests’ P values serve as adequate metrics of evidence? (ii) How can we quantify the value of the evidence? (iii) Can we turn a value-of-evidence metric into attribution probabilities? Our general conclusions are as follows. (i) P values have the unfortunate property of regularly detecting trivial effects when sample sizes are large. (ii) Likelihood ratios, rather than any kind of probability, are the better strength-of-evidence metric, addressing the question “what do these data say?” (iii) Attribution probabilities, addressing the question “what should I believe?,” can be calculated using Bayesian methods, relying in part on likelihood ratios but also invoking prior beliefs which therefore can be quite subjective. In legal settings a Bayesian analysis may be required, but the choice and sensitivity of prior assumptions should be made clear.

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