Reflections on Glass Standards: Statistical Tests and Legal Hypotheses

Statistical Applicata (Italian Journal of Applied Statistics) recently published several issues (volume 27, nos. 2 & 3) devoted to statistics in forensic science and law. They include an invited article I prepared in 2016 on the statistical logic of declaring pieces of glass "indistinguishable" in their physical properties. 1/ The article contains some of the views expressed in postings on this blog (e.g., Broken Glass: What Do the Data Show?). However, the issue is much broader than glass evidence. The article notes the potential for confusion in reporting that any kind of trace-evidence samples match (or cannot be distinguished) without also describing data on the frequency of such matches in a relevant population. I am informed that NIST's Organization of Scientific Area Committees on Forensic Science (OSAC) is preparing guidelines or standards for explaining the probative value of results obtained from ASTM-approved test methods.

Abstract

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The past 50 years have seen an abundance of statistical thinking on interpreting measurements of chemical and physical properties of glass fragments that might be associated with crime scenes. Yet, the most prominent standards for evaluating the degree of association between specimens of glass recovered from suspects and crime scenes have not benefitted from much of this work. Being confined to a binary match/no-match framework, they do not acknowledge the possibility of expressing the degree to which the data support competing hypotheses. And even within the limited match/no-match framework, they focus on the single step of deciding whether samples can be distinguished from one another and say little about the second stage of the matching paradigm–characterizing the probative value of a match. This article urges the extension of forensic-science standards to at least offer guidance for criminalists on the second stage of frequentist thinking. Toward that end, it clarifies some possible sources of confusion over statistical terminology such as “Type I” and “Type II” error in this area, and it argues that the legal requirement of proof beyond a reasonable doubt does not inform the significance level for tests of whether pairs of glass fragments have identical chemical or physical properties.

Note

1. The article is David H. Kaye, Reflections on Glass Standards: Statistical Tests and Legal Hypotheses, 27 Statistica Applicata -- Italian J. Applied Stat. 173 (2015). Despite the publication date assigned to the issue, the article, as stated above, was not written until 2016.