Thursday, March 3, 2016

What Is a "Conservative" Method in Forensic Statistics?

Statistical hypothesis testing involves a "null hypothesis" against an "alternative hypothesis." If data are not well outside the range of what would be expected if the null hypothesis is true, then that hypothesis cannot be rejected in favor of the specified alternative. It is usually thought that the more demanding the statistical test, the more "conservative" it is. For example, if a researcher claims to have discovered a new treatment that cures cancer, the null hypothesis is that the new therapy does not work. Sticking with this belief retains the status quo (of not using the novel treatment). In this example, the "conservative" thing to do is to insist on a small p-value (results that have a small probability of arising if the treatment is ineffective) before accepting the alternative.

Does this carry over to forensic science? Is it conservative to retain the null hypothesis unless there is strong evidence against it? Consider the following excerpt from an FBI publication on forensic glass comparisons 1/:
A conservative threshold will differentiate all samples from different sources but may also indicate that a difference exists in specimens that are actually from the same source. A high threshold for differentiation may not be able to differentiate all specimens from sources that are genuinely different but will not differentiate specimens that are actually from the same source.
The "conservative" scientific stance therefore tends to support or preserve the prosecution's case. The state can produce a witness who can testify "conservatively" to finding that the broken window at the crime scene is chemically indistinguishable from the bit of glass removed from the defendant's sweatshirt.

On the other hand, a committee of the National Academic of Sciences that studied forensic DNA testing defined "conservative" in terms of impact on a defendant's claim of innocence 2/:
Conservative—favoring the defendant. A conservative estimate is deliberately chosen to be more favorable to the defendant than the best (unbiased) estimate would be.
Plainly, the FBI document's use of "conservative" is difficult to square with the NAS committee's definition of the word. The FBI document treats the hypothesis that favors the hypothesis supporting the prosecution's case as the status quo that should be retained unless there is strong evidence to the contrary.

This use of the prosecution's hypothesis that the broken window is the source of the incriminating fragment as the null hypothesis is not necessarily wrong, but it engenders confusion. The confusion can be dispelled if the presentation of the findings includes a statement of how rare or common "indistinguishable" windows are in a relevant population. Evaluating the data about the glass thus would have two steps. In step 1, the data are classified as"indistinguishable" (or not). If the samples are indistinguishable, then a random match probability is provided to indicate its probative value with respect to the hypothesis that the glass originated from the broken window.

Of course, if one could articulate the probability of the data given the hypothesis that the source is broken window versus the probability that the glass associated with the defendant had a different origin, this two-step process would not be needed. The expert could present these probabilities.

  1. Maureen C. Bottrell, Forensic Glass Comparison: Background Information Used in Data Interpretation, 11 Forensic Sci. Communications No. 2 (2009)
  2. National Research Council, Committee on The Evaluation of Forensic DNA Evidence: An Update, The Evaluation of Forensic DNA Evidence 215 (1996)

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