TABLE K.13 Statistics on bullet 1,044, to illustrate “Chaining” (see Section 3.4 and Figure K.9)

 

As

Sb

Sn

Bi

Cu

Ag

Cd

Avg

0.0000

0.0000

0.0000

0.0121

0.00199

0.00207

0.00000

SD

0.0002

0.0002

0.0002

0.0002

0.00131

0.00003

0.00001

Avg(42 Avgs)

0.0004

0.0004

0.0005

0.0110

0.00215

0.00208

0.00001

SD(42 Avgs)

0.0006

0.0005

0.0009

0.0014

0.00411

0.00017

0.00001

Larger SDs lead to wider intervals and hence more matches. Using avg(42 avgs) ± 2SD(42 avgs) as the new 2-SD interval with which to compare the 2-SD interval from each of the 1,837 bullets results in a total of 58 matching bullets. (Even without the four bullets that have suspiciously wide 2-SD intervals, the algorithm yielded 57 matching bullets.) Although this illustration does not present a rigorous analysis of the FPP for chaining, it demonstrates that this method of assessing matches is likely to create even more false matches than either the 2-SD-overlap or the range-overlap procedure.

One of the questions presented to the committee (see Chapter 1) was, “Can known variations in compositions introduced in manufacturing processes be used to model specimen groupings and provide improved comparison criteria?” The authors of Ref. 8 (Carriquiry et al.) found considerable variability among the compositions in the 800-bullet data set; the analyses conducted here on the 1,837-bullet data set demonstrate that the variability in elemental compositions may be even greater than that seen in smaller data sets. Over 71,000 bullets have been chemically analyzed by the FBI during the last 15 years; thousands more will be analyzed, and millions more produced that will not be analyzed. In addition, thousands of statistical clustering algorithms have been proposed to identify groups in data with largely unknown success. For reasons outlined above, chaining, as one such algorithm, is unlikely to serve the desired purposes of identifying matching bullets with any degree of confidence or reliability. Because of the huge number of clustering algorithms designed for different purposes, this question on model specimen groupings posed to the committee cannot be answered at this time.

4. EQUIVALENCE TESTS

4.1 Concept of Equivalence Tests

Intuitively, the reason that the FPP could be higher than that claimed by the FBI is that the allowable range of the difference between the two sets of element concentrations is too wide. The FBI 2-SD-overlap procedure declares a match on an element if the mean difference in concentrations lies within twice the sum of the standard deviations; that is, if for all j = 1,2, …, 7



The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement