which estimates, and corresponding confidence intervals, for the probability in question can be obtained. No comprehensive information on this is currently available. Consequently, this chapter has given more attention to the only fully measurable component of variability in the problem, namely, the measurement error, and not to the other sources of variability (between-CIVL variability) which would be needed to estimate this probability.
Test statistics that measure the degree of closeness of the chemical compositions of two bullets are parameterized by critical values that define the specific ranges for the test statistics that determine which pairs of bullets are asserted to be matches and which are asserted to be non-matches. The error rates associated with false assertions of matches or non-matches are determined by these critical values. (These error rates we refer to here as the operating characteristics of a statistical test. The operating characteristics are often called the significance level or Type I error, and the power or Type II error.)
This chapter describes and critiques the statistical methods that the FBI currently uses, and proposes alternative methods that would be preferred for assessing the degree of consistency of two samples of bullet lead. In proposing improved methods, we will address the following issues:
General approaches to assessing the closeness of the measured chemical compositions of the PS and CS bullets,
Data sets that are currently available for understanding the characteristics of data on bullet lead composition,
Estimation of the standard deviation of measures of bullet lead composition, a crucial parameter in determining error rates, and
How to determine the false match and false non-match rates implied by different cut-off points (the critical values) for the statistical procedures advocated here to define ranges associated with matches, non-matches, and (possibly) an intermediate situation of no assertion of match status.
Before we address these four topics, we critique the procedures now used by the FBI. At the end, we will recommend statistical procedures for measuring the degree of consistency of two samples of bullet lead, leaving the critical values to be determined by those responsible for making the trade-offs involved.
The FBI currently uses the following three procedures to assert a “match,” that is, that a CS bullet and a PS bullet have compositions that are sufficiently similar3 for an FBI expert to assert that they were manufactured from CIVLs