Forensic Analysis Weighing Bullet Lead Evidence (2004) / Chapter Skim
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Appendix F: Simulating False Match Probabilities Based on Normal Theory
Appendix F: Simulating False Match Probabilities Based on Normal Theory
Pages 142-150
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From page 142... ...
The within-replicate variance is generally small, so we assume that the sample means of the three replicates are normally distributed; that is, x ~ N(,UX,CT2 / 3~; y ~ N(,ux + 6,cT2 / 3) , where "a" stands for "is distributed as." Thus, the difference in the means is 6.
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From page 143... ...
The equivalence t test proceeds as follows. Assume Ho |px—BY| 2 Hi : |~x—By | < where Ho is the null hypothesis that the true population means differ by at least 6, and the alternative hypothesis is that they are within ~ of each other.
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From page 144... ...
—q>(—Ka—~ I (sp~) = 0c where d>( ~ denotes the standard cumulative normal distribution function (for example, d>~1.645)
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From page 146... ...
146 TABLE F 1 continued APPENDIX F (6 I a)
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From page 147... ...
, and the resulting critical value comes from a noncentral F distribution (Ref. 15~.2 ESTIMATING MEASUREMENT UNCERTAINTY WITH POOLED STANDARD DEVIATIONS Chapter 3 states that a pooled estimate of the measurement uncertainty c,, sp, is more accurate and precise than an estimate based on only sx, the sample SD based on only three normally distributed measurements.
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From page 148... ...
One reviewer suggested that Spearman's rank correlation may be more appropriate, as it provides a nonparametric estimate of the monotonic association between two variables. Spearman's rank correlation coefficient takes the same form as Equation 2, but with the ranks of the values (numbers 1, 2, 3, ..., n = number of data
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From page 149... ...
The values in the cells on either side of the diagonal are the same because the correlation between, say, As and Sb is the same as that between Sb and As. For these offdiagonal cells, the first line reflects the conventional Pearson correlation coefficient based on the 1,373-bullet subset from the 1,837-bullet subset (bullets with all seven measured elements or with six measured and one imputed for Cd)
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From page 150... ...
All three sets of correlation coefficients are highly consistent with each other. Regardless of the method used to estimate the linear association between elements, associations between As and Sb, between As and Sn, between Sb and Sn, and between Ag and Bi are rather high.
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