Interpretation of glass composition measurements: the effects of match criteria on discrimination capability

The concentrations of ten elements in 209 unrelated glass specimens received as evidence were used to assess the frequencies of errors of false association (Type II errors) using several comparison criteria at specified significance levels (Type I errors). Pairwise comparisons of the samples using either the equal-variance t-test or Welch's modification (unequal variances) result in a small number of errors of false association, even when adjusting the significance level (Bonferroni correction) for multivariate comparisons. At the 95% confidence level (overall Type I error of 0.05, or individual element comparison error of 0.005), only two Type II errors are made in 21736 comparisons (0.009%) when using the equal-variance t-test for comparison of sample means. In this study, the range overlap test using three replicate measurements per specimen results in no errors of false association. Most specimen pairs in this data set are readily discriminated either by differences in the concentrations of several elements or by an extremely large difference in the concentrations of one or more element.