NCJ Number
225899
Journal
Journal of Forensic Sciences Volume: 54 Issue: 1 Dated: January 2009 Pages: 135-151
Date Published
January 2009
Length
7 pages
Annotation
This article offers recommendations for the choice of the size of a sample for estimating the characteristics (parameters) of a population that consists of discrete items that may belong to one and only one of a number of categories, with examples drawn from forensic science.
Abstract
Four sampling procedures are described for binary responses, where the number of possible categories is only two, for example, licit or illicit pills. One is based on priors informed from historical data. The other three are sequential. The first of these is a sequential probability ratio test with a stopping rule derived by controlling the probabilities of type one and type two errors. The second is a sequential variation of a procedure based on the predictive distribution of the data yet to be examined and the distribution of the data that have been examined, with a stopping rule determined by a prespecified threshold on the probability of a wrong decision. The third is a two-sided sequential criterion that stops sampling when one of two competitive hypotheses has a probability of being accepted that is larger than another predetermined threshold. A fifth sampling procedure extends the ideas developed for binary responses to multinomial responses, where the number of possible categories (e.g., types of drug or types of glass) may be more than two. The procedure is sequential and recommends stopping when the joint probability interval or ellipsoid for the estimates of the proportions is less than a given threshold in size. For trinomial data, this last procedure is illustrated with a ternary diagram with an ellipse formed around the sample proportions. There is a straightforward generalization of this approach to multinomial populations with more than three categories. 8 figures, 5 tables, appended probability distributions, and 24 references