Estimation of the Quantity of a Drug in a Consignment from Measurements on a Sample

• NCJ Number: 197321
• Journal: Journal of Forensic Sciences Volume: 47 Issue: 5 Dated: September 2002 Pages: 968-975
• Author(s): Colin G. G. Aitken Ph.D.; David Lucy Ph.D.
• Date Published: September 2002
• Length: 8 pages
• Publication Format: Article
• Publication Type: Report (Study/Research)
• Language: English
• Country: United States of America

Annotation

This paper describes procedures for selecting a sample size from a drug shipment and, following examination of the contents of the sample, for estimating the total quantity of drugs in the shipment.

Abstract

The procedures described are used when a shipment of individual packages is thought to contain illegal material, such as drugs, in some or all of the packages. A sample from the shipment is inspected, and the quantity of drugs in each package of the sample is measured. The investigation must then estimate the total quantity of drugs in the shipment. Since sampling variation is present in the original measurements, it is not sufficient just to adjust the sample mean pro rata. This paper describes an analysis that takes into account the uncertainty regarding the proportion of the packages that contain drugs and provides a probabilistic summary of the quantity of drugs in the shipment. The procedures described yield a probabilistic lower amount for the quantity of drugs in the shipment, which is dependent on the required standard of proof. The method described, which was developed by Tzidony and Ravreboy (1992), considers the shipment as a population and the constituent packages examined as a sample. The quantities (weights) of drugs in the packages are assumed to be random variables that are normally distributed, with mean and variance. The mean quantity in a package in the shipment is estimated by the mean of the quantities found in the sample. A confidence interval is determined for the mean based on the sample size, the sample mean, the sample standard deviation of the quantities of drugs in the packages examined and an associated t-distribution. An estimate of the total quantity of drugs in the shipment is then determined by considering the size of the shipment and the proportion of packages in the shipment thought to contain drugs. A confidence interval may then be constructed that may be said to contain the true quantity of drugs with a given level of confidence. 2 figures and 14 references