Contaminants in marine organisms: Pooling strategies for monitoring mean concentrations.

Abstract

Samples of marine organisms collected for contaminant monitoring are often pooled before being chemically analysed. The main reasons for pooling samples are: 1) to obtain a sufficient quantity of tissue to make the chemical analysis possible; 2) to reduce the overall cost of chemical analyses; 3) to improve the precision of the estimated mean contaminant concentration in a population by increasing the sample size without increasing the number of chemical analyses. However, there are several questions associated with pooling, including: • what is an appropriate pooling strategy? • how should data from pools be statistically analysed? • how should results derived from pooled data be interpreted? This document is an introduction to the statistical aspects of pooling. Unfortunately, it is not possible to consider all the situations in which pooling might arise, nor to describe the many types of statistical analysis that might be appropriate. The scope is too large, and we do not know all the answers. Here consideration is given to the relatively simple case of estimating the mean concentration of a contaminant in a population; it shows the typical problems encountered in devising an appropriate pooling strategy and statistically analysing data from pools. In particular, it shows how the choice of the number of pools and the number of individuals in each pool allows a balance to be made of the precision of the estimated mean concentration against the sampling and analytical costs incurred in obtaining that estimate. Although the level of statistical sophistication increases through the text (notably between Sections 3 and 4), it is hoped that all readers will understand the basic ideas and be able to use this document to develop sensible pooling strategies. Many readers will be able to develop the theory for their own particular monitoring problems; others will no doubt correct our mistakes and direct us to the literature we have missed. Much of the following material was developed by the ICES Working Group on Statistical Aspects of Trend Monitoring (ICES, 1987, 1988, 1989, 1990, 1991a, 1992), where pooling questions were addressed as part of the analysis of data collected in the Cooperative ICES Monitoring Studies Progranune (CMP) for contaminants in fish and shellfish. The contents of this document are as follows: • Section 2 discusses some practical and logistical problems associated with sample collection and pre-treatment. I • Section 3 develops the basic statistical theory of pooling for estimating the mean concentration of a contaminant in a population. For simplicity, the individual sample weights are assumed to be the same. It is shown how to formulate objective strategies for choosing the number of pools and the number of individuals in each pool and apply the results to a real example. • Section 4 generalizes the theory to allow for varying individual sample weights. • Section 5 provides a simple overview and summarizes important points that make the statistical analysis of data from pools straightforward. • Annexes I to 3 briefly describe extensions to the statistical theory,