When several measurements of different variables are available on each of the experimental subjects, this mixture of distributions situation ' becomes the well established discrim nant analysis and statistical classification problem. in our case of finding a mixture of distribu- RATIO ESTIMATION TECHNIQUES IN THE ANALYSIS OF ENVIRONMENTAL TRANSURANIC DATA tions in quality control data, the next statistical step is to go back to the laboratories involved. and coliect data on thair Operating pro- cedures and to collect quantitative data on as many variables as possible. A classical discriminant analysis on these additional data would then tell us which variables or factors are important in distinquishing "good" from "bad" Laboratories and what values of those variables are characteristic of a good laboratory. This information can then be used to help turn the "bad" laboratories into "good" laboratories--that's the Yeal purpose of quality control. Pamela G. Doctor and Richard 0. Gilbert Battelle Memorial Institute, Pacific Northwest Laboratory Richland, Washington ABSTRACT Ratios play a prominent role in the analysis of environmental transuranic data. The mathematical assumptions underlying the use of ratios are presented. The properties of seven different estimators of an average ratio and their standard errors are discussed with respect to their applicability to transuranic field studies. The behavior of these estimators, their standard errors, and confidence intervals are compared for three representative sets of data from safety-shot sites at the Nevada Test Site and Tonapah Test Range. Guidelines are given for deciding if an average ratio is appropriate. Recommendations for avoiding an inappropriate estimator are discussed. INTRODUCTION The purpose of this paper is to discuss the properties of ratios as they apply to environmental transuranic studies. We first review some ways ratios are used in transuranic field studies and some types of statistical analyses currently being appiied to ratios. We also discuss several methods for computing an average ratio giving the mathematical and statistical assumptions underlying each method and the factors to consider in choosing a method for a particular set of data. These methods are illustrated using data from Nevada Applied Ecolopy Group (NAEG) studies conducted at safetyshot sites at the Nevada Test Site (NTS) and Tonopah Test Range (TTR). Finally, some recommendations are listed for (1} deciding 1f an average ratio is a suitable quantity to summarize a set of data, and (if (1) is true) then (2) choosing the most appropriate estimator of the average ratio. 600 601