USE OF RATIOS IN TRANSURANIC FIELD STUDIES Ratios play a prominent role in environmental transuranic studies. A major application is to ecosystem models where a ratio is used to express the relationship between transuranic concentrations in various ecosystem components. Two examples are found in the Proceedings of the Workshop on Environmental Research for Transuranic Elements (1976, pp. 23-24): the concentration ratio (CR), defined as activity per weight of plant part : activity per weight of substrate or reference material and the inventory ratio (IR), defined as activity per unit area in product , activity per unit area in source Other uses of ratios in environmental transuranic studies include detecting whether differential movement between two elements, say Pu and Am, is occurring in the soil profile, and as a means of detecting local contamination by some transuranic element by noting a change in its ratio to another element (or isotope) from their background level ratio. This paper deals mainly with the use of average ratios. It is important to realize, however, that there are situations where an average ratio is not appropriate, e.g. when there is a systematic change in the ratio over space or time. An illustration of this is the detection of local contamination mentioned above. Suppose we have the situation in Figure 1: a ??9Pu source and sampling sites located downwind from it. Rather than calculate an average ratio of 239Pu to 238py over all sites, it would seem more appropriate to know how the ratios change with increasing distance from ground zero. Ratio data have been presented in a variety of ways in the environmental transuranic literature. A simple List of ratios or average ratios from different sites is sometimes given. This is appropriate when the data come from different study sites and there is no justification for pooling the data or for performing any further statistical treatment. Ratios have also been presented in histogram form. This was done, for example, by Emery et al. (1976), to compare the distribution of ratios in various ecosystem components in their study of U-pond at Hanford. One can also plot the numerator versus the denominator or the logarithms of the numerator versus logarithms of the denominator and view the estimation of a ratio as a regression 602 239 Py CONTAMINATION SOURCE Figure 1. AREA Change in Ratio 23%Pu/235Pu over Space through the origin. Alternatively, ratio data are often presented as an average ratio, sometimes with an estimated standard error, but often without any indication as to how the average or its standard error were calculated. There are certain problems associated with estimating an average ratio. The statistical properties of ratios have not been fully developed and the properties of average ratios that are known do not appear to be widely understood. It is known, e.g. that the estimated average ratio is often statistically biased and in most cases the variance of the estimate is only an approximation (Cochran, 1963, p. 160~163). The problem is further compounded by the many ways an average ratio can be estimated. 693