RA TIOS IN TRANSURANIC ELEMENT STUDIES 1 9 1 



X (ALIQUOT SIZE) 



Fig. 2 Theoretical relationship between activity and aliquot size. (Adapted from Doctor 

 and Gilbert, 1979.) 



assuming a symmetric distribution for Y about the fitted line, is that the variance of Y 

 must go to zero as X goes to zero. This is usually stated: the variance of Y at a particular 

 X is some function of X; i.e., 



a2(Y|X) = f(X) 



Snedecor and Cochran (1967, pp. 166-171) give methods for obtaining the weighted 

 least -squares estimates of 7 when f(X) = kX and kX' , where k is a constant. Doctor and 

 Gilbert (1^77) compared the behavior of these ratio estimates along with the sample 

 median of the ratios and the log-normal estimate of the median ratio for three sets of 

 transuranic data from Nevada Applied Ecology Group studies. 



This classic approach to ratio estimation is often not applicable for estimating the 

 true mean concentration horn a set of environmental radionuclide data for two reasons. 

 First, as the amount of sample material decreases, the variability in observed radionuclide 

 activity tends to increase rather than decrease. Second, in the case in which the sample 

 size is under the researcher's control, e.g., soil samples, the usual laboratory practice is to 

 analyze only one size aliquot; so regression analysis is impossible. The variability problem 

 of radionuclide concentrations is discussed in the context of two examples: first, ^^^Pu 

 soil concentrations in a desert environment as the result of a nuclear test and, second, 

 1 34-1 3 7(^g vegetation concentrations taken from a stream bed receiving reactor effluents. 



Soil Concentrations 



The data consist of twenty ^'*' Am concentrations from each of five aliquot sizes (1, 10, 

 25, 50, and 100 g) taken from the same composite soil sample collected near nuclear site 

 201 at the Nevada Test Site. The aliquoting procedure (discussed by Doctor and Gilbert, 

 1979) was designed to ensure as homogeneous a dispersal of the americium as possible. 

 The concentrations are plotted in Fig. 3, where the solid lines delineate the range of the 

 data. The variability tends to increase as aliquot size decreases; the variability of the 1-g 



