RATIOS IN TRANSURANIC ELEMENT STUDIES 193 



process (Parzen, 1967. p. 1 18). The Poisson distribution is a distribution of the number 



of randomly dispersed particles in a given volume. The appropriateness of this approach 



for describing the variability in observed radionuclide concentration as a function of 



aliquot size depends on the relationship between radionuclide concentration and the 



number of particles in a sample. We feel that the Poisson distribution as a model of 



radionuclide concentration witliin a sample deserves study. This skewness to large values 



is also characteristic of environmental radionuclide concentrations taken from samples at 



different locations; so perhaps the Poisson distribution would find use in this situation as 



well. 



Although it is unusual to analyze 20 aliquots per sample, it is instructive to compare 



the effects of this variability on the observed average concentration for each aliquot size. 



The sample median (middle value of the observed concentrations) is denoted by an 



asterisk in Fig. 3. Contrary to what might be expected, the medians show more variation 



with aliquot size than the sample arithmetic means (connected by the broken line). 



Skewness affects the median more than the mean, as evidenced by the 50- and 100-g data 



for which skewness is least pronounced, and the mean and median are very close [see 



Michels (1977) for theoretical justification] . Since aliquots of all sizes are all from the 



same composite sample, theoretically the means should remain constant across aUquot 



size. This appears to be the case here. 



It should be emphasized that this example illustrates within-sample variability and not 



variability due to different locations. However, in an environmental radionuclide study, 



one is faced with between-location variability as well. One value of this study is that it 



provides information on within-sample variabiUty which, in turn, permits an evaluation of 



the amount of observed variability due to location differences. Similar studies might 



precede a full-scale sampling effort that encompasses a new radionuclide, a new source, or 



a new medium. Such studies provide a rationale for choosing an aliquot size that will 



minimize within-sample variability under the constraints of laboratory capability and cost 



(Doctor and Gilbert, 1979). 



Vegetation Concentrations 



The problems of obtaining reliable vegetation concentrations in the picocurie range are 

 illustrated by data on plant uptake of i34-i 3 7q collected at the Savannah River Plant 

 near Aiken, S. C. [See Sharitz et al. (1975) for a description of the site.] Here the sample 

 or ahquot size, unlike that for soil concentrations, cannot be controlled by the researcher. 

 The data consist of fifty-five ' ^^-i 3 v^^^ concentrations and sample weights of leaves from 

 Hypericum walteri growing on the floodplain of a South Carolina stream receiving reactor 

 effluents. Since some sampling designs may require that the sample be collected from a 

 species at a particular location without regard to the size of the individual, the same type 

 of data as that illustrated in Fig. 4 may result. Except for two high values at 0.4 g, the 

 variability is dramatically increased for samples weighing <0.2 g. It appears that for these 

 samples the assumption of uniform dispersal is seriously violated, which shows that 

 observed concentration is not independent of sample size (compare with Fig. 1). The 

 errors in measuring the cesium are large relative to the weight of the sample. 

 Furthermore, if negative readings occur and are either disregarded or reanalyzed until 

 positive values are obtained, a positive bias will be introduced, and this bias will be greater 

 for the smaller samples. Even if the accuracy of determining radionuclide content is 

 controlled, variation due to small sample weights may still be a problem if the range of 

 sample weights is large. 



