182 TRANSURANIC ELEMENTS IN THE ENVIRONMENT 



Among the difficulties that need further review, we would like to mention the 

 following: 



1. A model has to be assumed; so it is usually desirable, or necessary, to consider 

 several candidate models. This then brings in a need to try to decide from the data which 

 is "the" correct model and hence statistical analysis and selection of the best sampling 

 scheme for discriminating between models. 



2. When several parameters are involved, the optimization process usually requires a 

 computer to perform the calculations. 



3. In most cases advance estimates of the parameters are required. This may be seen as 

 a rather severe restriction, but, since most of the important models to be considered are 

 nonlinear, experimentation is not very practical without a fair amount of advance 

 knowledge of the system anyhow. 



Some Common Problems 



A number of problems common to the several kinds of sampling described here and to 

 studies of transuranics and other trace substances nee<l further consideration. Those 

 associated with "counting statistics" and "counting errors" have been the subject of 

 many investigations but continue to pose difficulties. Gilbert (1975) has prepared a 

 review relative to counting statistics in studies of the transuranics. One common problem 

 with low-level measurements has to do with the "below background," "not detectable," 

 or "trace" measurements. An approach that we believe deserves further study is the use 

 of simple nonparametric methods. When a data set contains a number of below- 

 background measurements, simple averages are likely to be biased, the direction of the 

 bias depending on how the questionable measurements are handled. In such cases it seems 

 that the median may be a preferable measure of central tendency and that assessing 

 variability may be approached through order statistics. As an example, suppose one takes 

 30 samples and, after analysis for a transuranic, find that 10 results are reported as "not 

 detectable." If a mean is to be computed, one must then decide how to incorporate these 

 10 measurements. Should they all be assumed to contain none of the substance under 

 study and be assigned "zero" values? Usually this is not reasonable since a longer 

 counting time, larger sample mass, etc., would likely have turned up detectable levels in 

 some of the 10 samples. The procedure suggested here is simply not to use the mean but 

 to change over to the median, which does not require any decisions about the 

 troublesome 10 "not-detectable" samples (except that their levels were, in fact, less than 

 those for which levels were reported). Rather than calculating standard deviations, one 

 would need to calculate measures of variability based on order statistics (Conover, 1971; 

 Hollander and Wolfe, 1973). Random sampling is, however, also required for nonpara- 

 metric methods. 



Another common problem is how to deal with the practice of taking aliquots 

 (subsamples). A related issue is the compositing of a group of samples. Both are related to 

 the analytical (chemical) process. In the former instance sample mass is reduced to 

 facilitate analysis; in the latter, a number of samples are combined in an effort to reduce 

 costs. The very high sample-to-sample variability characteristic of the transuranic 

 elements may cause trouble for the unwary investigator in either case. In both cases we 

 believe repHcate samples should be taken to provide a measure of the variability inherent 

 in the process. Of course, doing this increases costs. Compositing samples needs some 

 careful study to see whether it does, in fact, offer the gains that are usually assumed 

 without any checking. A major question about compositing soil samples is whether or not 



