STATISTICS AND SAMPLING IN TRANS URANIC STUDIES 181 



1972) and have continued to study the issues (Gilbert and Eberhardt, 1976b). The main 

 difficuky again has to do with variability since rather large numbers of replicate 

 determinations are required to give reasonable assurance of detecting differences between 

 laboratories. Proper allocation of samples (replicates) to methods, elements, and 

 laboratories should help, but this has not been investigated in any detail. 



In a statistical analysis of transuranic data, frequency distributions are often 

 dramatically skewed (asymmetrical). Thus consideration should be given to transforming 

 the data before analysis. We have looked into this option in some detail (Eberhardt and 

 Gilbert. 1973: Eberhardt et al., 1976). Our recommendation is to use a logarithmic 

 transformation of the data before doing any statistical analyses involving significance tests 

 based on the normal distribution. A feasible alternative is to consider nonparametric (or 

 distribution-free) methods. We have begun some limited investigations in this area. We 

 particulariy do not recommend estimating means (averages) by transforming back the 

 mean of log-transformed data (Link and Koch, 1975). If interest is directed chiefly to 

 estimating means on the original (untransfomied) scale, we recommend use of the 

 ordinary aritlimetic average of the untransformed data. If interest is chiefly in a statistical 

 analysis, then the resuUs should be discussed in terms of the transformed data. The 

 problem of how to allocate samples to accommodate both purposes, however, seems to us 

 to need more attention. 



Sampling for Modeling 



Many sampling and statistical problems must be dealt with if modeling is eventually to 

 achieve truly satisfactory status in environmental studies. Most of the present prospects 

 for models contain a substantial number of rate functions that are little more than 

 guesses. Rather than go into these problems, which transcend statistical and sampling 

 issues, we will only mention some simple models. A few details of methods for finding 

 optimum sampling times for a rather simple, but widely applicable, model are given by 

 Eberhardt (1978). 



Three categories of simple models can alternatively be described as profiles of 

 concentration in time or space: (1) retention of some substance by an animal, 

 (2) measuring concentrations away from a point source, and (3) studying soil profiles. 

 Two facets of such studies may need to be considered in designing a study by sampling. 

 One is whether the investigator's main interest is in estimating rate constants or in 

 describing the profile itself since different sampling plans are then appropriate. A second 

 concerns the nature of replications. In retention studies individual animals can serve as 

 replicates, but. in the evaluation of soil profiles, the word "replicate" will not have the 

 same meaning; so sampling results may have rather different interpretations in the two 

 instances. Eberhardt (1978) gives some further details on sampling profiles. Essington 

 et al. ( 1976) give a number of details on actual soil profiles of several transuranics. 



The notion oi sampling for modeling, which can also be described as sampling for 

 curve fitting (in a more restricfive sense), appears to be new in environmental studies. As 

 such it poses a number of problems that need further evaluation. The reader interested in 

 technical details might well start with the review by Cochran (1973). which provides 

 addifional references. Papers by Atkinson and Hunter ( 1968). Box and Lucas (1959), and 

 Box (1968: 1970: 1971) should also be consulted. As has already been noted, our 

 attention has been focused on finding the optimum times (or depths, or distances) for 

 sampling in the interest of obtaining a maximum amount of information for a given 

 samphng cost. 



