/ 78 TRANSURANIC ELEMENTS IN THE ENVIRONMENT 



differences exist among them that may enable us to form or to verify hypotheses about 

 the forces at work in the population." Not much space is devoted to this topic in the 

 textbooks, perhaps because it is very similar to the older body of methodology 

 encompassed under the heading of the analysis of variance and mostly (but not 

 necessarily) used in an experimental context. As mentioned in the introduction, the 

 mechanical details of analysis are very much the same whether an experiment or a survey 

 is involved. It may be, however, that survey sampling methodology has something 

 additional to offer in the way of ideas on allocating samples to "domains of study." We 

 have been impressed by the potential advantages of using auxiliary variables to increase 

 efficiency, i.e., to reduce costs by use of the analysis of covariance (Eberhardt, 1975b). 



One of many comparisons that can be made is illustrated in Fig. 1 where the diagram 

 has been cut in two directions to suggest that an investigator may want to use statistical 

 methods to determine whether there are significant differences in concentrations along 

 transects in two (or more) directions. 



Sampling for Modeling 



Sampling for modeling covers a lot of ground. Perhaps one instance will serve to illustrate 

 the topic. Consider the uptake and retention of some radionuclide in an animal. Suppose 

 the analyses are expensive and involve sacrificing animals for each determination (ai, : 

 often the case for the transuranics). Since the process is a dynamic one, the outcomes 

 usually are represented by fitting a curve (modeling) and estimating rate constants (or 

 half-times). Some time, trouble, and money might be saved by studying ways to select 

 sampling times so as to obtain the "best" estimates of the parameters (rate constants). So 

 far as we can tell, this point has not been considered in the many thousands of laboratory 

 studies on radionucUdes and other trace substances over the last 30 yr in which 

 sampling times are either uniformly spaced or occasionally separated by geometrically 

 increasing intervals. One must, of course, also pay attention to determining the structure 

 of the models used and to various other points (Eberhardt et al., 1976; Eberhardt, 1978). 

 In Fig. 1 the basic idea is suggested by a heavy line denoting a specific model fitted to 

 concentrations in one direction from the source. In practice one might want to fit a 

 model to the entire surface. This might also involve comparisons to see whether a 

 directional component is needed in the model; so analytical aspects also may be involved. 



Sampling Methods and Research Needs 



In this section we cite additional references and identify problems that require additional 

 consideration. The discussions are arranged in the four categories of sampling methods 

 previously described and are followed by a section devoted to common problems. 



Descriptive Sampling 



The textbooks devoted to descriptive sampling discuss extensively a rather wide variety of 

 methods for estimating totals or means by sampling. We mention only those few methods 

 with which we have had some experience. The main method is stratified samphng, 

 wherein elements of the population to be sampled are assigned to one of a number of 

 strata. The basic idea is to assign elements to strata so that the elements in each are as 

 nearly alike as possible. If this is successful, then the variability within a given stratum is 

 kept small, and the costs of sampling are thereby reduced. Some advance knowledge on 

 which to base the stratification (the classification of population elements) is evidently 



