180 TRANSURANIC ELEMENTS IN THE ENVIRONMENT 



Two applications of sampling for spatial pattern are the evaluation of resuspension, 

 where the pattern of surface contamination obviously is a controlling factor, and the 

 difficult matter of determining what portions of an area of high concentration should be 

 cleaned up (i.e., soU removed etc.). Wallace and Romney (1975) give a detailed review of 

 past experience, methods, and problems in cleaning up contaminated areas. 



From a statistical point of view, many of the problems in designing a sampling plan 

 for measuring pattern remain unresolved or uncertain. The main technique for displaying 

 the results of sampling for pattern is a contour map. Such a map is prepared by computer 

 programs that interpolate between average concentrations assigned to points on a uniform 

 grid. The chief problems to be resolved are those associated with the weighting processes 

 used to transform the observed data into grid entries. At first glance, these problems may 

 seem to be minor — fine points of statistical technique. We have now compared enough 

 contours generated by various methods, however, to be able to demonstrate that the 

 differences are not minor ones; see, for example. Fig. 3 of the report by Gilbert et al. 

 (1976b, p. 457) and the series of graphs by Gilbert, Eberhardt, and Smith (1976). Some 

 technical aspects of the problems have been discussed by Gilbert (1976). 



Mapping the concentrations is only the first stage in the cleanup problem. If 

 contaminated soils are removed, then it is usually necessary to make certain that the job 

 is done adequately; i.e.. Are there areas of unacceptably high concentration remaining? 

 Gilbert and Eberhardt (1977) have described one possible sampling scheme for this 

 purpose (acceptance sampling). Since cleanup operations are expensive and usually 

 damaging to the environment, this matter needs further study. 



Analytical Sampling 



The statistical technology of analytical sampling is closely related to traditional methods 

 of statisfical analysis. An alternate designation that we find useful is "sampling for 

 comparisons." The area is a broad one and includes changes in sp^ce and time, analysis of 

 spatial patterns, etc. Some examples of statistical analysis that involve sampling follow. 



One of the more difficult features in analyzing data is the problem of dealing with 

 ratios of variable quantities. This well-known statistical problem is accentuated by the 

 very high variability associated with the transuranic elements. A common example is the 

 so-called "concentration factor," which is really a ratio. [The plant panel at the 1975 

 transuranic workshop in Seattle defined a "concentration ratio" (CR) and an "inventory 

 rafio" (IR), thus supplying accurate names to replace the former "concentration factor" 

 (Energy Research and Development Administration, 1976)]. The difficulties in dealing 

 with ratios have been addressed in a number of the reports cited previously, and a recent 

 evaluation is that of Doctor and Gilbert (1977). As these authors note, there are three 

 well-known ways ratios of variable quantities can be estimated: (1) by averaging ratios of 

 individual pairs of observafions, (2) by summing up the x and y observafions and 

 calculating a ratio of totals, and (3) by a calculation of the type used to obtain the slope 

 estimate in regression analysis (except that the "corrections for the means" are dropped 

 so that the slope is appropriate to a regression calculated through the origin, i.e., the 

 intercept is zero). They also describe two other possibilities and note that the several 

 methods can give quite different results. Thus there is not only the problem of which 

 method of estimation to use but also the issue of how to allocate sampling effort so as to 

 make comparisons (of ratios) that are as meaningful as possible. 



Another problem in statistical analysis is associated with interlaboratory comparisons. 

 We have pointed out something of the uncertainties involved (Eberhardt and Gilbert, 



