STATISTICS AND SAMPLING IN TRANS URANIC STUDIES 179 



necessary. Often this prior information can be obtained by some relatively inexpensive 

 means of measurement, or it may be known or inferred from information about the 

 source of contamination etc. 



Once the strata have been determined, the total sample must be allocated to the 

 several strata. Two general approaches have been used, proportional and optimum 

 allocation. In proportional allocation the sample is distributed simply in proportion to 

 the number of elements in each stratum (e.g., in soil sampling, to the area of the stratum). 

 This scheme is suitable if the variances are about the same in each stratum. Variances 

 associated with the transuranic elements, however, increase dramatically with mean 

 concentrations. We thus recommend optimum allocation, which is based on both size of 

 stratum and variability within the stratum. 



Our initial efforts at stratification for sampling soil for plutonium at the Nevada Test 

 Site are described by Eberhardt and Gilbert (1972). Many of the details of our 

 subsequent experience appear in Gilbert et al. (1975). An alternative approach to 

 stratified sampling is to use an accurate but expensive method (such as chemical analyses 

 for plutonium) to "calibrate" a less accurate but cheaper method. Methods of this sort 

 fall under the heading of double sampling in textbooks. Some details of an application of 

 double sampling to sampling for plutonium appear in Gilbert and Eberhardt (1976a). The 

 method uses ratios or regressions of rather variable quantities and thus poses some 

 statistical problems (mentioned again later in this chapter). An important action in 

 designing a double-sampling scheme is to use a cost function to find the combination that 

 yields minimum cost (or that maximizes precision). 



In soil sampling for inventory, sampling by depth needs further study. Much of 

 our work with stratified sampling has been concerned chiefly with a thin surface soil 

 layer. Since most of the plutonium is in that layer and resuspension questions focus there, 

 this is a logical approach. Some soil profiles, however, have been taken to investigate 

 vertical dispersion, and a detailed evaluation of allocation schemes for sampling in depth 

 is in order. The problem in profile sampling is, of course, the analytical costs. If 10 

 increments per profile are taken, costs of even a modest sampling scheme become 

 exorbitant. 



In summary, descriptive (inventory) sampling has a well-known technology. Applica- 

 tions in any new area do, however, require statistical attention and a certain amount of 

 research. Unfortunately, methods designed for a specific application are often used in 

 other situations where they are not appropriate, e.g., the use of methods developed for 

 global fallout surveys for entirely unrelated purposes (Eberhardt, 1976, pp. 201-202). 



Sampling for Spatial Pattern 



In a variety of situations, the main objective in sampling is to determine a geographical 

 pattern rather than to simply estimate total quantities of a substance present in any 

 particular area. As noted previously the objectives of a study should determine the 

 sampling scheme. Different objectives, for example, may require very different allocations 

 of samples to strata (see Eberhardt and Gilbert, 1976). An example of the remarkable 

 contrast in the way samples might be assigned to several strata according to sampling 

 plans tailored to three different objectives is shown in Fig. 3. The box labeled 

 "allocation" gives the distribution of samples to strata appropriate under three of the 

 objectives of Figs. 1 and 2. Two sets of figures are given for "inventory." One is the 

 sampling pattern actually used, and the other is based on the results of the survey. 



