STATISTICS AND SAMPLING IN TRANS URANIC STUDIES 183 



they can be adequately mixed. The basic idea is that the composite sample will provide an 

 accurate average value for the individual samples used to make up the composite. If the 

 entire composite is used for analysis, there should be no problem with the concept. For 

 many transuranic analyses, however, only a relatively small mass is used; so a composite 

 itself may be subsampled (aliquoted) at the chemical-analysis stage. Whether compositing 

 is worthwhile, then, depends on how weU the sample is, or can be, mixed. The 

 hot-particle problem in plutonium analyses, along with the common practice of using a 

 small sample mass for analysis, suggests that compositing may not be very effective. Some 

 further details and suggestions have been reported by Eberhardt (1976) and Eberhardt 

 et al. (1976). A statistical evaluation of compositing (Rohde, 1976) suggests that the 

 correct measure of variability for the average of composited samples is difficult to obtain. 



Transformation of skewed data has already been mentioned; it deserves some further 

 research. One of the difficulties has to do with transforming back; i.e., if a logarithmic 

 transformation is used for statistical analysis, many investigators prefer to express the 

 final results on an arithmetic scale. Simply using antilogarithms introduces a bias. In 

 many instances it may be quite feasible to simply stay on the logarithmic scale; the 

 consequences of doing so need to be further evaluated and explained (Agterberg, 1974, 

 pp. 289-300; Aitchison and Brown, 1966, pp. 44-48; Helen, 1968). An interesting 

 sidelight is that some investigators seem to believe that correlations calculated on 

 log- transformed data are not legitimate. Whether this is true or not depends on the 

 statistical model assumed; so that issue has to be resolved by specifying such a model. 

 There is, in fact, some reason to argue that correlations involving transuranics should be 

 done on log-transformed data. The usual model for correlation (bivariate normal 

 distribution) involves a linear model with normally distributed errors (deviations). As has 

 been pointed out several times, data on transuranics are generally not normally 

 distributed, and relationships between different variables may be nonlinear. 



A matter of substantial importance is the choice between random and systematic 

 sampling. We have thus far largely advocated random sampling since it is the only 

 approach generally accepted as providing unbiased estimates of population parameters. As 

 Cochran (1963, Chap. 8) shows, systematic samples are vulnerable to unsuspected 

 periodicities in the variable being studied, and no widely trustworthy method for 

 estimating the variance is known. On the other hand, if adjacent samples have closely 

 correlated values, then under random sampling two sample points that fall close together 

 essentially duplicate the same information. Hence a systematic sample gives more for the 

 money spent, i.e., a smaller sampling error (even though we may not get a suitable 

 estimate of the sampling error). This point has been particularly emphasized in references 

 on sampling for pattern. Some recent work by Barnes, Gilbert, and Delfiner (1977), using 

 the field instrument for the determination of low-energy radiation (FIDLER) data from a 

 safety-shot site on the Nevada Test Site, suggests that readings taken on a grid resuh in 

 more precise estimates of americium contours than do comparable (FIDLER) readings 

 taken at random within activity strata. These analyses were made with "kriging" 

 techniques (see Delfiner and Delhomme, 1975), a method we are currently studying for 

 potential applications in transuranic studies. 



In the first few years that we worked with field sampling for plutonium. very little 

 data on variabihty were available (Eberhardt and Gilbert, 1972). As more and more data 

 collected by random samphng have become available, we have come around to the 

 opinion that it will be worthwhile to look more carefully into systematic sampling and to 

 begin tests of its utility in a variety of field situations. Since most of the applications will 



