Statistics and Sampling inTransuranic 

 Studies 



L. L. EBERHARDT and R. 0. GILBERT 



The existing data on transuranics in the environment exhibit a remarkably high variability 

 from sample to sample (coefficients of variation of 100% or greater). This chapter stresses 

 the necessity of adequate sample size and suggests various ways to increase sampling 

 efficiency. Objectives in sampling are regarded as being of great importance in making 

 decisions as to sampling methodology. Four different classes of sampling methods are 

 described: (1 ) descriptive sampling, (2) sampling for spatial pattern, (3) analytical 

 sampling, and (4) sampling for modeling. A number of research needs are identified in the 

 various sampling categories along with several probletns that appear to be common to two 

 or more such areas. 



Most of the existing data on transuranic elements in the environment exhibits a 

 remarkably high variability from sample to sample. Since analytical procedures for these 

 elements are both complicated and expensive, many investigators use relatively few 

 replicates. In those few cases where moderately large samples have been taken, the 

 underlying frequency distributions generally have been badly skewed (nonsymmetrical). 

 The use of statistical methods in the design and analysis of studies and the use of efficient 

 sampling practices would help avoid the reporting of questionable conclusions. 



This chapter identifies some sources of information on sampling and statistical 

 methods relevant to transuranic studies and suggests further research on particular 

 problems along these lines. We believe that too many studies of transuranic elements are 

 currently being conducted with unrealistically small samples. In many such cases, 

 statistical analyses are limited to reporting "counting errors"; thus the inadequacy of the 

 sampling goes unrecognized, at least by those preparing a report on its outcome. This is, 

 of course, not universally true but is all too often the case. As time goes on, it is to be 

 hoped that statistical measures of the adequacy of the sampling and chemical-analysis 

 procedures will become more widely used. The need for efficient statistical designs should 

 then become immediately apparent to investigators and sponsors. Efficient sampling 

 plans, however, require that rather definite objectives be specified for the study. We 

 consider objectives and the appropriate sampling plans in this chapter. 



We will direct our discussion primarily to sampling designs rather than to 

 experimental designs since many of the "experiments" concerning transuranic elements 

 that we have encountered thus far are not replicated or have so few replicates that 

 statistical analysis of the results has little meaning. For purposes of this chapter, an 

 experiment occurs when the investigator controls, through randomization, the assignment 



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