RATIOS IN TRANSURANIC ELEMENT STUDIES 197 



0.08 0.16 0.24 0.32 0.40 0.48 0.56 



239pu, nCi/g 



Fig. 7 Relationship between ^ ^ ' Pu and ^ "• ' Am in soil at a safety shot site on the 

 Tonopah Test Range. (From Doctor and Gilbert, 1977.) 



individually. An example is provided by plant uptake of technetium, which appears to be 

 related more to the ratio of pertechnetate to sulfate in the soil than to pertechnetate soil 

 concentration (Cataldo, Wildung, and Garland, 1978). It would seem that this criterion 

 would be met if the relationship between numerator and denominator is multiplicative. 

 Two more examples include the plutonium/americium ratio just mentioned and the 

 concentration ratio between two components of an ecosystem compartment model with 

 a constant transfer coefficient. In these situations the reason for using ratios far 

 outweighs their potential disadvantages. However, in some cases there may be more 

 informative and less misleading ways to relate the two variables than by the use of a ratio. 

 Whether or not one can assume that the relationship between two random variables is 

 multiplicative, the approach to these data should be a multivariate one. A first step is to 

 plot the numerator vs. the denominator as in Fig. 7. The Pearson product moment 

 correlation coefficient (Snedecor and Cochran, 1967, p. 172), 



'■[A 



.S (Xi - X)(Yi _ Y) 

 1=1 



(Xi - X)^ .2 (Yi _ Y)^ 

 1=1 



measures the degree of linear association between two normally distributed random 

 variables. Although we cannot assume that radionuclide activity is normally distributed, 

 the correlation coefficient is still a useful piece of information. If the correlation is low, 

 the ratio will be highly variable. The correlation coefficient provides a measure of linear 

 association but not whether the relationship is multiplicative. That information can be 

 gained from a regression analysis. 



