204 TRANSURANIC ELEMENTS IN THE ENVIRONMENT 



of radionuclide in one compartment to that in another the same at the various sites? 

 Assume for ease of exposition that there are two sites and three compartments. Let v\^ 

 (i= 1,2; j = 1,2,3) represent the true radionucUde content of the ']th compartment at 

 site i. Then the IR of compartment 1 to compartment 2 at site 1 can be expressed as 

 V\ ilv\2- The rephrased question can be expressed as the statistical null hypothesis 



Ho: 



(6) 



Recall that In (X/Y) = In (X) - In (Y). By defining /iy = In v,^ , then 



in 



i^y-" 



1 -Mi2 



If the data are collected so that a measurement of radionuclide content for each 

 compartment is made at each sampling location, the hypothesis (Eq.6) can then be 

 expressed as 



H'o: 



A^i 1 -A'i2 



1^12 - f^l 3 



f^2l -A'22 

 M22 -^23 



(7) 



The terms (/ij j — ^j j+ , ) are estimated by 



^ --^ 1 V 



k=l 



where Xj j ^ is the radionuclide content observed at the ktfi sampling location in the jr/z 

 compartment at site i. Note that 



Vx..j+i.k/ 



Inxij^k -lnx,,j + i,k 



so consequently (/ij j -^(ij+, ) is the mean of the logarithms of the nj observed IR's of 

 compartment] to compartment] + 1 for site i. 



There are several reasons for doing this. First, instead of a nonlinear hypothesis on the 

 ratios of random variables, we now have a linear hypothesis tor which multivariate 

 techniques currently exist. Second, taking logarithms tends to equalize variability and 

 make the normality assumption more tractable; both of these conditions are assumed by 

 the test of H'q, which is discussed below. 



