According this book and Pearson paper. the correlations that you use are 'spurious' and you should not analize the relation between the two concentration data but the ratio data (in each physical sample) are the right statisitical variable such as R. O. Gilbert's book recommendation for asimmetrical data: No use geometric means but use sample medians.
Note that the ratio data are not the crude concentration ratios but the ratio between both activiy concentration divided by the nuclide specific activity of each nuclide.
Dear Rafael, thank you for your comment which is indeed very interesting. In our project we have tested a number of methods to quantify the activity of difficult (DTM) and impossible (ITM) to measure radionuclides (according the IAEA definition). Among the methods suggested in the reference standards (ISO 21238 and IAEA NW-T-1.18) some use the geometric mean, other linear regression and some other regression of higher order. We decided to test the various methods and compare the results. According to our experience (over hundreds tons of radioactive waste already characterized and disposed in final disposal facilities) there is very little or no difference when using the geometric mean or the median of the ratios. We have also tested other average content statistics (such the mean or the mode) and various statistical learning approaches. When the waste population is fairly low heterogeneous there is little impact on the final characterization and quantification of DTMs and ITMs which, in any case, play a minor role when calculating hazard factors. In our case only a very limited number of gamma-emitters are of interest and we measure them via direct gamma-spectrometry on each waste package. Do not hesitate to write back to me if you have specific/technical questions. Regards, Biagio
Just another detail: in our papers and projects we discuss the characterization of legacy very-low-level radioactive waste so we do not refer to either clearance of material from regulatory control or high-level radioactive waste for which dedicated methods must be considered.
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