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An Evaluation of the Use of Ratios in Environmental Transuranic Studies¹

ABSTRACT

This paper discusses statistical aspects of two types of ratios, concentrations and pure ratios, that are used extensively in environmental transuranic studies and have different uses and different statistical problems. A concentration gives units of numerator (Y) per unit of denominator (X), for example nCi of ²³⁸Pu per gram of soil, where is assumed to be proportional to X. The choice of aliquot size permitting a reliable estimate of concentration is a major problem with this type of ratio. For a pure ratio the numerator and denominator are measured in the same units, for example nCi of ²³⁸Pu over nCi of ¹³⁹Pu. Pure ratios often appear as a ratio of concentrations: for example, concentration ratios and inventory ratios. However, pure ratios provide accurate information on the relationship between Y and X only when Y is proportional to X. The statistical problems of pure ratios center on an assessment of whether the multiplicative assumption is valid. Multivariate statistical techniques offer alternatives to a pure ratio for expressing the relationship between Y and X. The purpose of this paper is to stimulate critical thinking about the use of ratios and to suggest approaches to the task of ratio estimation compatible with the behavior of environmental radionuclide data.

Key Words: statistics • radionuclides • concentration ratios • inventory ratios • multivariate procedures

¹ The research was supported by the U.S. Dep. of Energy under Contract DE-AC06-76RL0 1830.

² Senior Research Scientist and Staff Scientist, Statistics and Materials Safeguards Section, Energy Systems Dep., Battelle, Pacific Northwest Lab., Richland, WA 99352; and Research Associate, Savannah River Ecol. Lab., P.O. Drawer E, Aiken, SC 29801; respectively.

Received for publication June 27, 1979.