Statistical assessment of subsampling procedures

As shown by the examples in this paper, the concentrations in subsamples are not necessarily independently and normally distributed despite vigorous grinding and mixing of the original sample. Studies of the statistical properties of subsample concentrations should test for deviations from independence and normality and, if deviations are found, should model the observed distribution. The tests include an analysis of variance to check for less variation among nearby subsamples than among widely spaced subsamples, as well as the computation of the probability plot correlation coefficient to check for nonnormality. These tests are illustrated with ${}^{239}\text{Pu}\text{+}{}^{240}\text{Pu}$ measurements on subsamples prepared for use as standard reference materials. These materials are used in quality assurance for environmental radioactivity measurements. The material consisting of Human Liver (SRM 4352) exhibits dependence, which may be due to inadequate mixing or to later handling that caused segregation. The material consisting of Human Lung (SRM 4351) and the material consisting of soil from Rocky Flats (SRM 4353) exhibit nonnormality due to the particulate nature of some plutonium-bearing fractions of the material. The lung measurements are modeled with the gamma distribution. The soil measurements are modeled with a combination of the normal distribution and a distribution that models the occurrence of outliers. The use of these models to describe the subsamples involves assessment of the contribution of the measurement error.