A Brief Review of Heterogeneity Tests for Estimating the Variance of the Fundamental Sampling Error
DOI: 10.62178/sst.002.003
Abstract
The fundamental sampling error (FSE) is generated whenever a sample with mass MS is randomly selected, fragment by fragment, each with the same probability, from a particulate material lot with mass ML. FSE represents the sampling error between the actual (but unknown) grade of a lot and the grade estimated from a selected sample. This is the smallest possible error for a sample selected under ideal conditions, hence the term “Fundamental Sampling Error”. FSE is characterized by its variance, calculated relative to the measured grade of the lot, using the well-known “Gy’s formula”. The variance of FSE can either be calculated theoretically by applying a set of material factors or can be estimated experimentally by conducting empirical heterogeneity tests to estimate the constant factor of constitution heterogeneity, aka the “Intrinsic Heterogeneity of the Lot,” IHL. Several ‘competing’ ways to conduct heterogeneity tests and to calculate IHL have been proposed historically, but a perennial question in the sampling community is: “Which procedure and formulation reveal the actual variance of the fundamental sampling error?” To this day, this question has not been answered to the satisfaction of everybody, because (to paraphrase Edward Deming) “without data, you’re just another person with an opinion,” and no study has so far proven superior validity of one method over another. This paper surveys and explains, in a simplified way, the main experimental methodologies and formulations for estimating the variance of the fundamental sampling error, highlighting the many remaining challenges of heterogeneity testing, which can be seen as a most fascinating topic, however, because of its complexity. It is possible that no singular best approach should be sought in view of the highly complex realm of economic geology and its many types of ore and mineralisation.
Published in Issue 2 · November 2024
Citing this article
Chieregati, A. C. (2024). A Brief Review of Heterogeneity Tests for Estimating the Variance of the Fundamental Sampling Error. Sampling Science & Technology, November 2024(2), 19-29. https://doi.org/10.62178/sst.002.003
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