Skip to Main Content
Skip Nav Destination
GEOREF RECORD

The fundamental relationship between sample mass and sampling variance in real geological samples and corresponding statistical models

Cliff R. Stanley
The fundamental relationship between sample mass and sampling variance in real geological samples and corresponding statistical models
Exploration and Mining Geology (January 2007) 16 (1-2): 109-123

Abstract

In mineral exploration and mining applications, it is sometimes necessary to reduce sampling error in order to improve representivity of individual sample assays. Historic efforts to reduce sampling error have relied on the belief that larger samples exhibit less sampling error. Justifications for this belief traditionally have coupled the binomial theorem with an ideal geological material consisting of ore and gangue particles of equal size and shape (an equant grain model) and empirical tests of geological materials, to illustrate an inverse relationship between sample size and sampling variance. To date, no proof exists of this sample size-sampling variance relationship in real geological materials exhibiting variations in grain size, shape, composition, and degree of liberation. Using first principles calculus and the formula for the mean, sample mass and sampling variance are proven to be inversely proportional in all geological materials. Distribution assumptions and physically ideal geological models are not used in this proof. Furthermore, algebraic manipulations of expressions describing the variances of equant grain models consistent with binomial, hypergeometric, and Poisson distributions reveal that these models also exhibit an inverse sample size-sampling variance relationship. Thus, the sampling behaviors of these models are numerically consistent with the sampling behaviors of real geological materials, and these models can be used to estimate sampling errors in real geological materials using simple sampling parameters.


ISSN: 0964-1823
Serial Title: Exploration and Mining Geology
Serial Volume: 16
Serial Issue: 1-2
Title: The fundamental relationship between sample mass and sampling variance in real geological samples and corresponding statistical models
Author(s): Stanley, Cliff R.
Affiliation: Acadia University, Department of Earth and Environmental Science, Wolfville, NS, Canada
Pages: 109-123
Published: 200701
Text Language: English
Publisher: Canadian Institute of Mining, Metallurgy and Petroleum, Montreal, QC, Canada
References: 33
Accession Number: 2007-101976
Categories: General geochemistry
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus.
Country of Publication: Canada
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute. Abstract, Copyright, Geological Society of CIM. Reference includes data from GeoScienceWorld, Alexandria, VA, United States
Update Code: 200744
Close Modal

or Create an Account

Close Modal
Close Modal