Sampling errors produced when geological materials (rocks, soils, tills, drainage sediments) are collected have been estimated empirically using variance decomposition methods or theoretically using Poisson or binomial statistics. Unfortunately, historical distribution-based approaches assume that the element of interest occurs in only one mineral. Although this may be true in some cases, most major oxide and many trace elements reside in more than one mineral in most geological materials. As a result, historical distribution-based approaches do not estimate sampling errors correctly.
An alternative theoretical approach to sampling error estimation is proposed that employs both Poisson and hypergeometric statistics, depending on whether the elements of interest reside in rare or common grains. It is intended for use in advance of sampling to ensure that samples in a survey will be colleted in sufficient size to achieve a desired level of sampling precision. This method requires estimates of the proportions, sizes and compositions of the minerals making up the geological material, and thus is based on information readily available from a few (orientation) samples of the material to be sampled.
This approach accommodates cases where more than one mineral contains an element of interest. It involves first estimating the sampling error for the minerals present in the geological material. Then, the mineral sampling errors are used to make estimates of the sampling error of all elements within these minerals simultaneously using a simple propagation of variance approach. An EXCEL spreadsheet is provided that undertakes the relevant calculations, and this can be adapted to consider any suite of minerals and elements in geological materials.