Statistics – Methodology
Scientific paper
May 1962
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1962gecoa..26..545w&link_type=abstract
Geochimica et Cosmochimica Acta, vol. 26, Issue 5, pp.545-560
Statistics
Methodology
1
Scientific paper
Realistic average values are needed for geochemical and petrogenetic studies; heretofore no accurate method has been available for calculating the true average composition of a granitic mass. Recent published work has shown that the quantitative areal composition and variability of modal or chemical variates can be closely approximated by surfaces computed by mathematical analysis of the mapped variates (partial trend surfaces). The surface representing each variate can be expressed as X n = f ( U , V ), where U and V are geographic co-ordinates. The proposed new method employs the definite double integral , which, when divided by the outcrop area of the granite mass, provides an estimate of the average value of each variable over the whole outcrop area. In general such values are more accurate than, and significantly different from, the arithmetic means of observed values for a set of irregularly-spaced (non-orthogonal) samples. The method can be extended to triple integration for three-dimensional analyses. The Wollaston (Ontario) and Lacorne (Quebec) granites and the "older granite" of Donegal (Eire) provide examples which illustrate the methodology and its application. Satisfactory results are obtained if 1. (a) the sampling plan is such as to justify making inferences about the whole mass (target population) on the basis of the samples used, and 2. (b) the confidence level (determined by analysis of variance techniques) associated with each trend surface is high.
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