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The technique of discriminant function has been applied to data previously presented (Middleton, 1960, G.S.A. Bulletin) in order to confirm that the chemical composition of sandstones varies significantly with the tectonic environment of the basin of deposition. After rejection of all sandstones with less than 5% Al2O3, the remainder were distributed between three classes: A, eugeosynclinal sandstones; B, exogeosynclinal sandstones and others; C, taphrogeosynclinal sandstones.
Discriminate function coefficients (which correspond with rules for the assignment of sandstones of unknown tectonic setting to a tectonic classification) have been calculated for the three groups, based on the original data, a logarithmic transformation and an Arc sin square-root transformation. By the logarithmic transformation (for example) the discrimination is highly significant, and the probability of misclassification is as follows: between A & B, 0.17; between A & C, 0.06; between B & C, 0.13.
The reliability of the discriminate function was tested empirically by its application to 19 eugeosynclinal sandstones and 4 exogeosynclinal sandstones whose analyses were not used to calculate the function. Of these, only 2 eugeosynclinal sandstones and one exogeosynclinal sandstone were misclassified. The number misclassified corresponds closely with prediction, and the use of the technique may be considered to be vindicated, in spite of the failure of the data to follow closely the assumptions of the mathematical model.
An attempt has also been made to use factor analysis to indicate significant groupings of chemical variables and to suggest the basis for a chemical classification of sandstones.
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