- GeoRef, Copyright 2008, American Geological Institute.
Twelve petrographic variables observed in duplicate thin sections for each of 65 Cincinnatian calcarenites are the basis for a multivariate classification. The observed variables are: broken and whole brachiopods, broken and whole bryozoans, crinoids, total broken and total whole skeletal grains, total skeletal grains, micrite, sparite and insoluble residue. One thin section per sample was randomly selected to form sample A. Initial clustering of this sample by means of Q-mode factor analysis suggested four subgroups (1-2A, 3A, 1LA, 3SA), which correspond to limestone classes 1-2, 3, 1L and 3S. Null hypotheses concerning (1) group dispersion, and (2) equality of sample centroids were accepted and rejected at the 0.05 and 0.01 levels of significance respectively. All combinations of non-diagonal elements were tested by the Generalized Mahalanobis D 2 Statistic (V) and a probability of <0.001 was indicated for each combination. Discriminant functions and a classification matrix were then computed for sample A. Interclass and intraclass variation was tested by use of the remaining 65 thin sections (sample B). All combinations of the A and B subgroups were tested using the V Statistic. The null hypothesis for 1LA versus 1LB and 3SA versus 3SB was rejected, thus eliminating classes 1L and 3S. Subgroups 1-2A and 1-2B and 3A and 3B were pooled using sample means. Factor analysis of the pooled sample suggests two groups, which correspond to classes 1-2 and 3. A discriminant function and a classification matrix were computed for the pooled sample. Ninety-two percent of the samples belonging to class 1-2 and 88 percent of those belonging to class 3 were correctly classified. The computed discriminant functions classify more efficiently than associated factor clusters.