An optimum empirical classification is defined as one in which there is exactly one category for each group of samples separated from other groups by discontinuities in the ranges of their observed properties. A statistical scheme for identifying discrete sample groupings (if they exist) in a set of data is developed which gives equal weight to any number of properties, and treats nonhomogeneous properties simultaneously. Essential features of the scheme are (1) representation of each sample as a vector in an n-coordinate system, where n is the number of attributes considered, (2) use of the angle of separation between sample vectors as an inverse measure of similarity, (3) application of factor analysis to determine the minimum number of coordinates necessary to express ain features of the data efficiently, and (4) inspection of the resulting vector array for discrete vector clusters.

Applied to 200 samples of modern Bahamian carbonate sediments studied by Purdy, this scheme identifies five discrete sample groups (oolite, oolitic, grapestone, coralgal, and lime mud facies) whose discrete character is not apparent if only a small number of attributes are considered simultaneously.

The same 200 samples are treated according to Folk's limestone classification, and the results compared with the optimum classification scheme. Application of Folk's criteria yields nine named categories belonging to Type I (sparry allochemical limestone) and Type II (microcrystalline allochemical limestone), although it is difficult to make the I-II distinction in many samples. In general, correspondence between the two classifications is good in Type I, and poor in Type II.