The simultaneous evaluation of a number of mineral or chemical constituents in rock samples requires statistical methods designed to handle several variables at a time. This is accomplished for certain kinds of areal studies by use of a method especially designed to handle any number of variables that can be expressed as proportions or percentages, where the total adds up to 100 percent. The statistical questions related to the design are concerned with the regional or local homogeneity of rock bodies at several sampling levels. Examples are included of pebble distribution in glacial drift, heavy minerals in beach sand, and the distribution of lithologic types in a subsurface stratigraphic unit. It is shown that in some instances there may be a broad regional homogeneity with smaller scaled heterogeneity superimposed upon it. The reverse situation may also occur. Extensions of the method permit comparison of two or more rock bodies in terms of selected constituents. In addition to its uses in sedimentary, igneous, and metamorphic petrology, the method appears to have applications in paleontology, geomorphology, and other branches of geology. The statistical model, which crosses constituents with a nested sampling design, is described in a technical Appendix that also shows the method of computation.

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