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Growing demand for geochemical surveys of large areas for environmental purposes involves costs and technical rigor that necessitate increased concern for sampling design. In order to supply data for which the degree of uncertainty is known and to use both field and laboratory resources efficiently, formal experimental design procedures must be used. Optimum final sampling designs can be determined only from the results of preliminary pilot studies in which analysis of variance techniques is a powerful tool.

Analysis of variance techniques can be applied to the study of conceptual units that make up the landscape (such as rock units, soils, plant communities, and hydrologic units) or to areal studies of undifferentiated surface materials. The techniques applied to data from a pilot study provide estimates of the total geochemical variation: for example, of a shale unit as a whole and of the variation among (1) stratigraphic sections of the shale, (2) major parts of the sections sampled, (3) the samples themselves, and (4) duplicate analyses of the samples. From these results, a final sampling plan can be designed that includes an adequate density of sampling, in both geographic and stratigraphic senses, and independent information on the precision of analytical methods, as well as information on the adequacy of this precision for the problem at hand. In addition, comparison of the variance among mean values for either conceptual subunits or areal units with the error variance associated with the mean values gives insight to the reproducibility of the differences observed among the mean values. The reproducibility of such differences can be brought to almost any desired degree of confidence by adjusting the sampling plan so that the variance of each mean is small compared with the variance between the means. Once it has been determined that the data at hand will adequately describe differences in concentrations of elements, background geochemical maps of known reliability can be made. The expectable 68 and 95 percent ranges in composition permit confident recognition of extreme values.

Examples of the application of analysis of variance techniques are given for the study of the composition of uncultivated soils in vegetation type areas in Missouri and for undifferentiated surface materials in the Front Range Urban Corridor of Colorado.

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