Abstract
Statistical procedures for (1) sampling, (2) testing the existence of a preferred direction, and (3) testing homogeneity of twodimensional directional data, which have been developed by the authors for paleocurrent studies, are presented. It is well known that conventional methods of statistical analysis are not applicable to directional data (e.g., crossbedding and ripplemark directions, grain lineations, etc.) which are “circularly distributed” on a compass dial. A sampling technique for directional data has been developed using the circular measures of dispersion and approximate ANOVA of G. S. Watson. On the basis of a pilot survey, it is possible to compute the minimum sample size required for estimating, with a desired precision, the mean paleocurrent direction of a formation. The optimum allocation of sample size between and within outcrops also can be accomplished at a minimum cost. The procedure described for testing uniformity (or lack of preferred direction) is based on the arc lengths made by successive sample points and is simple to use if the sample size is moderate. A table of critical points and a numerical example are given after a description of the test procedure. Finally, the procedures for testing the homogeneity of directional data from several geological formations are described by (1) tests for equality of the resultant directions (polar vectors) and (2) tests for equality of dispersions. With these tests it is possible to determine whether the paleocurrent directions from different geological formations belong to significantly different populations.
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research sponsored by the Air Force Office of Scientific Research, AFSC, USAF, under Grant No. AFOSR 71-2009. The United States Government is authorized to reproduce and distribute reprints for Government purposes notwithstanding any copyright notation hereon.
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Rao, J.S., Sengupta, S. Mathematical techniques for paleocurrent analysis: Treatment of directional data. Mathematical Geology 4, 235–248 (1972). https://doi.org/10.1007/BF02311720
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DOI: https://doi.org/10.1007/BF02311720