AN EMPIRICAL–STATISTICAL STUDY OF THREE-DIMENSIONAL FABRIC DIAGRAMS AS USED IN STRUCTURAL ANALYSIS

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Abstract
A random arrangement of points on a sphere does not result in an isotropic distribution (unless a very large number of points is present), and different samples taken from an infinite number of points arranged into point-maximum or great-circle girdle patterns vary considerably, depending on the concentration strength and the number of points in the sample.Existing statistical tests are of limited use only, and visual determinations of symmetry and cell grouping are presently the best way to determine the nature of 'preferred-orientations', provided that the effects of sample size are given full consideration. It is unwise to consider as significant any feature of a natural fabric that could reasonably have occurred as a natural sampling variation.

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