On Watson's ANOVA for Directions

Abstract : Watson's ANOVA technique for analyzing unit vectors in p dimensions has been usually used with directional data, with p=2 or 3. It is shown how the one-way ANOVA can be extended to a multiway layout, and an example is given using coal-cleat directions. The accuracy of the techniques is reexamined, and it is shown why this can be expected to be greater for p=3 than for p=2, and possibly also for p > 3. Finally, conditional tests for directions are compared with the unconditional ANOVA test. It is shown that a characterization of the gamma distribution permits the conditional significance points to be found from the unconditional points using an argument which, in general, is valid.