In this paper, methods are described for the analysis of complex multifactorial sets of angular data. Analogues of techniques of analysis of variance are demonstrated that allow partitioning of the resultant vectors of sets of angular data to serve as a basis for tests of significance. Resultants are partitioned into components corresponding to any identifiable or planned source of variation in the experiment, allowing hierarchical, factorial and mixed experimental designs (as with linear models for analyses of variance). Because the statistical properties of these partitions are at present unknown, significance tests are then done by randomization procedures on each set of data. The randomizations produce an empirical distribution of a test statistic (in this case, analogous to F-ratios in linear analyses of variance), against which the calculated statistic for the given set of data can be compared.

These techniques are illustrated for experiments on the directions of movement of a small intertidal snail, Littorina unifasciata Gray, on sandstone shores in New South Wales. Various experimental designs are discussed, including two and three experimental factors, in nested and orthogonal analyses. The results revealed that the movements of this species are influenced by many factors, and that the effects of these vary from time to time and place to place on the shore.

The complexity of these results is discussed with respect to previous, simpler experiments about movements of gastropods. The potential advantages of multifactorial comparisons using the methods described here are indicated for various aspects of the study of directional movements of intertidal snails.