On the statistical analysis of orientation data

The statistical analysis of data in the form of orientations is a relatively new discipline and results from the literature on this subject are not yet widely known outside the statistics community. This paper provides an introduction to and the key references for statistical methods for analysing orientation data. More specifically, the problem of estimating an unknown orientation is considered and results on the precision of such an estimated orientation are described. The calculation of average orientation and dispersion parameters for a sample of orientations is also considered. Finally, procedures for generating and testing for random orientations are described. The methodology is illustrated with crystal orientation data obtained from the analysis of electron back-scattering patterns.