On the statistical significance of grain-scale lattice rotation results

The statistical significance of grain-scale lattice rotation results is analysed. The case of the results of Ref. [1] is specifically considered. Quantitative elements of the theory of statistics are applied to determine precisions (standard errors) of the results and the size of the representative volume element (RVE), in terms of the minimal number of grains necessary to obtain the results. It is shown that the results of Ref. [1] are defined to sufficient precision to support the conclusions made. In general, the RVE size, i.e. the numbers of grains necessary to derive conclusions on the rotation trends over all grains, range between a few tens and about 200. The proposed method is general and can easily be applied to other data sets to determine their own precisions and RVE sizes.