The errors (100 X [estimate-actual]/[actual]), for individual crystals, tended to be large (mean on order of 50%). However the assumption implicit in using the relationships is that when applied to a large enough group of crystals the errors cancel. That is, the relationship is assumed accurate on average. We explore the validity of this assumption via a bootstrap style analysis and thus test the robustness of using the individual, habit conditioned, relationships as opposed to using a single relationship for all crystal types. We find that the individual relationships are not robust enough to warrant their use.
We reanalyze the Mitchell data to explore the possibility of improving these relationships by using more than maximum dimension to represent the crystal sizes. For example, area and perimeter can now be calculated with automatic image processing software.