On the statistical analysis of the rock magnetic S-ratio

The S-ratio is a rock magnetic parameter employed to provide a relative measure of the contributions of low and high coercivity material to a sample's saturation isothermal remanent magnetization (SIRM). The current form of expressing the S-ratio involves reporting a single value that represents the relative contribution of the low coercivity material, such as magnetite, to the overall SIRM. Expressing the S-ratio in this form is somewhat misleading, suggesting that the derived values are real numbers held in a Euclidian sample space. In fact, S-ratio data are constrained to a 1-D unit-simplex, meaning that many of the descriptive statistics reported for collections of data, for example, means and standard deviations, are in error because the employed statistical methods are designed for unconstrained data only. A simple example of this problem will be given, followed by a demonstration of how meaningful statistics for the S-ratio can be obtained using the additive-log-ratio transform of Aitchison.