| Abstract: | Determining whether a reaction can be written between a set of minerals within error is an example of the more general problem of determining whether a set of compositions are coplanar within error. Generally if the compositions are of minerals, ‘within error’ should allow the minerals to maintain stoichiometry. The problem is addressed via the addition of a ‘bogus’ composition to the set, and calculating the reaction coefficients for a reaction between the compositions in this augmented set. A reaction can be written if a confidence interval on the reaction coefficient of ‘bogus’ includes zero. The reaction coefficients can be solved for directly when the problem is posed in terms of least squares with equality constraints. The confidence interval is determined with a bootstrap method, allowing the result to depend on the scatter of the data around the solution of the least squares problem, not on the data uncertainties |
