Statistically rigorous confidence intervals calculated from analyses of basaltic volcanic samples obtained from two large geochemical databases (PetDB and GEOROC) demonstrate that published binary and ternary discrimination diagrams seldom correctly classify samples from mid-ocean ridges, island arcs, and ocean islands with better than 60% accuracy. The confidence intervals provide a measure of certainty that was previously absent from these diagrams, allowing for a more robust analysis of results. A new probabilistic method for geochemical discrimination is developed using the geochemical databases. The new method is N-dimensional and uses a priori data to construct probability distribution functions from which a posteriori probabilities are generated. Tests of the new method demonstrate single analysis classification success rates for volcanic rocks from island arcs to be 83%, from ocean islands to be 75%, and from mid-ocean ridges to be 76%.