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The chemical composition and origin of the isotopically identified end-member mantle components have been difficult to describe because their melted samples - oceanic basalts - are affected by many processes such as variable degrees of partial melting. Exploratory data analysis [multidimensional scaling (MDS)] applied to ∼200 basalts from French Polynesia reveals over 100 ratios of similarly incompatible elements (SIER) that are minimally affected by these processes. Ratios from elements with dissimilar incompatibility are identified as affected by melting percentages. When basalt samples are compared simultaneously using ∼100 SIER and MDS, they organise in the same way that they would with isotopes, according to mantle component type. Applying discriminant analysis to the most extreme French Polynesia samples representing each mantle component yields preliminary discrimination diagrams that improve the description of chemical variation in the mantle. As a test of their utility and reliability, they are used to classify averages of known EM1, EM2, and HIMU basalts on oceanic islands from outside French Polynesia with reasonable success. Although they are preliminary and should be used cautiously, two of the diagrams based on large numbers of samples and ≥10 SIER can be used to screen 'unknown' basalt samples for mantle component character. They can also help test models for component origin. As an example of their application, it is shown that the EM1-like (isotopically) Shonkin Sag basaltic sill (Montana) has extreme EM1 trace-element characteristics suggesting that EM1 in the ocean basins represents Archean subcontinental lithospheric mantle, recycled into the convecting oceanic mantle. [ABSTRACT FROM AUTHOR]