Geochemical data, from the Mars Meteorite Compendium web site, for 13 basaltic meteorites, possibly from only four localities on Mars, are used to study Martian petrogenetic processes. To achieve this goal, an exploratory data analysis technique, multidimensional scaling (MDS), is used to quantitatively assess the relative behavior (measured with correlation coefficients) of 160 incompatible element ratios involving 25 'trace' elements. The ratios behave as in Earth basalts, suggesting that relative element incompatibility is similar in both planets. Because mineralogy controls incompatibility, the mineralogy of Earth and Mars mantles appears similar. In addition, results suggest that ratios involving elements with highly different incompatibility (e.g., La/Yb) are dominantly controlled by % melting. Plots of SiO2 (pressure proxy; decreases with increasing pressure) versus La/Yb and Nb/Y (decrease as melting increases) imply that Mars basalts, like Earth tholeiites, reflect high percentages of melting, but opposite to Earth, % melting appears to increase with increasing pressure. The moderately correlated, positive, SiO2-La/Yb Mars relationship parallels highly correlated Lunar KREEP data and contrasts with Earth's negative correlation. The positive relationships may reflect restricted mantle convection in some (Mars and the Moon are smaller) planetary bodies. Using similarly incompatible element ratios that are sensitive to source composition, to compare Mars and Earth with MDS, Mars sources most resemble depleted Earth mantle. Additionally, these ratios group Mars sources into enriched, depleted, and intermediate types. The groupings are the same as those suggested by isotopes, and we conclude that trace element data support the hypothesis that chemical variation in Mars may reflect crystallization of a Mars magma ocean. The natural patterns in ratios and samples revealed using MDS, which has no a priori information about relationships, support integrity of the geochemical data set, despite potential shortcomings such as small sample sizes, alteration, and weathering. However, whether the meteorites are representative of Mars as a whole is unknown. [ABSTRACT FROM AUTHOR]