Probability plotting is a simple, powerful analytical method that can graphically separate and define the components of mixed statistical distributions. Measurement data from animal populations contain normally distributed components that represent size groupings. These components can arise from yearly age groups in animals that have a distinct breeding season, sexual dimorphism, heterochrony, and other causes. We introduce the use of probability plotting, a method previously employed in engineering sciences, to resolve component distributions in morphometric data for the dinosaurs Coelophysis, Allosaurus, Maisaura, and two extant outgroups, alligators and cassowaries.
Resolved component distributions define the proportions of adults and juveniles, yearly size groupings of juveniles, extent of sexual dimorphism, and growth of asymptotes for these taxa. Where enough specimens are known, growth curves can be constructed. We show that the sexual dimorphism indices (SDI) of the dinosaurs fall between those of the bird and crocodilian outgroups (significance uncertain). Within our small sample the data obey Rensch's rule (SDI increases with size where males are larger); probably males were the robust forms in Coelophysis and Allosaurus. In every group, proportions of robust and gracile adults are equal to within 33%, and juveniles always outnumber either adult morph. We also compare hypothetical growth curves for the dinosaurs to the outgroups. Additionally, we show that the size of the Peterson quarry theropod is much greater than the growth asymptote of Allosaurus and therefore cannot represent an exceptionally large individual of that genus.