What does geometric mean, mean geometrically? Assessing the utility of geometric mean and other size variables in studies of skull allometry

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Abstract
This study investigated the effects of using different size variables for interpretations of relative orbit size and mandibular robusticity. Thirty-three skull measurements taken on 385 platyrrhines representing 12 of 16 New World monkey genera (in addition to body mass and total body length) were used singly and in combinations (by taking the geometric mean of all measurements) as size variables to produce relative size indices of orbit area and mandibular thickness. These indices were then compared to investigate which size variables proved effective at differentiating nocturnal from diurnal taxa and hard object from soft object feeders based upon results from previous biomechanical studies. It was found that certain groups of size variables consistently produced the a priori expectations and resulted in lower coefficients of variation. The general principles shared by these size variables were that they sampled anatomically remote regions of the skull that appear to be functionally independent from the trait being evaluated and they were nearly always geometric mean combinations composed of a relatively high number (≥12) of large measurements. Suggestions are also presented for amending these principles for use with incomplete material such as fossils. Am J Phys Anthropol, 2008.