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Boyer diss 2009 1046..

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plesiadapid samples have the same mean. When linear or area measurements are<br />

compared among taxa, the values were first natural-log transformed. This was done<br />

because variance in measurements of biological populations is typically only meaningful<br />

in proportion to the average value of the measurements for that population. A<br />

distributional result of this fact is that populations of biological measurements are<br />

theoretically (even if sometimes statistically imperceptibly) right skewed (Sokal and<br />

Rohlf, 1997; Gingerich, 2000). Logarithms express metrical data in terms of proportions<br />

and thereby provide a data format that can be analyzed to meaningfully address<br />

biological questions. For instance, the observation that an elephant population has<br />

absolutely greater variance in body mass than a mouse population is not very informative.<br />

However, finding a difference in variance in logarithms of body mass would deserve<br />

further consideration.<br />

Multivariate comparisons.—Principal coordinates (PC) analyses of Euclidean<br />

distance matrices are used to compare various sets of measurements of P. cookei to those<br />

of samples of extant and fossil taxa. Specifically, PC analyses are undertaken on<br />

variables sampling aspects of the skeleton in six different ways including variables<br />

sampling (1) the distal end of the humerus, (2) metacarpals, (3) astragalus, (4) calcaneum,<br />

(5) aspects of the vertebral column, and (6) combinations of long bone and body segment<br />

lengths. Size-standardized variables were created for these analyses by dividing each<br />

measurement for a given specimen by the geometric mean of all, or a subset, of the linear<br />

measurements for that specimen. This method of size-standardization has been shown to<br />

be successful by numerous researchers (e.g., Mosimann and Malley, 1979, Jungers et al.,<br />

1995; Hamrick et al., 1999). Any measurements that could conceivably have values of<br />

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