Quantifying asymmetry: ratios and alternatives

Traditionally, the study of metric skeletal asymmetry has relied largely on univariate analyses, utilizing ratio transformations when the goal is comparing asymmetries in skeletal elements or populations of dissimilar dimensions. Under this approach, raw asymmetries are divided by a size marker, such as a bilateral average, in an attempt to produce size-free asymmetry indices. Henceforth, this will be referred to as "controlling for size" (see Smith: Curr Anthropol 46 (2005) 249-273). Ratios obtained in this manner often require further transformations to interpret the meaning and sources of asymmetry. This model frequently ignores the fundamental assumption of ratios: the relationship between the variables entered in the ratio must be isometric. Violations of this assumption can obscure existing asymmetries and render spurious results. In this study, we examined the performance of the classic indices in detecting and portraying the asymmetry patterns in four human appendicular bones and explored potential methodological alternatives. Examination of the ratio model revealed that it does not fulfill its intended goals in the bones examined, as the numerator and denominator are independent in all cases. The ratios also introduced strong biases in the comparisons between different elements and variables, generating spurious asymmetry patterns. Multivariate analyses strongly suggest that any transformation to control for overall size or variable range must be conducted before, rather than after, calculating the asymmetries. A combination of exploratory multivariate techniques, such as Principal Components Analysis, and confirmatory linear methods, such as regression and analysis of covariance, appear as a promising and powerful alternative to the use of ratios.