Determination of relative size: the "criterion of subtraction" problem in allometry

By providing a predicted value against which to judge observed values, allometric equations are often used as a "criterion of subtraction" to calculate measurements corrected for the effects of overall size. The observed and predicted values have been used to calculate several different versions of a size-adjusted measurement; two of the more common being (observed/predicted) and (log observed-log predicted). Using data on brain size, tooth size, metabolic rate, and long bone shape, it is found that the manner in which the relative size value is calculated can alter interpretations and statistical results. Some of the assumptions underlying use of a criterion of subtraction calculated from empirical data are reviewed. It is suggested that predicted values determined from a priori theoretical equations often have several advantages over those from empirical equations.