The logarithmic transformation in bivariate allometry
Gary C. Packard
Abstract
Abstract The field of biological allometry has been dominated since early in the last century by the logarithmic transformation, which is widely perceived to be necessary for the proper analysis of bivariate data relating the size of a structure or the intensity of a process to some measure of body size. Some investigators argue that transformation is needed to align the analysis with underlying theory; others assert that transformation is required to describe multiplicative growth in living substance; and still other workers believe that transformation is necessary to accommodate multiplicative variation in the response variable (heteroscedasticity) and/or a lognormal distribution for residuals from the fitted equation. None of these beliefs is true. Moreover, constraints imposed by logarithmic transformation typically result in data being ‘fitted’ to a predetermined statistical model instead of a model being fitted to the data, thereby leading in many instances to erroneous perceptions of pattern in the data, misinterpretation of the findings and misdirection for future research. Robust statistical models with different functional form and different assumptions about random error can be fitted directly to the original data by non-linear regression, thereby obviating transformation altogether. The utility of the regression protocol is illustrated in a re-analysis of published data.