Only a small number of numerical skills are required to deal with body size relationships, and most of these are straightforward. They include a basic understanding of simple algebra, an ability to manipulate numbers expressed as powers and logarithms, a grasp of the implications of power formulas like Equation 1.1, and an appreciation of the strengths and weaknesses of regression analysis. This chapter is intended as a crutch for those who are nervous with the algebra of body size. Many readers will find this chapter a tedious exercise in the obvious and should pass over it.

Basic tools

Logarithms

Most analyses of body size relations begin by converting or “transforming” observed values to their logarithms. Logarithmic transformation is a simple device to ease and improve diagrammatic and statistical descriptions of the effect of body size on other attributes. This primer, therefore, begins by recalling the basic characteristics of logarithms.

Like any numbers, logarithms can be added, subtracted, multiplied, and divided, provided all logarithms in the calculation are converted to the same base. However, addition, subtraction, multiplication, and division performed with logarithms do not correspond to the same operations in “normal” arithmetic based on the antilogarithms. Because logarithms represent the power to which some base must be raised, a change of one logarithmic unit corresponds to an order of magnitude change in the antilogarithm.