Biological significance and statistical significance

Properly calculated allometric equations (or regression lines) will be accompanied by statistics that give information about significance and confidence limits. Statistics are necessary because we cannot rely on subjective evaluations of whether or not data and numbers are significant.

Allometric equations, y = axb (or corresponding linear-regression lines), have two important numerical terms: the proportionality coefficient a (the intercept at unity) and the exponent b (the slope of the regression line). These two terms have different meanings and can answer different questions. An example will help.

The proportionality coefficient can be used to answer questions such as this: Do marsupials, in general, have lower metabolic rates than eutherian mammals (see p. 64)? The equations for the metabolic rates of these two groups have the same exponent, and we can therefore directly compare the proportionality coefficients, which are lower for marsupials. This tells us that marsupials, in general, have lower metabolic rates than eutherian mammals. The exponent, on the other hand, tells us that the metabolic rate changes with changing body size in the same way in marsupials and eutherian mammals. This suggests that the same principles determine the scaling of metabolic rates in the two groups (although the coefficient told us that the levels of their metabolic rates differ systematically).