The Misuse of Ratios, Indices, and Percentages in Ecophysiological Research

Abstract

Ratios are used by many ecological physiologists to adjust (or scale) data that vary allometrically with body size. We use two sets of real data from our laboratory to illustrate in detail how investigators may be misled by statistical analyses performed on such ratios. The first example concerns the use of ratios to increase the precision of data gathered in planned experiments where body size varies within experimental groups but not among them. The second example concerns the use of ratios to remove confounding effects of body size from studies where animals in one group are larger than those in other groups, as a result either of the experimental manipulation itself or of the procedure for assigning animals to treatment groups. In both of these examples, statistical analyses of ratios lead to conclusions that are inconsistent with impressions gained from visual examinations of data displayed in bivariate plots. In comparison, analyses of covariance lead to conclusions that agree with impressions gained from these same plots. We therefore recommend that ecological physiologists discontinue using ratios to scale data and that they use the ANCOVA instead.