Measurement and meaning in biology.

Measurement--the assignment of numbers to attributes of the natural world--is central to all scientific inference. Measurement theory concerns the relationship between measurements and reality; its goal is ensuring that inferences about measurements reflect the underlying reality we intend to represent. The key principle of measurement theory is that theoretical context, the rationale for collecting measurements, is essential to defining appropriate measurements and interpreting their values. Theoretical context determines the scale type of measurements and which transformations of those measurements can be made without compromising their meaningfulness. Despite this central role, measurement theory is almost unknown in biology, and its principles are frequently violated. In this review, we present the basic ideas of measurement theory and show how it applies to theoretical as well as empirical work. We then consider examples of empirical and theoretical evolutionary studies whose meaningfulness have been compromised by violations of measurement-theoretic principles. Common errors include not paying attention to theoretical context, inappropriate transformations of data, and inadequate reporting of units, effect sizes, or estimation error. The frequency of such violations reveals the importance of raising awareness of measurement theory among biologists.