Explorations in statistics: the analysis of ratios and normalized data

Learning about statistics is a lot like learning about science: the learning is more meaningful if you can actively explore. This ninth installment of Explorations in Statistics explores the analysis of ratios and normalized- or standardized-data. As researchers, we compute a ratio-a numerator divided by a denominator-to compute a proportion for some biological response or to derive some standardized variable. In each situation, we want to control for differences in the denominator when the thing we really care about is the numerator. But there is peril lurking in a ratio: only if the relationship between numerator and denominator is a straight line through the origin will the ratio be meaningful. If not, the ratio will misrepresent the true relationship between numerator and denominator. In contrast, regression techniques-these include analysis of covariance-are versatile: they can accommodate an analysis of the relationship between numerator and denominator when a ratio is useless.