Proportionality: A Valid Alternative to Correlation for Relative Data

Abstract

In the life sciences, many measurement methods yield only the relative abundances of different components in a sample. With such relative—or compositional—data, differential expression needs careful interpretation, and correlation—a statistical workhorse for analyzing pairwise relationships—is an inappropriate measure of association. Using yeast gene expression data we show how correlation can be misleading and present proportionality as a valid alternative for relative data. We show how the strength of proportionality between two variables can be meaningfully and interpretably described by a new statistic ϕ which can be used instead of correlation as the basis of familiar analyses and visualisation methods, including co-expression networks and clustered heatmaps. While the main aim of this study is to present proportionality as a means to analyse relative data, it also raises intriguing questions about the molecular mechanisms underlying the proportional regulation of a range of yeast genes. Relative abundance data is common in the life sciences, but appreciation that it needs special analysis and interpretation is scarce. Correlation is popular as a statistical measure of pairwise association but should not be used on data that carry only relative information. Using timecourse yeast gene expression data, we show how correlation of relative abundances can lead to conclusions opposite to those drawn from absolute abundances, and that its value changes when different components are included in the analysis. Once all absolute information has been removed, only a subset of those associations will reliably endure in the remaining relative data, specifically, associations where pairs of values behave proportionally across observations. We propose a new statistic ϕ to describe the strength of proportionality between two variables and demonstrate how it can be straightforwardly used instead of correlation as the basis of familiar analyses and visualization methods.