Looking beyond the mean: quantile regression for comparative physiologists

Abstract

Statistical analyses that physiologists use to test hypotheses predominantly centre on means, but the tail ends of the response distribution can behave quite differently and underpin important scientific phenomena. We demonstrate that quantile regression (QR) offers a way to bypass some limitations of least squares regression (LSR) by building a picture of independent variable effects across the whole distribution of a dependent variable. We used LSR and QR with simulated and real datasets. With simulated data, LSR showed no change in the mean response but missed significant effects in the tails of the distribution found using QR. With real data, LSR showed a significant change in the mean response but missed a lack of response in the upper quantiles which was biologically revealing. Together, this highlights that QR can help to ask and answer more questions about variation in nature.