Regression to the mean in vegetation science
Leonie Mazalla, Martin Diekmann
Abstract
Abstract Aims We present a possible pitfall in the statistical evaluation of vegetation resurvey studies and longitudinal experimental studies caused by the stochastic phenomenon called ‘regression to the mean’. It manifests itself in a negative correlation of change scores (the difference between an initial and a follow‐up measurement) with the initially measured values. If disregarded, analyses of the drivers of change may be misleading. The aim of this paper is to raise awareness of this issue in vegetation science. Methods The relevance of ‘regression to the mean’ is shown using four exemplary data sets, two from grasslands and two from forests with time gaps for the survey periods between 11 and 32 years, using in total 26 variables. The stochastic mechanism behind it is explained in detail and visualised with artificial data. A suggestion for how to deal with this phenomenon in the analysis of models regressing change in a variable on a predictor variable is made based on one of the exemplary data sets. Results We found the effect of ‘regression to the mean’ in 24 out of 26 examined variables. It also had a significant impact on the results of models that aimed to explain the change in an observed variable (e.g., change in species number) with another variable (e.g., soil nitrogen content). Conclusions The effects of ‘regression to the mean’ are important to keep in mind when interpreting results of resurvey studies, but also when evaluating treatments in experimental studies. We propose to always include the initial values of a variable as a predictor when calculating models of its change scores or evaluating treatment effects. This is especially important when the initial values are already correlated with potential predictor variables.