## Introduction

Data analysis in ecology and evolution is largely based on the use of linear regression models such as anova, ancova, multiple regression, GLM or mixed models (Quinn & Keough 2002; Faraway 2005; Bolker *et al.* 2009). Linear models involve a response of interest and a set of predictors, possibly including some interactions among input variables. Such models can be used to test null hypotheses about the significance of individual predictors and to estimate effect sizes and their standard errors (Nakagawa & Cuthill 2007; Stephens, Buskirk, & del Rio 2007; Garamszegi *et al.* 2009). In this article, I will advertise the use of centred predictors as a simple means to greatly improve the interpretability of parameter estimates. Furthermore, I will advocate looking at estimates for standardized input variables that are valuable as standardized effect size estimates for between-study comparisons. Standardized estimates are frequently used in other fields but are not in widespread use in ecology and evolution. For simplicity, I will introduce my suggestions for general linear models, but the methods easily generalize to GLM and mixed models (see ‘Extensions’).

Although the estimation and interpretation of at least some of the estimates and associated *P* values is possible on the original scale and without centring, centring and scaling of input variables and responses has several advantages. First, in the presence of interactions, it enables the interpretation of main effects, which are biologically meaningless otherwise (Engqvist 2005). Second, it enables the estimation of curvature and synergistic effects of continuous predictors that can be interpreted independent of the main effects. Third, they facilitate the interpretation and comparison of the relative importance of predictors within models by looking at the estimates rather than the *P* values (Gelman & Hill 2007). Fourth, they can serve as standardized effect size estimates for between-study comparisons. Furthermore, I will present an easily applied method to extract group mean and group slope estimates and their appropriate standard errors from linear models. Although these points are not new and are well treated in the statistical literature (see, e.g. Aiken & West 1991; Neter *et al.* 1996; Gelman & Hill 2007), they are surprisingly little used in the study of ecology and evolution. The aim of this paper is to encourage the use of standardizations and to give a guideline for parameter interpretation.

Some of the points I raise are indeed a matter of convenience and preference. Whether predictors are interpreted on the original scale or on the standardized scale will depend partly on the system of study. In some contexts, unstandardized effect size estimates may be more easily interpreted than standardized effect size estimates, because the latter depend on the phenotypic variation in each study population. Other points, like the centring of input variables that are involved in interactions, are also not strictly necessary, but are very advisable, since they safeguard against potential misinterpretations. Main effects are not biologically interpretable if involved in interactions without centring the input variables and the same is true for linear terms in the presence of quadratic terms. In many cases, centring will circumvent the need for model simplification, since parameter estimates in complex models can be directly interpreted. Therefore, centring of the input variables will avoid several critical issues and will thus allow fitting complex, but meaningful models. At the same time, it helps putting the focus on parameter estimates rather than *P* values.