On the misuse of residuals in ecology: testing regression residuals vs. the analysis of covariance

<jats:title>Summary</jats:title><jats:p> <jats:list list-type="explicit-label"> <jats:list-item><jats:p>An analysis of variance (<jats:sc>anova</jats:sc>) or other linear models of the residuals of a simple linear regression is being increasingly used in ecology to compare two or more groups. Such a procedure (hereafter, ‘residual index’) was used in 8% and 2% of the papers published during 1999 in the <jats:italic>Journal of Animal Ecology</jats:italic> and in <jats:italic>Ecology</jats:italic>, respectively, and has been recently recommended for studying condition.</jats:p></jats:list-item> <jats:list-item><jats:p>Although the residual index is similar to an analysis of covariance (<jats:sc>ancova</jats:sc>), it is not identical and is incorrect for at least four reasons:</jats:p></jats:list-item> <jats:list-item><jats:p> the regression coefficient used by the residual index differs from the one used in <jats:sc>ancova</jats:sc> and is not the least‐squares estimator of the model.</jats:p></jats:list-item> <jats:list-item><jats:p>in contrast to the <jats:sc>ancova</jats:sc>, the error d.f. in the residual index are overestimated because of the estimation of the regression coefficient.</jats:p></jats:list-item> <jats:list-item><jats:p>the residual index also assumes the homogeneity of regression coefficients (parallelism assumption), which should be tested with a special <jats:sc>ancova</jats:sc> design.</jats:p></jats:list-item> <jats:list-item><jats:p>even if the assumptions of the linear model hold for the original variables, they will not hold for the residuals.</jats:p></jats:list-item> <jats:list-item><jats:p>More importantly, the residual index is an <jats:italic>ad hoc</jats:italic> sequential procedure with no statistical justification, unlike the well‐known <jats:sc>ancova</jats:sc>. For these reasons, I suggest that a <jats:italic>t</jats:italic>‐test or an <jats:sc>anova</jats:sc> of the residuals should never be used in place of an <jats:sc>ancova</jats:sc> to study condition or any other variable.</jats:p></jats:list-item> </jats:list> </jats:p>