On the misuse of residuals in ecology: testing regression residuals vs. the analysis of covariance
Dr E. García-Berthou, Departament de Ciències Ambientals & Institut d’Ecologia Aquàtica, Universitat de Girona, E-17071 Girona, Catalonia, Spain. Tel: + 34 972418 467. Fax: + 34 972418 150. E-mail:firstname.lastname@example.org
- 1An analysis of variance (anova) 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 Journal of Animal Ecology and in Ecology, respectively, and has been recently recommended for studying condition.
- 2Although the residual index is similar to an analysis of covariance (ancova), it is not identical and is incorrect for at least four reasons:
- (i) the regression coefficient used by the residual index differs from the one used in ancova and is not the least-squares estimator of the model.
- (ii)in contrast to the ancova, the error d.f. in the residual index are overestimated because of the estimation of the regression coefficient.
- (iii)the residual index also assumes the homogeneity of regression coefficients (parallelism assumption), which should be tested with a special ancova design.
- (iv)even if the assumptions of the linear model hold for the original variables, they will not hold for the residuals.
- 3More importantly, the residual index is an ad hoc sequential procedure with no statistical justification, unlike the well-known ancova. For these reasons, I suggest that a t-test or an anova of the residuals should never be used in place of an ancova to study condition or any other variable.