The mistreatment of covariate interaction terms in linear model analyses of behavioural and evolutionary ecology studies

In behavioural and evolutionary ecology, there are often large phenotypic differences between individuals in, for example, body size or large variation in abiotic conditions such as temperature, between measurements. This often inevitable source of variation may mask any effect of experimental treatment as it can have a large impact on the dependent variable of interest. In such cases, conventional statistical comparisons may have much lower power than desired. The inclusion of covariates in statistical analyses has proven a powerful method to control for such nonrandom differences between individual data points that cannot be controlled experimentally (Huitema 1980). To make correct conclusions, it is important to understand the basic assumptions underlying such a covariate analysis. In this paper I argue that this has evidently not been completely acknowledged in the scientific community. Sophisticated models relating responses to both one or more continuous covariates and one or more factors can be problematic. Factor is here used in the meaning of a categorical independent variable and its value divides individuals into discrete groups or categories, for instance experimental treatments. In the following, I use a simple one-factor ANCOVA design as an example, but the same general problem outlined here applies to all linear models with one or more covariates, including generalized linear models (GLIM) such as logistic regressions and even survival analysis. The basic design of a one-factor fixed effect ANCOVA can be written as: