Use and Misuse of Mixed Model Analysis of Variance in Ecological Studies

Analysis of variance is one of the most commonly used statistical techniques among ecologists and evolutionary biologists. Because many ecological experiments involve random as well as fixed effects, the most appropriate analysis of variance model to use is often the mixed model. Consideration of effects in an analysis of variance as fixed or random is critical if correct tests are to be made and if correct inferences are to be drawn from these tests. A literature review was conducted to determine whether authors are generally aware of the differences between fixed and random effects and whether they are performing analyses consistent with their consideration. All articles (excluding Notes and Comments) in Ecology and Evolution for the years 1990 and 1991 were reviewed. In general, authors that stated that their model contained both fixed and random effects correctly analyzed it as a mixed model. There were two cases, however, where authors attempted to define fixed effects as random in order to justify broader generalizations about the effects. Most commonly (63% of articles using two—way or greater ANOVA), authors neglected to mention whether they were dealing with a completely fixed, random, or mixed model. In such instances, it was not clear if the author was aware of the distinction between fixed and random effects, and it was often difficult to ascertain from the article whether their analysis was consistent with their experimental methods. These findings suggest several statistical guidelines that should be followed. In particular, the inclusion of explicit consideration of effects as fixed or random and clear descriptions of F tests of interest would provide the reader with confidence that the author has performed the analysis correctly. In addition, such an explicit statement would clarify the limits of the inferences about significant effects.