Prevalence and ambiguity of repeated measures ANOVA in ecological literature

Background/Question/Methods

The repeated measurement of experimental units over time is central to many ecological investigations. However, a fundamental assumption of analysis of variance (ANOVA) is independence which is violated when analyzing repeated measures (RM) data. Several statistical techniques have been employed to account for non-independence, but all suffer shortcomings. Mixed model capabilities have allowed for precise analysis of RM data within the univariate ANOVA framework, but the flexibility of the approach has increased potential for erroneous analyses and/or ambiguous reporting of statistical methodology. We surveyed the literature to determine the prevalence of RMANOVA in ecological literature and assessed the methodological descriptions of the analyses. To demonstrate an adequate approach for analyzing RMANOVA, we use data from a balanced randomized complete block design investigating the effect of fertilization on tree height. Within each block, one plot received fertilization whereas the other plot was treated as a non-fertilized control. Thus, our model consists of a fixed treatment factor (fertilization) with two levels and a fixed repeated factor (year) with four levels. Individual plot was considered the subject. The response variable, tree height, was the mean of 54 trees in each plot measured annually; thus, temporal spacing was similar within and among our subjects.

Results/Conclusions

Averaged across sample journals, 15% of published articles employed RMANOVA. Among those articles using RMANOVA, 35% used SAS for analysis, making it the most frequently used statistical package for RMANOVA in each journal. Among those articles using SAS, 63% used PROC MIXED. This result may be somewhat conservative because detailed procedures were not always provided. Among those articles using PROC MIXED, 31% either mentioned the covariance structure or described how it was selected. Overall, our literature review exercise supported our original hypothesis that RMANOVA approaches are both prevalent and ambiguously described in ecological literature.

We executed our model using a number of candidate covariance structures appropriate given the expected correlation and temporal spacing of observations. We compared AIC_C for the candidate covariance structures and determined the structure that best modeled the correlation of our data. Had we arbitrarily implemented the default or a different covariance structure, we would have erroneously concluded a main effect of fertilization. Likewise, had we arbitrarily implemented a different covariance structure, we would have inappropriately concluded the presence of an interaction. Indeed, treatment means did not suggest a main effect or an interaction, thus lending further support to the selected covariance structure.