Efficient analysis of split-plot experimental designs using model averaging

Abstract

Split-plot experimental data are often analyzed as if the data came from a completely randomized design. As is well known, ignoring the different levels of randomization and replication can lead to serious inferential errors. However, in some experiments, including many of the ocean global change experiments that motivated this research, variation between whole-plot experimental units may be small relative to variation between subplot units. Even though a factorial analysis will often perform poorly in general, in this special case it outperforms a split-plot analysis, providing narrower confidence intervals for treatment means and differences with coverage rates close to the desired level. The performance of the proposed model-averaged analysis was compared to a classical split-plot analysis via a simulation study, and its utility demonstrated for an ocean global change experiment examining growth and condition of a juvenile mussel species. In our simulation study, model-averaged confidence intervals for whole-plot treatment means or comparisons of means were up to 40% narrower than split-plot confidence intervals while maintaining close to nominal coverage rates. In our example experiment, we observed narrowing of up to 25%. We recommend model averaging as a preferred approach when variation between whole-plot experimental units is expected to be less than between subplot units, with a few caveats for studies with very few replicates.