Analyzing Binomial Data in a Split-Plot Design: Classical Approach or Modern Techniques?

Binomial data are often generated in split-plot experimental designs in agricultural, biological, and environmental research. Modeling non-normality and random effects are the two major challenges in analyzing binomial data in split-plot designs. In this study, seven statistical methods for testing whole-plot and subplot treatment effects using mixed, generalized linear, or generalized linear mixed models are compared for the size and power of the tests. This study shows that analyzing random effects properly is more important than adjusting the analysis for non-normality. Methods based on mixed and generalized linear mixed models hold Type I error rates better than generalized linear models. Whole-plot tests tend to be conservative in some cases, but these tests can be improved by removing the lower bound of zero from variance parameter estimation or by increasing the number of whole-plot replications. Mixed model methods tend to have higher power than generalized linear mixed models when the sample size is small. However, they perform equally well as the sample size becomes large.