Towards understanding and use of mixed-model analysis of agricultural experiments

Despite the presence of both fixed and random effects in most agricultural experiments, many crop researchers have continued use of the conventional analysis of variance (ANOVA) model or general linear model (GLM) that provides a correct analysis only if all the effects are fixed. Ignoring or mistreating random effects may have inadvertently led to inappropriate analyses and thus to dubious conclusions appearing in the scientific literature. The objective of this paper is to provide a tutorial account of the mixed-model methodology and its applications to the analysis of agricultural experiments. The description and discussion on ANOVA vs. mixed-effect models center on the use of PROC GLM vs. PROC MIXED of the SAS ® System. This paper points out the need for mixed-model analysis, describes and discusses key new features and properties of mixed-model analysis that would facilitate the understanding and use of PROC MIXED. Additionally, it analyzes and interprets three examples: comparison between two samples, and analyses of randomized complete design and split-plot design. Appendices include SAS code and theory underlying mixed-model analysis which will help gain hands-on experiences and ensure correct interpretation of SAS outputs by PROC MIXED. Such a comparative assessment of GLM vs. MIXED procedures will help to underscore the key advantages of PROC MIXED and to convince GLM users to make a true transition towards the increased and appropriate use of PROC MIXED in agricultural experiments.Key words: Analysis of variance, fixed vs. random effects, general linear models, inference spaces, mixed models, randomized complete block design, split-plot design