Using the randomisation in specifying the ANOVA model and table for properly and improperly replicated grazing trials

A method for deriving the analysis of variance for an experiment is presented and applied to grazing trials. A special feature of grazing trials, specifically utilised by our method, is that they involve at least 2 randomisations: treatments are randomised to field units (for example paddocks or plots), and field units are randomised to animals. Randomisation results in the confounding ('mixing up') of terms and our method includes separate terms in the analysis of variance table for confounded terms so that all sources of variability in the experiment have terms for them included in the table and the confounding between the sources of variability in the experiment is explicitly displayed in the table. This information is used in determining the valid error terms and we will present examples that show how to ascertain these for effects of interest and hence which effects can be tested. In this it fulfils the same role as the contentious process of identifying the experimental unit. It will be demonstrated that the inclusion of separate terms for confounded terms results in improper replication in grazing trials being automatically signalled, and makes its ramifications clear.