Exploring Treatment By Trial Interaction Using Treatment Stability/Trial Dendrogram Plots.

In the analysis of combined agricultural experiments, the interaction between treatment and environment is of particular concern. When cross-over interactions are present, the recommendation for superior treatment will differ depending on environment.

One common method for analyzing interaction is to plot treatment-in-trial means against the grand trial mean. The stability of treatments across trials is examined, with highly stable treatments varying less with trial mean than low-stability treatments. The treatment stability plot also allows trials to be ranked as low or high performing trials.

Cluster analysis is also used to classify trials based on the performance of treatments within those trials. Dendrograms are used to show the rankings among trials and the relative distances between groups of trials. In the combined treatment stability/trial dendrogram plot, the position of "leaves" in the dendrogram is constrained to match the position of trial means in the treatment stability plot.

In the absence of interaction, the ranking and relative distance between trials in the dendrogram will be proportional to the trial mean. With interaction, trial dendrograms will cross when trial means are out of proportion relative the the performance of treatments within trials. For example, a low-performing trial may cluster with high-performing trials based on relative treatment performance. Other examples will be presented, and the use of geospatial mapping to supplement trial cluster analysis will be demonstrated.