246 Least Squares Means Comparisons for Interaction Means in a Two-factor Study in Apple Rootstock Trials

Abstract

Trunk cross-sectional area data for an NC-140 apple rootstock trial were collected in 1998. There were 18 rootstocks and 20 states, and these factors were arranged in a factorial structure; the interaction term (variety × state) was statistically significant (P < 0.05). There were 10 trees of each rootstock planted in each state, but some trees died and this created unequal numbers of observations. Historically these data would have been analyzed using PROC GLM in SAS, correctly identifying the interaction significance, and then analyzing differences for states within a rootstock, and differences for rootstocks within a state. This analysis would not take advantage of all the replication available in the study. To more appropriately utilize the available replication, and to account for the unbalanced number of observations, a macro program was written in SAS. The slice option in PROC MIXED generates individual significance levels for the rootstock factor within a state, but does not make comparisons between rootstocks within a state. The SAS macro was written to use the individual error terms and least squares means generated from PROC MIXED to make each individual Tukey's multiple comparison between rootstocks within a state. The justification for this analytical approach, the SAS macro, and the results of the analysis will be presented.