Empirical Models for the Analysis of Unreplicated Lattice‐Split‐Plot Cultivar Trials¹

“Lattice‐split‐plot“ designs have been devised for the evaluation of a large number, k 2 . of cultivars, the subplot factor, at several levels of another factor which constitutes the main‐plot factor. Examples of possible mainplot factors are plant density levels or fertilizer treatments. The arrangement of cultivars within a main plot is that of a lattice design, each plot corresponding to a lattice replicate. The experiment may or may not have true replication. If not, a regression model which describes cultivar response to the main‐plot factor is used to make error estimable and adjustment for lattice blocks possible. This paper describes techniques for obtaining an empirical model in the event that the appropriate choice of a parametric model is unknown. These techniques, most of which use a principal components approach, are illustrated for an example of an unreplicated 7 X 7 lattice‐split‐plot experiment in which 49 maize ( Zea mays L .) cultivars are evaluated with four plant‐density levels as main plots. Six empirical models were found for which results of analyses agreed closely with results obtained using what is believed to be the appropriate parametric model.