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In many designed experiments in agriculture and the life sciences, a researcher can anticipate the direction that responses will take when treatments are varied. For example, in a 2way factorial, a researcher may know that increasing the levels of nitrogen and phosphorus will increase yields of a crop. Classical analysis of variance does not take into account a known ordering among population means. However, it can be shown that by restricting the estimates of means to have the same ordering as the anticipated ordering of popUlation means, a reduction in mean-squared errors of estimators will likely occur, often by more than 50%. A procedure used to create such estimates is called isotonic regression. 95 In this article, a recently proposed method of isotonic regression for lattice-ordered means will be presented after first reviewing well-established methods. The newer method will be illustrated using data from an entomology experiment. In addition, standard errors of the estimators will be approximated using a bootstrap procedure.

USING ISOTONIC REGRESSION TO IMPROVE ESTIMATION IN FACTORIAL EXPERIMENTS WITH ORDERED FACTOR LEVELS