Analysis of Augmented Unreplicated Factorial Designs Repeated in Time

Abstract

Unreplicated designs are fairly common in industrial applications; however, there is resistance to their use in agricultural science. In the agriculture community, there is still a belief that lack of replication may prevent the experimenter from getting useful conclusions. Nevertheless, sound statistical methods that permit valid comparisons in unreplicated studies are available for many types of designs. The objective of this paper is to present an analysis procedure for unreplicated designs combining typical characteristics found in industrial experimentation (factorial designs augmented with center points) and in agricultural applications (inclusion of control treatments and repeated measurements). We illustrate the method through a real experiment to evaluate the use of sugarcane by-products in chicken diet. Specifically, it is an unreplicated two-level factorial design with two additional runs (a center point and a control treatment), with experimental units measured in two periods of time. Replication was initially planned in the case study, but the actual treatment application led to an unreplicated design. The application of the proposed method allows interpretation of the data collected. We conclude that the appropriate use of unreplicated designs in agricultural and biological research may reduce overall costs and lessen the use of in vivo testing.

Extensions and variants of mixed‐level split‐plot designs for manufacturing planning and optimization

“…After this adjustment, normal (or half‐normal) probability plots can be made to identify the active factors. Vivacqua, Pinho, and Ho illustrate this procedure.…”