Incomplete Split-Plot Designs Supplemented by a Single Control

Abstract

The article deals with the constructing methods for experiments carried out in an incomplete split-plot design supplemented by an additional treatment, called a single control. The control treatment has been treated usually as one specific factor level while not necessarily. The control cannot be connected with treatment combinations in an experiment. This distinguishes this article from others in the area considered. The proposed supplementation of whole incomplete split-plot designs leads to the designs with generally accepted methodological requirements, especially randomization. Moreover, we propose a few methods for constructing considered types of the designs with desirable statistical properties such as general balance and efficiency balance of the design with respect to treatment contrasts.

Keywords:

• Control treatment
• Efficiency factor
• General balance
• Incomplete block design
• Incomplete split-plot design

2000 Mathematics Subject Classification:

• 62K15
• 62K10

Acknowledgments

The authors would like to thank to JSPS and PAN for giving them the opportunity to carry out this joint research in Japan and in Poland. The research was also partially supported by JSPS, Grant-in-Aid for Scientific Research (C) 21540142 and Polish National Science Centre, NN310111640 and NN310111740.