Incomplete Block Designs for Comparing Treatments with a Control. I. General Theory.
Abstract
This is the first paper of a series in which we outline a theory of optimal incomplete block designs for comparing several treatments with a control, and give plans of optimal designs to use for this purpose. In the present paper we develop the basic theory of the incomplete block designs which are appropriate for the many-to-one comparisons problem; the optimality considerations for such designs will be addressed in subsequent papers. For this problem we propose a new general class of incomplete block designs which are balanced with respect to test treatments. We shall use the abbreviation BTIB to refer to such designs. We study their structure, and give some methods of construction. A procedure for making exact joint confidence statements for our multiple comparisons problem is described. Using a new concept of admissibility of designs, it is shown how 'inferior' designs can be eliminated from consideration. Some open problems concerning construction of BTIB designs are posed. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1979
- Accession Number
- ADA078330
Entities
People
- Ajit C. Tamhane
- Robert E. Bechhofer
Organizations
- Cornell University College of Engineering