A Theorem on Trend-Free Block Designs.
Abstract
An earlier, referenced report considered the existence of trend-free block designs and gave some general results for general block designs and some special results for complete block designs. This report presents a new existence theorem that is sufficiently general to cover broad classes of incomplete block designs and suggests a design construction method. Suppose that a common trend affecting treatment responses exists over the plots within blocks of a block design with usual design parameters, v,b,k,r. A trend-free block design, if it exists, is one for which treatments are assigned to plots within blocks so that treatment and block contrasts are orthogonal to specified trend components. We prove that, if a given block design is constructed and the common trend is linear, the necessary and sufficient condition for the existence of a trend-free block design with the same incidence matrix is that 1/2r(k+1) be an integer. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1981
- Accession Number
- ADA096575
Entities
People
- Ching-ming Yeh
- Ralph A. Bradley
Organizations
- Florida State University