Trend-Free Block Designs: Existence and Construction Results
Abstract
Designs for which treatment and block contrasts are orthogonal to specified common trend components within blocks have been called trend-free block designs. Necessary and sufficient conditions for the existence of such designs were given in a reference. A matrix sum was required to have certain properties. It is shown now that the existence of a matrix with the required properties assures the existence of the necessary component matrices. The existence of trend-free block designs for specified trends in one or more dimensions is examined in a number of theorems and corollaries. Initial results are general and then trends in one dimension are considered. An alternative formulation of the necessary and sufficient conditions for a trend-free block design is given when each treatment has the same number of replications. Some special results are obtained for complete and balanced incomplete block designs. Youden Square designs are trend-free balanced incomplete block designs for up to p orthonormal, one-dimensional trend components, p < k, the block size. Some design construction methods are developed to establish the existence of certain trend-free block design. But, apart from the matter of treatment labelling, trend-free block designs may not be unique. The construction methods used may lead to designs particularly vulnerable to incorrect modelling of trend components.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1979
- Accession Number
- ADA072138
Entities
People
- Ching-ming Yeh
- Ralph A. Bradley
Organizations
- Florida State University