INTRABLOCK ANALYSIS OF DESIGNS WITH MULTIPLE BLOCKING CRITERIA

• 成果类型: Article
• 署名作者: BRADLEY, RA; STEWART, FP
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• 发表日期: 1991
• 页码: 792-797
• 关键词: orthogonal designs; youden designs; nested rows; CONSTRUCTION; columns

摘要

A multidimensional block design (MBD) is an amalgamation of d < 1 component block designs. It may be represented as a d-dimensional lattice with b* = PI-s = 1d b(s) nodes, where b(s) is the number of blocks in the sth component block design. The (j1, ..., j(d))-node of the lattice may have h(i, j1, ..., j(d)) greater-than-or-equal-to 0 experimental units assigned to treatment i, i = 1, ..., nu, j(s) = 1, ..., b(s), s = 1, ..., d, where nu is the number of treatments. If each node of the lattice is used, the design is structurally complete; if some of the nodes are empty, the design is structurally incomplete. Particular MBD's may be specified through choices of the h(i, j1, ..., j(d)), designs that may be cross-classifications by blocking criteria, nested classifications, combinations of crossed and nested classifications, or much less orderly multidimensional arrays. The investigation of multidimensional block designs is accordingly very general. The main results provide needed parameter estimators and the intrablock analysis of variance for a general MBD. Given these results, analyses for new special classes of structurally complete or incomplete MBD's are easily obtained. Design efficiencies are considered and examples provided.