Intrablock Analysis of Designs With Multiple Blocking Criteria
研究了多维区组设计（MBD）的区内方差分析和参数估计方法，适用于结构完整或不完整的交叉分类、嵌套分类等复杂设计，为实际应用提供分析工具。
Abstract A multidimensional block design (MBD) is an amalgamation of d > 1 component block designs. It may be represented as a d-dimensional lattice with nodes, where b (s) is the number of blocks in the sth component block design. The (j 1, …, jd )-node of the lattice may have h(i, j 1, …, jd ) ≥ 0 experimental units assigned to treatment i, i = 1, …, v, js , = 1, …, b (s), s = 1, …, d, where v 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, j 1, …, jd ), 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.