On the construction of trend resistant PBIB designs

In agricultural, animal, fisheries and industrial experimentation under block design setup, systematic trend may affect the response under consideration. Although remote, these effects may still have high influence on response and hence should be incorporated in the model for proper model specification. Completely trend resistant block designs, also known as trend free block designs, are an important class of designs where the analysis can be done in usual manner as in case of normal block designs since trend effects and treatment effects are orthogonal. Literature is available on different aspects of trend resistant incomplete block designs mainly focusing on balanced incomplete block designs. This article deals with the construction of completely trend resistant Partially Balanced Incomplete Block (TR-PBIB) designs. Two methods of constructing such designs have been discussed. The information matrices for the class of designs developed have been derived and SAS code for the generation of the developed designs has also been provided.在区组设计（block design）框架下开展的农业、畜牧、水产及工业试验中，系统性趋势效应可能对所研究的响应变量产生影响。尽管此类效应看似影响有限，但仍可能对响应变量产生显著作用，因此为完成正确的模型设定，需将其纳入模型之中。完全抗趋势区组设计（completely trend resistant block design），亦称无趋势区组设计，是一类重要的试验设计：由于趋势效应与处理效应相互正交，其分析可按照常规区组设计的标准流程进行。现有文献已围绕抗趋势不完全区组设计的诸多方面展开研究，其中核心研究对象为平衡不完全区组设计（balanced incomplete block design）。本文针对完全抗趋势部分平衡不完全区组（TR-PBIB）设计的构造方法展开研究，共讨论了两类构造此类设计的方案。文中推导了所提出这类设计的信息矩阵，并提供了用于生成该类设计的SAS代码。