The statistical design and analysis of experiments and combinatorial design

该提案包括一系列相互关联的研究，在临床试验，制造业和农业中具有潜在的应用，旨在验证申请人杰出研究生涯中最有前途的统计调查“松散”。 重点是实验设计的统计研究，特别是但不限于比较处理具有相对复杂结构的情况。要研究的问题是：（i）一种特殊类型的设计，一个不完全的析因设计，用于医学临床试验，预后因素来自患者进入试验时的状况。此外，“加权”因素将被考虑，以极端的因素组合被包括在内，从而允许的设计被判断为“道德”;（ii）扩展到一个特定类型的设计称为格子广场设计，主要用于医疗应用和他们的链接到两个阶段的设计。此外，格子方格设计在工业上用于研究制造过程中的产品可靠性可能是自然的。重要的一点是提供设计或数据收集指南，平衡协变量效应的最佳估计与足够的统计功效，以检测各种治疗效应之间的差异（如果存在）;（iii）确定不完全区组设计和数学图论之间的关系，这将增加对设计稳健性程度的了解，即什么样的结论可以作出时，一些意见是失踪或虚假的;和（iv）最近邻设计（配置）和广义数独平方的关系，也给数据压缩的可能性。在9 x9的数独正方形中，只有17个数字产生一个81个数字的唯一正方形。实际应用可能包括数据压缩或加密。虽然数独游戏最初是作为一种娱乐形式开发的，但它可能会揭示一些实验问题的统计设计，本身就是一个有趣的变化。

The proposal consists of a range of interrelated studies having potential applications in clinical trials, the manufacturing industry and agriculture, and aims to validate the most promising "loose ends" of statistical investigation in the applicant's distinguished research career. The focus is the statistical study of the design of experiments dealing especially but not exclusively with situations in which the treatments under comparison have a relatively complex structure. The issues to be studied are: (i) a special type of design, an incomplete factorial design, to be used in clinical trials in medicine with prognostic factors derived from the condition of the patient at entry to the trial. Also "weighted" factors will be considered in order for extreme combinations of factors to be included, thus permitting the designs to be judged to be "ethical"; (ii) extensions to a particular type of design called a plaid-square design, for use chiefly in medical applications and their link to two-phase designs. In addition, the plaid-square designs may be natural in industry for studies on reliability of products in manufacturing processes. The important point is to provide design or data-collection guidance which balances optimal estimation of covariate effects with sufficient statistical power to detect differences between various treatment effects if they were present; (iii) the determination of relationships between incomplete block designs and the mathematical theory of graphs which will add insight into the degree of robustness of a design, i.e. what conclusions can be made when some observations are missing or spurious; and (iv) the relationship of nearest-neighbour designs (configurations) and the generalized Sudoku square giving the possibility also of data compression. In the 9x9 Sudoku square, only seventeen numbers produce a unique square of 81 numbers. Practical applications might include data compression or encryption. Although the Sudoku puzzle was originally developed as a form of entertainment, it may shed light on some statistical design of experiment problems and be of itself an intriguing variation.