William I Notz

Bio: William I Notz is an academic researcher. The author has contributed to research in topics: Optimal design & Block (telecommunications). The author has an hindex of 2, co-authored 2 publications receiving 113 citations.

Optimal Incomplete Block Designs for Comparing Treatments with a Control

Abstract: The problem of finding optimal incomplete blocks designs for comparing $p$ test treatments with a control is studied. B.I.B. designs are found to be $D$-optimal. $A$- and $E$-optimal designs are also obtained. For a large class of functions $\phi$, conditions for a design to be $\phi$-optimal are found. Most of the optimal designs are certain types of B.T.I.B. designs, introduced by Bechhofer and Tamhane (1981), which are binary in test treatments.

On the Optimality of Spring Balance Weighing Designs

Abstract: This paper deals with techniques for finding $\Phi$-optimal designs for weighing $v$ objects in $b$ weighings using a spring balance. The optimality functions considered encompass a large class of functions. Results are applied to find $A$-, $D$- and $E$-optimal designs and the optimal designs obtained are seen to be related to certain types of well known block designs.

Experimental Design: Review and Comment

Abstract: We review major developments in the design of experiments, offer our thoughts on important directions for the future, and make specific recommendations for experimenters and statisticians who are students and teachers of experimental design, practitioners of experimental design, and researchers jointly exploring new frontiers. Specific topics covered are optimal design, computer-aided design, robust design, response surface design, mixture design, factorial design, block design, and designs for nonlinear models.

Handbook of Design and Analysis of Experiments

Abstract: General Principles History and Overview of Design and Analysis of Experiments Klaus Hinkelmann Introduction to Linear Models Linda M. Haines Designs for Linear Models Blocking with Independent Responses John P. Morgan Crossover Designs Mausumi Bose and Aloke Dey Response Surface Experiments and Designs Andre I. Khuri and Siuli Mukhopadhyay Design for Linear Regression Models with Correlated Errors Holger Dette, Andrey Pepelyshev, and Anatoly Zhigljavsky Designs Accommodating Multiple Factor Regular Fractional Factorial Designs Robert Mee and Angela Dean Multistratum Fractional Factorial Designs Derek Bingham Nonregular Factorial and Supersaturated Designs Hongquan Xu Structures Defined by Factors R.A. Bailey Algebraic Method in Experimental Design Hugo Maruri-Aguilar and Henry P. Wynn Optimal Design for Nonlinear and Spatial Models Optimal Design for Nonlinear and Spatial Models: Introduction and Historical Overview Douglas P. Wiens Designs for Generalized Linear Models Anthony C. Atkinson and David C. Woods Designs for Selected Nonlinear Models Stefanie Biedermann and Min Yang Optimal Design for Spatial Models Zhengyuan Zhu and Evangelos Evangelou Computer Experiments Design of Computer Experiments: Introduction and Background Max Morris and Leslie Moore Latin Hypercubes and Space-Filling Designs C. Devon Lin and Boxin Tang Design for Sensitivity Analysis William Becker and Andrea Saltelli Expected Improvement Designs William I. Notz Cross-Cutting Issues Robustness of Design Douglas P. Wiens Algorithmic Searches for Optimal Designs Abhyuday Mandal, Weng Kee Wong, and Yaming Yu Design for Contemporary Applications Design for Discrete Choice Experiments Heiko Grossmann and Rainer Schwabe Plate Designs in High-Throughput Screening Experiments for Drug Discovery Xianggui Qu (Harvey) and Stanley Young Up-and-Down Designs for Dose-Finding Nancy Flournoy and Assaf P. Oron Optimal Design for Event-Related fMRI Studies Jason Ming-Hung Kao and John Stufken Index

Optimal designs for comparing test treatments with controls

Abstract: This article outlines existing knowledge on optimal designs for comparing test treatments with controls under 0-, 1- and 2-way elimination of heterogeneity models. The results are motivated through numerical examples.

Recent Discoveries on Optimal Designs for Comparing Test Treatments with Controls.

Abstract: : The authors introduce the problem with an example. How should we design an experiment to compare 4 test treatments with a control, using 18 experimental units? As a statistical question we will not be able to answer it unless it is asked in a more precise manner. To begin with we need to postulate a model for the response observed upon application of a treatment, test treatment or control, to an experimental unit. This paper shall consider three possible models: 1) O-way elimination of heterogeneity model in which all experimental units are homogeneous before application of treatments; 2) 1-way elimination of heterogeneity model in which experimental units can be divided into several homogeneous blocks; and 3) 2-way elimination of heterogeneity model in which the experimental units can be conceptually arranged according to rows and columns.

Recent Developments in the Methods of Optimum and Related Experimental Designs

Abstract: Summary A survey is given of recent statistical work on the design of experiments, based on the literature of the last six years. The emphasis is on nonstandard applications of optimum design theory. Reference is made to surveys on the theory of optimum experimental design, crossover designs and incomplete block designs.