Optimal Experimental Design with R

About this book

Experimental design is often overlooked in the literature of applied and mathematical statistics: statistics is taught and understood as merely a collection of methods for analyzing data. Consequently, experimenters seldom think about optimal design, including prerequisites such as the necessary sample size needed for a precise answer for an experimental question. This book provides a concise introduction to experimental design theory.

Contents

Introduction Experimentation and empirical research Designing experiments Some basic definitions Block designs About the R-programs Determining the Minimal Size of an Experiment for Given Precision Sample Size Determination in Completely Randomised Designs Introduction Confidence estimation Selection procedures Testing hypotheses Summary of sample size formulae Size of Experiments in Analysis of Variance Models Introduction One-way layout Two-way layout Three-way layout Sample Size Determination in Model II of Regression Analysis Introduction Confidence intervals Hypothesis testing Selection procedures Sequential Designs Introduction Wald's sequential likelihood ratio test (SLRT) for one-parametric exponential families Test about means for unknown variances Triangular designs A sequential selection procedure Construction of Optimal Designs Constructing Balanced Incomplete Block Designs Introduction Basic definitions Construction of BIBD Constructing Fractional Factorial Designs Introduction and basic notations Factorial designs|basic definitions Fractional factorials design with two levels of each factor (2p-k designs) Fractional factorial designs with three levels of each factor (3p-k-designs) Exact Optimal Designs and Sample Sizes in Model I of Regression Analysis Introduction Exact I|-optimal designs Determining the size of an experiment Special Designs Second Order Designs Central composite designs Doehlert designs D-optimum and G-optimum second order designs Comparing the determinant criterion for some examples Mixture Designs Introduction The simplex lattice designs Simplex centroid designs Extreme vertice designs Augmented designs Constructing optimal mixture designs with R An example Theoretical Background Non-central distributions Groups, fields and finite geometries Difference sets Hadamard matrices Existence and non-existence of non-trivial BIBD Conference matrices Index

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Biography

Dieter Rasch: Currently Senior Consultant at the Centre of Experimental Design: University of Natural Resources and Life Sciences, Vienna, Dr. Rasch is an Elected Member of the International Statistical Institute (ISI), a Fellow of the IMS, and author/co-author of 46 books and more than 260 scientific papers. From 1958- 1990, Dr. Rasch was Head of the Deparment (and Institute) of Biometry at the Research Centre Dummerstorf-Rostock, Germany. Afterwards, Dr. Rasch was professor of Mathematical Statistics at the University of Wageningen, The Netherlands from 1991 to 2000. Since 2000, he has served as a guest professor at the Math. Inst. of the University of Klagenfurt, the University Vienna, and at the Institute of Applied Statistics and Computing, University of Natural Resources and Life Sciences (2007 to 2010). Albrecht Gebhardt: Assistant professor at the Institute of Statistics, University of Klagenfurt since 2004. Jurgen Pilz: Professor and Chair of Applied Statistics at the University of Klagenfurt (UniKlu), Austria since 1994, and the head of the Department of Statistics at UniKlu since 2007. He has held many guest professorships, including at Purdue University, USA, Charles University, Prague,Czech Republic, the University of Augsburg, Germany, and the University of British Columbia, Vancouver, Canada. He is an Elected Member of the Int. Statist. Institute (ISI), a Fellow of the IMS, and author/co-author of six books and more than 100 scientific papers. Rob Verdooren: A Consultant Statistician at Danone Research, Centre for Spceialised Nutrition, Wageningen, the Netherlands. He is retired Associate Professor in Experimental Design and Analysis at the Agricultural Uniiversity Wageningen, the Netherlands. Besides Experimental Design, his interests lies in Biostatistics and the design and analysis of breeding trials of Oil Palms in Indonesia.