Optimal Experimental Design with R
Chapman and Hall/CRC – 2011 – 345 pages
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.
Providing a concise introduction to experimental design theory, Optimal Experimental Design with R:
Provides an easy process for constructing experimental designs and calculating necessary sample size using R programs
Teaches by example using a custom made R program package: OPDOE
Consisting of detailed, data-rich examples, this book introduces experimenters to the philosophy of experimentation, experimental design, and data collection. It gives researchers and statisticians guidance in the construction of optimum experimental designs using R programs, including sample size calculations, hypothesis testing, and confidence estimation. A final chapter of in-depth theoretical details is included for interested mathematical statisticians.
the book provides an impressive amount of information that will be greatly helpful to OPDOE users. … the book provides many examples, mainly from the fields of agriculture and animal science. … readers will benefit from learning about a number of nifty functions in OPDOE, for example, its sample size solvers.
—Wayne Adams and Mark Anderson, Technometrics, May 2012
Overall, I think that mathematically apt readers, who want to do sample size determination for nontrivial experimental setups or are interested in the ins and outs of balanced incomplete block designs, will benefit most from the book.
—Ulrike Grömping, Journal of Statistical Software, October 2011
Experimentation and empirical research
Some basic definitions
About the R-programs
Determining the Minimal Size of an Experiment for Given Precision
Sample Size Determination in Completely Randomised Designs
Summary of sample size formulae
Size of Experiments in Analysis of Variance Models
Sample Size Determination in Model II of Regression Analysis
Wald's sequential likelihood ratio test (SLRT) for one-parametric exponential families
Test about means for unknown variances
A sequential selection procedure
Construction of Optimal Designs
Constructing Balanced Incomplete Block Designs
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
Exact Φ-optimal designs
Determining the size of an experiment
Second Order Designs
Central composite designs
D-optimum and G-optimum second order designs
Comparing the determinant criterion for some examples
The simplex lattice designs
Simplex centroid designs
Extreme vertice designs
Constructing optimal mixture designs with R
Groups, fields and finite geometries
Existence and non-existence of non-trivial BIBD
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.
Jürgen 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.