Optimal Experimental Design with R (Hardback) book cover

Optimal Experimental Design with R

By Dieter Rasch, Jurgen Pilz, L.R. Verdooren, Albrecht Gebhardt

© 2011 – Chapman and Hall/CRC

345 pages | 15 B/W Illus.

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Hardback: 9781439816974
pub: 2011-05-18
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pub: 2011-05-18
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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:

  • Introduces the philosophy of experimental design

    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

Table of Contents


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


Confidence estimation

Selection procedures

Testing hypotheses

Summary of sample size formulae

Size of Experiments in Analysis of Variance Models


One-way layout

Two-way layout

Three-way layout

Sample Size Determination in Model II of Regression Analysis


Confidence intervals

Hypothesis testing

Selection procedures

Sequential Designs


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


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


Exact Φ-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


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


About the Authors

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.

Subject Categories

BISAC Subject Codes/Headings:
MATHEMATICS / Probability & Statistics / General