Rasch / Pilz / Verdooren Optimal Experimental Design with R

1. Auflage 2011
ISBN: 978-1-4398-1698-1
Verlag: Taylor & Francis
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 345 Seiten

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.

Zielgruppe

Statisticians in experimental design; applied scientists in the natural sciences, agriculture, medicine, engineering, and environmental science.

Autoren/Hrsg.

Rasch, Dieter

Pilz, Jurgen

Verdooren, L.R.

Gebhardt, Albrecht

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik

Inhaltsverzeichnis

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 F-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

Über Autor(innen)

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.