Optimal Experimental Design with R
Purchasing Options
Features
- A thorough, concise introduction to experimental design theory
- Guidance on the construction of experiments, including sample size calculations, hypothesis testing, and confidence estimation
- Examples using real-world data illustrate how R programs should be applied, including R programs for sample-size calculations
Summary
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.
Table of 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 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
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
Author Bio(s)
Editorial Reviews
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
Downloads Updates
| Resource | OS Platform | Updated | Description | Instructions |
|---|---|---|---|---|
| Cross Platform | June 22, 2011 | Author's Web Page link | click on http://wwwu.uni-klu.ac.at/agebhard/OPDOE/ |
