Optimal Experimental Design with R

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.

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