Graphical Methods for the Design of Experiments: (143 Lecture Notes in Statistics)

Graphical methods have played an important role in the statistical analysis of experimental data, but have not been used as extensively for experiment design, at least as it is presented in most design of experiments texts. Yet graphical methods are particularly attractive for the design of experiments because they exploit our creative right-brain capabilities. Creative activity is clearly important in any kind of design, certainly for the design ofan experiment. The experimenter must somehow select a set of run conditions that will meet the goals for a particular experiment in a cost-efficient way. Graphical Methods for Experiment Design goes beyond graphical methods for choosing run conditions for an experiment. It looks at the entire pre-experiment planning process, and presents in one place a collection of graphical methods for defining experiment goals, identifying and classifying variables, for choosing a model, for developing a design, and for assessing the adequacy of a design for estimating the unknown coefficients in the proposed statistical model. In addition, tools for developing a design also provide a platform for viewing the results of the experiment, a platform that provides insights that cannot be obtained by examination ofregression coefficients. These techniques can be applied to a variety of situations, including experimental runs of computer simulation models. Factorial and fractional-factorial designs are the focus of the graphical representations, although mixture experiments and experiments involving random effects and blocking are designed and represented in similar ways.

Table of Contents:
1 Introduction.- The role of experiment design in statistical methodology.- The five main steps in the design of an experiment.- Summary of topics.- The videodisk pressing example.- Study questions.- 2 Planning for a Designed Experiment.- Goal hierarchy plots.- Individual experiment goals and form of the statistical model.- Experiment goals: other aspects.- Key terms in experiment design.- Identifying and classifying variables.- Choosing a model: a priori main effect and interaction plots.- Summary.- Study questions.- 3 Design-Plots for Factorial and Fractional-Factorial Designs.- Factorial designs.- Graphical presentation of factorial designs.- Factorial designs and corresponding regression models.- Graphical projections and the notion of effect sparsity.- Confounding in fractional-factorial designs.- Geometric patterns of confounding relations.- Design-plots for other designs.- Study questions.- 4 Designing Experiments Graphically.- Constructing two-level fractional-factorial designs.- Designing fractional-factorial experiments with three or more levels.- Videodisk pressing example.- Graphical design of mixture experiments.- Graphical designs for blocking and nested effects.- Confounding graphs.- Experiment designs for robust design.- Designing pilot experiments.- Study questions.- 5 Assessing Experiment Designs.- A videodisk experiment design.- Numerical measures for design assessment.- Design assessment and `optimal’ designs.- Graphical methods for assessing confounding in regular 2k-pdesigns.- Prediction error plots.- Designs for a manufacturing simulation study.- Shaded-block matrix plots.- Parallel coordinate plots.- A model with dependent random perturbations.- Study questions.- 6 Presenting Results Graphically.- Traditional graphical displays of experimentalresults.- Response-scaled design-plots.- Constructing a response-scaled design-plot.- Interpreting response-scaled design-plots.- Response-scaled design-plots and robust design.- Model-free interpretation of experimental results.- Study questions.