THE DESIGN AND ANALYSIS OF EXPERIMENTS. By Oscar Kempthorne. New York, John Wiley and Sons, Inc., 1952. 631 pp. $8.50. This book by a teacher of statistics (as well as a consultant for \"experimenters\") is a comprehensive study of the philosophical background for the statistical design of experiment. It is necessary to have some facility with algebraic notation and manipulation to be able to use the volume intelligently. The problems are presented from the theoretical point of view, without such practical examples as would be helpful for those not acquainted with mathematics. The mathematical justification for the techniques is given. As a somewhat advanced treatment of the design and analysis of experiments, this volume will be interesting and helpful for many who approach statistics theoretically as well as practically. With emphasis on the \"why,\" and with description given broadly, the author relates the subject matter to the general theory of statistics and to the general problem of experimental inference. MARGARET J. ROBERTSON

The Design and Analysis of Experiments

System of experimental design : engineering methods to optimize quality and minimize costs

SLEP: Sparse Learning with Efficient Projections

Researchers designing experiments in which a sample of participants responds to a sample of stimuli are faced with difficult questions about optimal study design. The conventional procedures of statistical power analysis fail to provide appropriate answers to these questions because they are based on statistical models in which stimuli are not assumed to be a source of random variation in the data, models that are inappropriate for experiments involving crossed random factors of participants and stimuli. In this article, we present new methods of power analysis for designs with crossed random factors, and we give detailed, practical guidance to psychology researchers planning experiments in which a sample of participants responds to a sample of stimuli. We extensively examine 5 commonly used experimental designs, describe how to estimate statistical power in each, and provide power analysis results based on a reasonable set of default parameter values. We then develop general conclusions and formulate rules of thumb concerning the optimal design of experiments in which a sample of participants responds to a sample of stimuli. We show that in crossed designs, statistical power typically does not approach unity as the number of participants goes to infinity but instead approaches a maximum attainable power value that is possibly small, depending on the stimulus sample. We also consider the statistical merits of designs involving multiple stimulus blocks. Finally, we provide a simple and flexible Web-based power application to aid researchers in planning studies with samples of stimuli.

Statistical power and optimal design in experiments in which samples of participants respond to samples of stimuli.

Should evolutionary geneticists worry about higher-order epistasis?

This article documents a meta-analysis of 113 data sets from published factorial experiments. The study quantifies regularities observed among factor effects and multifactor interactions. Such regularities are known to be critical to efficient planning and analysis of experiments and to robust design of engineering systems. Three previously observed properties are analyzed: effect sparsity, hierarchy, and heredity. A new regularity is introduced and shown to be statistically significant. It is shown that a preponderance of active two-factor interaction effects are synergistic, meaning that when main effects are used to increase the system response, the interaction provides an additional increase and that when main effects are used to decrease the response, the interactions generally counteract the main effects. © 2006 Wiley Periodicals, Inc. Complexity 11: 32– 45, 2006

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Regularities in Data from Factorial Experiments

This paper discusses validation of design methods. The challenges and opportunities in validation are illustrated by means of an analogy with medical research and development. Inspired by this analogy, a model-based process is presented for validating robust-parameter-design methods. A hierarchical probability model was used to create a large number of polynomial response surfaces with hierarchy and inheritance properties similar to those of an ensemble of 62 engineering responses from published experiments. Various robust-parameter-design methods were applied to each response surface and the robustness of the resulting designs was assessed. It was shown that crossed array methods are more effective than combined array methods if there is a reasonable probability of three-factor interactions. It is also shown that one-factor-at-time methods provide even greater effectiveness than crossed arrays methods.Copyright © 2004 by ASME

Validating Robust-Parameter-Design Methods

﻿A hierarchical probability model is proposed for evaluating the effectiveness of robust parameter design (RPD) models. The model is used to create responses to which alternative robust parameter design methods published in the literature are applied. T..

Using Hierarchical Probability Models to Evaluate Robust Parameter Design Methods

Model-Based Validation of Design Methods

This article documents a meta-analysis of 113 data sets from published factorial experiments. The study quantifies regularities observed among factor effects and multifactor interactions. Such regularities are known to be critical to efficient planning and analysis of experiments and to robust design of engineering systems. Three previously observed properties are analyzed: effect sparsity, hierarchy, and heredity. A new regularity is introduced and shown to be statistically significant. It is shown that a preponderance of active two-factor interaction effects are synergistic, meaning that when main effects are used to increase the system response, the interaction provides an additional increase and that when main effects are used to decrease the response, the interactions generally counteract the main effects. © 2006 Wiley Periodicals, Inc. Complexity 11: 32–45, 2006This paper was submitted as an invited paper resulting from the “Understanding Complex Systems” conference held at the University of Illinois–Urbana Champaign, May 2005

Xiang Li

Papers

Regularities in Data from Factorial Experiments

Validating Robust-Parameter-Design Methods

Using Hierarchical Probability Models to Evaluate Robust Parameter Design Methods

Model-Based Validation of Design Methods

Regularities in data from factorial experiments: Research Articles