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

25. Multiple Imputation for Nonresponse in Surveys. By D. B. Rubin. ISBN 0 471 08705 X. Wiley, Chichester, 1987. 258 pp. £30.25.

Multiple Imputation for Nonresponse in Surveys

Generalized Linear Models (2nd ed.)

Maximizing data information requires careful selection, termed design, of the points at which data are observed. Experimental design is reviewed here for broad classes of data collection and analysis problems, including: fractioning techniques based on orthogonal arrays, Latin hypercube designs and their variants for computer experimentation, efficient design for data mining and machine learning applications, and sequential design for active learning. © 2012 Wiley Periodicals, Inc. © 2012 Wiley Periodicals, Inc.

Experimental design

Survey experiments are a core tool for causal inference. Yet, the design of classical survey experiments prevents them from identifying which components of a multidimensional treatment are influential. Here, we show how conjoint analysis, an experimental design yet to be widely applied in political science, enables researchers to estimate the causal effects of multiple treatment components and assess several causal hypotheses simultaneously. In conjoint analysis, respondents score a set of alternatives, where each has randomly varied attributes. Here, we undertake a formal identification analysis to integrate conjoint analysis with the potential outcomes framework for causal inference. We propose a new causal estimand and show that it can be nonparametrically identified and easily estimated from conjoint data using a fully randomized design. The analysis enables us to propose diagnostic checks for the identification assumptions. We then demonstrate the value of these techniques through empirical applications to voter decision making and attitudes toward immigrants.

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Causal Inference in Conjoint Analysis: Understanding Multidimensional Choices via Stated Preference Experiments

While the minimum aberration criterion is popular for selecting good designs with qualitative factors under an ANOVA model, the minimum $\beta$-aberration criterion is more suitable for selecting designs with quantitative factors under a polynomial model In this paper, we propose the concept of wordlength enumerator to unify these two criteria The wordlength enumerator is defined as an average similarity of contrasts among all possible pairs of runs The wordlength enumerator is easy and fast to compute, and can be used to compare and rank designs efficiently Based on the wordlength enumerator, we develop simple and fast methods for calculating both the generalized wordlength pattern and the $\beta$-wordlength pattern We further obtain a lower bound of the wordlength enumerator for three-level designs and characterize the combinatorial structure of designs achieving the lower bound Finally, we propose two methods for constructing supersaturated designs that have both generalized minimum aberration and minimum $\beta$-aberration

Wordlength enumerator for fractional factorial designs

The concept of universal optimality from optimum design theory is intro- duced into computer experiments, modeled as realizations of stationary Gaussian processes. When the correlation function is a nondecreasing and convex function of a distance measure, it is shown that a design is universally optimal if it is equidis- tant and of maximum average distance. Examples of universally optimal designs are given with respect to rectangular, Euclidean, Hamming, and Lee distances.

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Universally optimal designs for computer experiments

Chen and Cheng [Ann. Statist. 34 (2006) 546--558] discussed the method of doubling for constructing two-level fractional factorial designs. They showed that for $9N/32\le n\le 5N/16$, all minimum aberration designs with $N$ runs and $n$ factors are projections of the maximal design with $5N/16$ factors which is constructed by repeatedly doubling the $2^{5-1}$ design defined by $I=ABCDE$. This paper develops a general complementary design theory for doubling. For any design obtained by repeated doubling, general identities are established to link the wordlength patterns of each pair of complementary projection designs. A rule is developed for choosing minimum aberration projection designs from the maximal design with $5N/16$ factors. It is further shown that for $17N/64\le n\le 5N/16$, all minimum aberration designs with $N$ runs and $n$ factors are projections of the maximal design with $N$ runs and $5N/16$ factors.

A complementary design theory for doubling

Two-level orthogonal arrays of strength 3 permit the study of the main effects and the two-factor interactions of the experimental factors. These arrays are classified into regular and nonr...

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Construction of Two-Level Nonregular Designs of Strength Three With Large Run Sizes

When there is interest to study n chemicals using x dose levels each, factorial designs that require xn treatment groups have been put forward as one of the valuable statistical approaches for hazard assessment of chemical mixtures. Exemplary applications and cost-eﬃciency comparisons of full factorial designs and regular fractional factorial designs in toxicity studies can be found in Nesnow et al. (1995), Narotsky et al. (1995), and Groten et al. (1996,1997). We introduce nonregular fractional factorial designs and show their beneﬁts using two studies reported in Groten et al. (1996). Study 1 shows nonregular designs can provide the same amount of information using 75% of the experimental costs required in a regular design. Study 2 demonstrates nonregular designs can additionally estimate some partially aliased eﬀects, which cannot be done using regular designs. We also provide a statistical method to evaluate the quality of an assumption made by experts in Study 2 of Groten et al. (1996).

Hongquan Xu

Papers

Wordlength enumerator for fractional factorial designs

Universally optimal designs for computer experiments

A complementary design theory for doubling

Construction of Two-Level Nonregular Designs of Strength Three With Large Run Sizes

The Use of Nonregular Fractional Factorial Designs in Combination Toxicity Studies