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

Efforts to understand and mitigate the health effects of particulate matter (PM) air pollution have a rich and interesting history. This review focuses on six substantial lines of research that have been pursued since 1997 that have helped elucidate our understanding about the effects of PM on human health. There has been substantial progress in the evaluation of PM health effects at different time-scales of exposure and in the exploration of the shape of the concentration-response function. There has also been emerging evidence of PM-related cardiovascular health effects and growing knowledge regarding interconnected general pathophysiological pathways that link PM exposure with cardiopulmonary morbidity and mortality. Despite important gaps in scientific knowledge and continued reasons for some skepticism, a comprehensive evaluation of the research findings provides persuasive evidence that exposure to fine particulate air pollution has adverse effects on cardiopulmonary health. Although much of this research has been motivated by environmental public health policy, these results have important scientific, medical, and public health implications that are broader than debates over legally mandated air quality standards.

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Health effects of fine particulate air pollution: lines that connect

1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

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

Statistical Analysis with Missing Data

We consider a finite population mixed model that accommodates response errors and show how to obtain optimal estimators of the finite population parameters in a pretest-posttest context. We illustrate the method with the estimation of the difference in gain between two interventions and consider a simulation study to compare the empirical version of the proposed estimator (obtained by replacing variance components with estimates) with the estimator obtained via covariance analysis usually employed in such settings. The results indicate that in many instances, the proposed estimator has a smaller mean squared error than that obtained from the standard analysis of covariance model.

Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors

https://link.springer.com/content/pdf/10.1007/s40300-021-00225-6.pdf

A fair comparison of credible and confidence intervals: an example with binomial proportions

Mixed models may be defined with or without reference to sampling, and can be used to predict realized random effects, as when estimating the latent values of study subjects measured with response error. When the model is specified without reference to sampling, a simple mixed model includes two random variables, one stemming from an exchangeable distribution of latent values of study subjects and the other, from the study subjects’ response error distributions. Positive probabilities are assigned to both potentially realizable responses and artificial responses that are not potentially realizable, resulting in artificial latent values. In contrast, finite population mixed models represent the two-stage process of sampling subjects and measuring their responses, where positive probabilities are only assigned to potentially realizable responses. A comparison of the estimators over the same potentially realizable responses indicates that the optimal linear mixed model estimator (the usual best linear unbias...

Sampling, WLS, and Mixed Models

Conselho Nacional de Desenvolvimento Cientifico e Tecnologico (CNPq), Brazil [3304126/2015-2]

Fitting mixed models to messy longitudinal data: A case study involving estimation of post mortem intervals

We use a finite population mixed model that accommodates response error in the survey variable of interest and auxiliary information to obtain optimal estimators of population parameters from data collected via simple random sampling. We illustrate the method with the estimation of a regression coefficient and conduct a simulation study to compare the performance of the empirical version of the proposed estimator (obtained by replacing variance components with estimates) with that of the least squares estimator usually employed in such settings. The results suggest that when the auxiliary variable distribution is skewed, the proposed estimator has a smaller mean squared error.

Julio M. Singer

Papers

Finite Population Mixed Models for Pretest-Posttest Designs with Response Errors

A fair comparison of credible and confidence intervals: an example with binomial proportions

Sampling, WLS, and Mixed Models

Fitting mixed models to messy longitudinal data: A case study involving estimation of post mortem intervals

Estimation of Finite Population Parameters With Auxiliary Information and Response Error