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Multiple Comparisons introduces simultaneous statistical inference and covers the theory and techniques for all-pairwise comparisons, multiple comparisons with the best, and multiple comparisons with a control. The author describes confidence intervals methods and stepwise exposes abuses and misconceptions, and guides readers to the correct method for each problem. Discussions also include the connections with bioequivalence, drug stability, and toxicity studies Real data sets analyzed by computer software packages illustrate the applications presented.
Multiple Comparisons Using R by Frank Bretz,Torsten Hothorn,Peter Westfall Pdf
Adopting a unifying theme based on maximum statistics, Multiple Comparisons Using R describes the common underlying theory of multiple comparison procedures through numerous examples. It also presents a detailed description of available software implementations in R. The R packages and source code for the analyses are available at http://CRAN.R-project.org After giving examples of multiplicity problems, the book covers general concepts and basic multiple comparisons procedures, including the Bonferroni method and Simes’ test. It then shows how to perform parametric multiple comparisons in standard linear models and general parametric models. It also introduces the multcomp package in R, which offers a convenient interface to perform multiple comparisons in a general context. Following this theoretical framework, the book explores applications involving the Dunnett test, Tukey’s all pairwise comparisons, and general multiple contrast tests for standard regression models, mixed-effects models, and parametric survival models. The last chapter reviews other multiple comparison procedures, such as resampling-based procedures, methods for group sequential or adaptive designs, and the combination of multiple comparison procedures with modeling techniques. Controlling multiplicity in experiments ensures better decision making and safeguards against false claims. A self-contained introduction to multiple comparison procedures, this book offers strategies for constructing the procedures and illustrates the framework for multiple hypotheses testing in general parametric models. It is suitable for readers with R experience but limited knowledge of multiple comparison procedures and vice versa. See Dr. Bretz discuss the book.
Handbook of Multiple Comparisons by Xinping Cui,Thorsten Dickhaus,Ying Ding,Jason C. Hsu Pdf
Treats the topics of multiple comparisons, simultaneous and selective inference from avariety of different perspectives. The need for a systematic treatment of the eld originates from the relevanceof multiple comparisons in many applications (medicine, industry, economics), and from the diversityof approaches and developments.
Multiple Comparison Procedures by Larry E. Toothaker Pdf
If you conduct research with more than two groups and want to find out if they are significantly different when compared two at a time, then you need Multiple Comparison Procedures. Using examples to illustrate major concepts, this concise volume is your guide to multiple comparisons. Toothaker thoroughly explains such essential issues as planned vs. post-hoc comparisons, stepwise vs. simultaneous test procedures, types of error rate, unequal sample sizes and variances, and interaction tests vs. cell mean tests.
Understanding Statistics and Experimental Design by Michael H. Herzog,Gregory Francis,Aaron Clarke Pdf
This open access textbook provides the background needed to correctly use, interpret and understand statistics and statistical data in diverse settings. Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III provides insight into meta-statistics (statistics of statistics) and demonstrates why experiments often do not replicate. Finally, the textbook shows how complex statistics can be avoided by using clever experimental design. Both non-scientists and students in Biology, Biomedicine and Engineering will benefit from the book by learning the statistical basis of scientific claims and by discovering ways to evaluate the quality of scientific reports in academic journals and news outlets.
Multiple Comparison Procedures by Yosef Hochberg,Ajit C. Tamhane Pdf
Offering a balanced, up-to-date view of multiple comparison procedures, this book refutes the belief held by some statisticians that such procedures have no place in data analysis. With equal emphasis on theory and applications, it establishes the advantages of multiple comparison techniques in reducing error rates and in ensuring the validity of statistical inferences. Provides detailed descriptions of the derivation and implementation of a variety of procedures, paying particular attention to classical approaches and confidence estimation procedures. Also discusses the benefits and drawbacks of other methods. Numerous examples and tables for implementing procedures are included, making this work both practical and informative.
Multiple Comparisons and Multiple Tests by Peter H. Westfall,Randall D. Tobias Pdf
Does your work require multiple inferences? Are you a statistics teacher looking for a study guide to supplement the usually incomplete or outdated multiple comparisons/multiple testing material in your textbook? This workbook, the companion guide written specifically for use with Multiple Comparisons and Multiple Tests Using the SAS System, provides the supplement you need. Use this workbook and you will find problems and solutions that will enhance your understanding of the material within the main text. The workbook also provides updated information about multiple comparisons procedures, including enhancements for Release 8.1 of the SAS System. The chapters correlate with the chapters of the main text, and the format is clear and easy to use. This book and the companion text are quite useful as supplements for learning multiple comparisons procedures in standard linear models, multivariate analysis, categorical analysis, and regression and nonparametric statistics. Book jacket.
Multiple Comparisons introduces simultaneous statistical inference and covers the theory and techniques for all-pairwise comparisons, multiple comparisons with the best, and multiple comparisons with a control. The author describes confidence intervals methods and stepwise exposes abuses and misconceptions, and guides readers to the correct method
Multiple Comparisons by Alan J. Klockars,Gilbert Sax Pdf
Describes the most important methods used to investigate differences between levels of an independent variable within an experimental design. Readers will learn not only how to conduct multiple comparisons in experimental designs but also how to better understand and evaluate published research. "A highly readable introduction to multiple comparison methods, which demands little from its reader in the way of background other than some familiarity with analysis of variance." --The Statistician
Multiple Comparisons, Selection and Applications in Biometry by Fred. M. Hoppe Pdf
Aims to provide in-depth descriptions of the latest developments in multiple comparison methods and selection procedures, while emphasizing biometry. This text is published in honour of the 70th birthday of Charles W. Dunnett - a pioneer in statistical methodology.
Pairwise Multiple Comparisons by Taka-aki Shiraishi,Hiroshi Sugiura,Shin-ichi Matsuda Pdf
This book focuses on all-pairwise multiple comparisons of means in multi-sample models, introducing closed testing procedures based on maximum absolute values of some two-sample t-test statistics and on F-test statistics in homoscedastic multi-sample models. It shows that (1) the multi-step procedures are more powerful than single-step procedures and the Ryan/Einot–Gabriel/Welsh tests, and (2) the confidence regions induced by the multi-step procedures are equivalent to simultaneous confidence intervals. Next, it describes the multi-step test procedure in heteroscedastic multi-sample models, which is superior to the single-step Games–Howell procedure. In the context of simple ordered restrictions of means, the authors also discuss closed testing procedures based on maximum values of two-sample one-sided t-test statistics and based on Bartholomew's statistics. Furthermore, the book presents distribution-free procedures and describes simulation studies performed under the null hypothesis and some alternative hypotheses. Although single-step multiple comparison procedures are generally used, the closed testing procedures described are more powerful than the single-step procedures. In order to execute the multiple comparison procedures, the upper 100α percentiles of the complicated distributions are required. Classical integral formulas such as Simpson's rule and the Gaussian rule have been used for the calculation of the integral transform that appears in statistical calculations. However, these formulas are not effective for the complicated distribution. As such, the authors introduce the sinc method, which is optimal in terms of accuracy and computational cost.
Handbook of Multiple Comparisons by Xinping Cui,Thorsten Dickhaus,Ying Ding,Jason C. Hsu Pdf
Written by experts that include originators of some key ideas, chapters in the Handbook of Multiple Testing cover multiple comparison problems big and small, with guidance toward error rate control and insights on how principles developed earlier can be applied to current and emerging problems. Some highlights of the coverages are as follows. Error rate control is useful for controlling the incorrect decision rate. Chapter 1 introduces Tukey's original multiple comparison error rates and point to how they have been applied and adapted to modern multiple comparison problems as discussed in the later chapters. Principles endure. While the closed testing principle is more familiar, Chapter 4 shows the partitioning principle can derive confidence sets for multiple tests, which may become important as the profession goes beyond making decisions based on p-values. Multiple comparisons of treatment efficacy often involve multiple doses and endpoints. Chapter 12 on multiple endpoints explains how different choices of endpoint types lead to different multiplicity adjustment strategies, while Chapter 11 on the MCP-Mod approach is particularly useful for dose-finding. To assess efficacy in clinical trials with multiple doses and multiple endpoints, the reader can see the traditional approach in Chapter 2, the Graphical approach in Chapter 5, and the multivariate approach in Chapter 3. Personalized/precision medicine based on targeted therapies, already a reality, naturally leads to analysis of efficacy in subgroups. Chapter 13 draws attention to subtle logical issues in inferences on subgroups and their mixtures, with a principled solution that resolves these issues. This chapter has implication toward meeting the ICHE9R1 Estimands requirement. Besides the mere multiple testing methodology itself, the handbook also covers related topics like the statistical task of model selection in Chapter 7 or the estimation of the proportion of true null hypotheses (or, in other words, the signal prevalence) in Chapter 8. It also contains decision-theoretic considerations regarding the admissibility of multiple tests in Chapter 6. The issue of selected inference is addressed in Chapter 9. Comparison of responses can involve millions of voxels in medical imaging or SNPs in genome-wide association studies (GWAS). Chapter 14 and Chapter 15 provide state of the art methods for large scale simultaneous inference in these settings.
Peter H. Westfall,Randall D. Tobias,Russell D. Wolfinger
Author : Peter H. Westfall,Randall D. Tobias,Russell D. Wolfinger Publisher : SAS Institute Page : 645 pages File Size : 43,7 Mb Release : 2011 Category : Computers ISBN : 9781607648857
Multiple Comparisons and Multiple Tests Using SAS, Second Edition by Peter H. Westfall,Randall D. Tobias,Russell D. Wolfinger Pdf
New and extensively updated for SAS 9 and later, this work provides cutting-edge methods, specialized macros, and proven best bet procedures. The book also discusses the pitfalls and advantages of various methods, thereby helping readers to decide which is the most appropriate for their purposes. 644 pp. Pub. 7/11.
Multiple Comparisons for Bernoulli Data by Taka-aki Shiraishi Pdf
This book focuses on multiple comparisons of proportions in multi-sample models with Bernoulli responses. First, the author explains the one-sample and two-sample methods that form the basis of multiple comparisons. Then, regularity conditions are stated in detail. Simultaneous inference for all proportions based on exact confidence limits and based on asymptotic theory is discussed. Closed testing procedures based on some one-sample statistics are introduced. For all-pairwise multiple comparisons of proportions, the author uses arcsine square root transformation of sample means. Closed testing procedures based on maximum absolute values of some two-sample test statistics and based on chi-square test statistics are introduced. It is shown that the multi-step procedures are more powerful than single-step procedures and the Ryan–Einot–Gabriel–Welsch (REGW)-type tests. Furthermore, the author discusses multiple comparisons with a control. Under simple ordered restrictions of proportions, the author also discusses closed testing procedures based on maximum values of two-sample test statistics and based on Bartholomew's statistics. Last, serial gatekeeping procedures based on the above-mentioned closed testing procedures are proposed although Bonferroni inequalities are used in serial gatekeeping procedures of many.
Advances in Ranking and Selection, Multiple Comparisons, and Reliability by N. Balakrishnan,Nandini Kannan,H. N. Nagaraja Pdf
S. Panchapakesan has made significant contributions to ranking and selection and has published in many other areas of statistics, including order statistics, reliability theory, stochastic inequalities, and inference. Written in his honor, the twenty invited articles in this volume reflect recent advances in these areas and form a tribute to Panchapakesan’s influence and impact on these areas. Featuring theory, methods, applications, and extensive bibliographies with special emphasis on recent literature, this comprehensive reference work will serve researchers, practitioners, and graduate students in the statistical and applied mathematics communities.