Author: Peter H. Westfall
Publisher: John Wiley & Sons
ISBN: 9780471557616
Category : Mathematics
Languages : en
Pages : 382
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Book Description
Combines recent developments in resampling technology (including the bootstrap) with new methods for multiple testing that are easy to use, convenient to report and widely applicable. Software from SAS Institute is available to execute many of the methods and programming is straightforward for other applications. Explains how to summarize results using adjusted p-values which do not necessitate cumbersome table look-ups. Demonstrates how to incorporate logical constraints among hypotheses, further improving power.
Author: Sandrine Dudoit
Publisher: Springer Science & Business Media
ISBN: 0387493174
Category : Science
Languages : en
Pages : 590
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Book Description
This book establishes the theoretical foundations of a general methodology for multiple hypothesis testing and discusses its software implementation in R and SAS. These are applied to a range of problems in biomedical and genomic research, including identification of differentially expressed and co-expressed genes in high-throughput gene expression experiments; tests of association between gene expression measures and biological annotation metadata; sequence analysis; and genetic mapping of complex traits using single nucleotide polymorphisms. The procedures are based on a test statistics joint null distribution and provide Type I error control in testing problems involving general data generating distributions, null hypotheses, and test statistics.
Author: Yifan Huang
Publisher:
ISBN:
Category : Bootstrap (Statistics)
Languages : en
Pages :
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Book Description
Abstract: Multiple hypotheses testing is a common problem in practice. For instance, in microarray experiments, whether the goal is to select maintenance genes for normalization or to identify differentially expressed genes between samples, multiple genes are under consideration. Multiplicity inflates the type I error rate of the hypothesis testing, so we need to adjust the testing procedure to control the overly error rate. My research focuses on the strong control of Familywise Error Rate (FWER). There are mainly two different types of approaches to multiple testing. One is modelling based approach and the other non-modelling based. Modelling based approaches fit models to the data so that the joint distribution of the test statistics is tractable. Non-modelling based approaches consist of inequality based methods and resampling based methods. They require less or no information about the joint distribution of the test statistics. I have shown in Chapter 1 that frequently used Hochberg's step-up method is a special case of partition testing based on Simes' test. This is a new result. Hochberg's step-up method is an inequity based non-modelling partition testing. Modelling based partition testing is applicable whether the joint distribution of the test statistics is known or not. By applying modelling based partition testing when the joint distribution of test statistics is known, I illustrate that modelling based approaches are often more powerful than inequality based non-modelling approaches. In Chapter 2, I construct counterexamples to the validity of permutation test, demonstrating that the resampling based methods are often invalid. My results suggest recommendation of modelling based approaches. When the joint distribution of the test statistics is untractable, modelling followed by bootstrap can be applied. I use modelling followed by bootstrap in Chapter 3 to select maintenance genes for normalizing the gene expression data.
Author: Alex Dmitrienko
Publisher: CRC Press
ISBN: 1584889853
Category : Mathematics
Languages : en
Pages : 323
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Book Description
Useful Statistical Approaches for Addressing Multiplicity IssuesIncludes practical examples from recent trials Bringing together leading statisticians, scientists, and clinicians from the pharmaceutical industry, academia, and regulatory agencies, Multiple Testing Problems in Pharmaceutical Statistics explores the rapidly growing area of multiple c
Author: Frank Bretz
Publisher: CRC Press
ISBN: 9781420010909
Category : Mathematics
Languages : en
Pages : 205
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Book Description
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.
Author: Robert Gentleman
Publisher: Springer Science & Business Media
ISBN: 0387293620
Category : Computers
Languages : en
Pages : 478
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Book Description
Full four-color book. Some of the editors created the Bioconductor project and Robert Gentleman is one of the two originators of R. All methods are illustrated with publicly available data, and a major section of the book is devoted to fully worked case studies. Code underlying all of the computations that are shown is made available on a companion website, and readers can reproduce every number, figure, and table on their own computers.
Author: Michael Wolf
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
It is common in econometric applications that several hypothesis tests are carried out at the same time. The problem then becomes how to decide which hypotheses to reject, accounting for the multitude of tests. In this paper, we suggest a stepwise multiple testing procedure which asymptotically controls the familywise error rate at a desired level. Compared to related single-step methods, our procedure is more powerful in the sense that it often will reject more false hypotheses. Unlike some stepwise methods, our method implicitly captures the joint dependence structure of the test statistics, which results in increased ability to detect alternative hypotheses. We prove our method asymptotically controls the familywise error rate under minimal assumptions. Some simulation studies show the improvements of our methods over previous proposals. We also provide an application to a set of real data.
Author: Peter C. Bruce
Publisher: John Wiley & Sons
ISBN: 1118881338
Category : Mathematics
Languages : en
Pages : 320
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Book Description
Concise, thoroughly class-tested primer that features basic statistical concepts in the concepts in the context of analytics, resampling, and the bootstrap A uniquely developed presentation of key statistical topics, Introductory Statistics and Analytics: A Resampling Perspective provides an accessible approach to statistical analytics, resampling, and the bootstrap for readers with various levels of exposure to basic probability and statistics. Originally class-tested at one of the first online learning companies in the discipline, www.statistics.com, the book primarily focuses on applications of statistical concepts developed via resampling, with a background discussion of mathematical theory. This feature stresses statistical literacy and understanding, which demonstrates the fundamental basis for statistical inference and demystifies traditional formulas. The book begins with illustrations that have the essential statistical topics interwoven throughout before moving on to demonstrate the proper design of studies. Meeting all of the Guidelines for Assessment and Instruction in Statistics Education (GAISE) requirements for an introductory statistics course, Introductory Statistics and Analytics: A Resampling Perspective also includes: Over 300 “Try It Yourself” exercises and intermittent practice questions, which challenge readers at multiple levels to investigate and explore key statistical concepts Numerous interactive links designed to provide solutions to exercises and further information on crucial concepts Linkages that connect statistics to the rapidly growing field of data science Multiple discussions of various software systems, such as Microsoft Office Excel®, StatCrunch, and R, to develop and analyze data Areas of concern and/or contrasting points-of-view indicated through the use of “Caution” icons Introductory Statistics and Analytics: A Resampling Perspective is an excellent primary textbook for courses in preliminary statistics as well as a supplement for courses in upper-level statistics and related fields, such as biostatistics and econometrics. The book is also a general reference for readers interested in revisiting the value of statistics.
Author: Phillip Good
Publisher: Springer Science & Business Media
ISBN: 147573235X
Category : Mathematics
Languages : en
Pages : 288
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Book Description
A step-by-step manual on the application of permutation tests in biology, business, medicine, science, and engineering. Its intuitive and informal style make it ideal for students and researchers, whether experienced or coming to these resampling methods for the first time. The real-world problems of missing and censored data, multiple comparisons, nonresponders, after-the-fact covariates, and outliers are all dealt with at length. This new edition has more than 100 additional pages, and includes streamlined statistics for the k-sample comparison and analysis of variance plus expanded sections on computational techniques, multiple comparisons, multiple regression, comparing variances, and testing interactions in balanced designs. The comprehensive author and subject indexes, plus an expert-system guide to methods, provide for further ease of use, while the exercises at the end of every chapter have been supplemented with drills and a number of graduate-level thesis problems.
Author: Phillip Good
Publisher: Springer Science & Business Media
ISBN: 1475723466
Category : Mathematics
Languages : en
Pages : 238
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Book Description
A step-by-step guide to the application of permutation tests in biology, medicine, science, and engineering. The intuitive and informal style makes this manual ideally suitable for students and researchers approaching these methods for the first time. In particular, it shows how to handle the problems of missing and censored data, nonresponders, after-the-fact covariates, and outliers.
