A Multiple-Testing Approach to the Multivariate Behrens-Fisher Problem


Book Description

​​ ​ In statistics, the Behrens–Fisher problem is the problem of interval estimation and hypothesis testing concerning the difference between the means of two normally distributed populations when the variances of the two populations are not assumed to be equal, based on two independent samples. In his 1935 paper, Fisher outlined an approach to the Behrens-Fisher problem. Since high-speed computers were not available in Fisher’s time, this approach was not implementable and was soon forgotten. Fortunately, now that high-speed computers are available, this approach can easily be implemented using just a desktop or a laptop computer. Furthermore, Fisher’s approach was proposed for univariate samples. But this approach can also be generalized to the multivariate case. In this monograph, we present the solution to the afore-mentioned multivariate generalization of the Behrens-Fisher problem. We start out by presenting a test of multivariate normality, proceed to test(s) of equality of covariance matrices, and end with our solution to the multivariate Behrens-Fisher problem. All methods proposed in this monograph will be include both the randomly-incomplete-data case as well as the complete-data case. Moreover, all methods considered in this monograph will be tested using both simulations and examples. ​




Applied Multivariate Statistical Analysis in Medicine


Book Description

Applied Multivariate Statistical Analysis in Medicine provides a multivariate conceptual framework that allows readers to understand the interconnectivity and interrelations among variables, which maintains the intrinsic precision of statistical theories. With a strong focus on the fundamental concepts of multivariate statistical analysis, the book also gives insight into the applications of multivariate distribution in biomedical fields. In 14 chapters, Applied Multivariate Statistical Analysis in Medicine covers the main topics of multivariate analysis methods widely used in health science research. The content is organized progressively from fundamental concepts to sophisticated methods. It begins with basic descriptive statistics in multivariate analysis and follows with parameter estimation, in addition to the hypothesis testing of a multivariate normal distribution, which has heavy applications in biomedical fields where the relationships among approximately normal variables are of great interest. Keeping mathematics to a minimum, considerable emphasis is placed on explanations and real-world applications of core principles to maintain a good balance between introducing theory and cultivating problem-solving skills. This book is a very valuable reference text for clinicians, medical researchers, and other researchers across medical and biomedical disciplines, all of whom confront increasingly complex statistical methods during the analysis and presentation of their results. Gives understanding and mastering of the multivariate analysis techniques in the medical sciences Maintains a balance between the introduction of statistical analysis theory and the cultivation of practical skills Exposes a variety of well-designed real-life cases that integrate concepts and analytical techniques Includes substantive exercises, online coding sources, and case discussions to solidify a conceptual understanding




Permutation Tests for Complex Data


Book Description

Complex multivariate testing problems are frequently encountered in many scientific disciplines, such as engineering, medicine and the social sciences. As a result, modern statistics needs permutation testing for complex data with low sample size and many variables, especially in observational studies. The Authors give a general overview on permutation tests with a focus on recent theoretical advances within univariate and multivariate complex permutation testing problems, this book brings the reader completely up to date with today’s current thinking. Key Features: Examines the most up-to-date methodologies of univariate and multivariate permutation testing. Includes extensive software codes in MATLAB, R and SAS, featuring worked examples, and uses real case studies from both experimental and observational studies. Includes a standalone free software NPC Test Release 10 with a graphical interface which allows practitioners from every scientific field to easily implement almost all complex testing procedures included in the book. Presents and discusses solutions to the most important and frequently encountered real problems in multivariate analyses. A supplementary website containing all of the data sets examined in the book along with ready to use software codes. Together with a wide set of application cases, the Authors present a thorough theory of permutation testing both with formal description and proofs, and analysing real case studies. Practitioners and researchers, working in different scientific fields such as engineering, biostatistics, psychology or medicine will benefit from this book.




An Author and Permuted Title Index to Selected Statistical Journals


Book Description

All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.




Statistics in Industry


Book Description

This volume presents an exposition of topics in industrial statistics. It serves as a reference for researchers in industrial statistics/industrial engineering and a source of information for practicing statisticians/industrial engineers. A variety of topics in the areas of industrial process monitoring, industrial experimentation, industrial modelling and data analysis are covered and are authored by leading researchers or practitioners in the particular specialized topic. Targeting the audiences of researchers in academia as well as practitioners and consultants in industry, the book provides comprehensive accounts of the relevant topics. In addition, whenever applicable ample data analytic illustrations are provided with the help of real world data.




Statistical Hypothesis Testing in Context


Book Description

This coherent guide equips applied statisticians to make good choices and proper interpretations in real investigations facing real data.




Applying Contemporary Statistical Techniques


Book Description

Applying Contemporary Statistical Techniques explains why traditional statistical methods are often inadequate or outdated when applied to modern problems. Wilcox demonstrates how new and more powerful techniques address these problems far more effectively, making these modern robust methods understandable, practical, and easily accessible.* Assumes no previous training in statistics * Explains how and why modern statistical methods provide more accurate results than conventional methods* Covers the latest developments on multiple comparisons * Includes recent advances in risk-based methods * Features many illustrations and examples using data from real studies * Describes and illustrates easy-to-use s-plus functions for applying cutting-edge techniques * Covers many contemporary ANOVA (analysis of variance) and regression methods not found in other books




College of Engineering


Book Description




University of Michigan Official Publication


Book Description

Each number is the catalogue of a specific school or college of the University.




Quantitative Methods for Traditional Chinese Medicine Development


Book Description

In recent years, many pharmaceutical companies and clinical research organizations have been focusing on the development of traditional Chinese (herbal) medicines (TCMs) as alternatives to treating critical or life-threatening diseases and as pathways to personalized medicine. Quantitative Methods for Traditional Chinese Medicine Development is the first book entirely devoted to the design and analysis of TCM development from a Western perspective, i.e., evidence-based clinical research and development. The book provides not only a comprehensive summary of innovative quantitative methods for developing TCMs but also a useful desk reference for principal investigators involved in personalized medicine. Written by one of the world's most prominent biostatistics researchers, the book connects the pharmaceutical industry, regulatory agencies, and academia. It presents a state-of-the-art examination of the subject for: Scientists and researchers who are engaged in pharmaceutical/clinical research and development of TCMs Those in regulatory agencies who make decisions in the review and approval process of TCM regulatory submissions Biostatisticians who provide statistical support to assess clinical safety and effectiveness of TCMs and related issues regarding quality control and assurance as well as to test for consistency in the manufacturing processes for TCMs This book covers all of the statistical issues encountered at various stages of pharmaceutical/clinical development of a TCM. It explains regulatory requirements; product specifications and standards; and various statistical techniques for evaluation of TCMs, validation of diagnostic procedures, and testing consistency