Theory of Rank Tests


Book Description

The first edition of Theory of Rank Tests (1967) has been the precursor to a unified and theoretically motivated treatise of the basic theory of tests based on ranks of the sample observations. For more than 25 years, it helped raise a generation of statisticians in cultivating their theoretical research in this fertile area, as well as in using these tools in their application oriented research. The present edition not only aims to revive this classical text by updating the findings but also by incorporating several other important areas which were either not properly developed before 1965 or have gone through an evolutionary development during the past 30 years. This edition therefore aims to fulfill the needs of academic as well as professional statisticians who want to pursue nonparametrics in their academic projects, consultation, and applied research works. Asymptotic Methods Nonparametrics Convergence of Probability Measures Statistical Inference




Theory of Rank Tests


Book Description

Kniha shrnuje nejnovější, většinou ještě neuveřejněné poznatky z teorie statistických pořadových testů, z nichž některé jsou dílem autorů knihy. Podává ucelený systematický výklad a zdůrazňuje přitom studium optimality a.



















Contributions to the Theory of Rank Tests


Book Description

The purpose of this study is to investigate the asymptotic behaviour of certain (conditional) rank tests for comparative experiments proposed by Hodges and Lehmann (1962), and their extensions and variations. The results obtained in this thesis are extensions of the results of Mehra and Sarangi (1965) (where the case of complete designs was discussed) to the case of balanced and partially balanced incomplete block designs. The methods employed are based on certain properties of the U-statistics derived by Hoeffding (1948). In Chapter I, a brief resume of the relevant earlier work has been given and the test proposed by Hodges and Lehmann described. In Chapter II, a simplified large sample version of this test is discussed, which reduces its application to reading the critical value from the chi-square tables. In Chapter III, the asymptotic distribution of the test statistic, under a sequence of alternatives approaching the null hypothesis has been found to follow a non-central chi-square law. This helps us to study the power properties and the Pitman efficiency of the test statistics in Chapter IV. Explicit numerical evaluations of the expressions for asymptotic efficiency, which has been limited to the normal form of the parent distribution, indicates a rather high degree of efficiency of the test. Chapters IV and V contain several remarks that follow from the results of our investigation, including a useful lower bound for the asymptotic efficiency of the investigated test relative to the classical F-test. Further investigations that will throw more light on our present findings have been suggested at suitable places.




A Unified Approach to Constructing Nonparametric Rank Tests


Book Description

One shortcoming of the present theory of rank tests is that such stests have usually been constructed on a case by case basis, in a quite ad hoc (albeit clever) manner. This paper attempts to provide the basis for a more unified approach to rank tests. It investigates a general, yet simple construction, which simultaneously generates many rank test statistics, for a multitude of hypothesis testing situations. The proposed construction uses metrics on the permutation group in a novel way: the proposed test statistic is the distance between two sets of permutations. This new construction is applied systematically to the two-sample and multi-sample location problems, the two-way layout problem, the one-sample location problem, the two-sample dispersion problem with equal medians, and the problem of testing for trend. It is shown that the construction: works in a variety of testing situations; gives rise to many familiar rank test statistics; produces several other test statistics which are less familiar, yet equally plausible; and enables one to extend rank tests to other hypothesis testing situations. Some connections with the existing nonparametric theory are discussed.




Handbook for Clinical Research


Book Description

With over 80 information-packed chapters, Handbook for Clinical Research delivers the practical insights and expert tips necessary for successful research design, analysis, and implementation. Using clear language and an accessible bullet point format, the authors present the knowledge and expertise developed over time and traditionally shared from mentor to mentee and colleague to colleague. Organized for quick access to key topics and replete with practical examples, the book describes a variety of research designs and statistical methods and explains how to choose the best design for a particular project. Research implementation, including regulatory issues and grant writing, is also covered. The book opens with a section on the basics of research design, discussing the many ways in which studies can be organized, executed, and evaluated. The second section is devoted to statistics and explains how to choose the correct statistical approach and reviews the varieties of data types, descriptive and inferential statistics, methods for demonstrating associations, hypothesis testing and prediction, specialized methods, and considerations in epidemiological studies and measure construction. The third section covers implementation, including how to develop a grant application step by step, the project budget, and the nuts and bolts of the timely and successful completion of a research project and documentation of findings: procedural manuals and case report forms collecting, managing and securing data operational structure and ongoing monitoring and evaluation and ethical and regulatory concerns in research with human subjects. With a concise presentation of the essentials for successful research, the Handbook for Clinical Research is a valuable addition to the library of any student, research professional, or clinician interested in expanding the knowledge base of his or her field. Key Features: Delivers the essential elements, practical insights, and trade secrets for ensuring successful research design, analysis, and implementation Presents the nuts and bolts of statistical analysis Organized for quick access to a wealth of information Replete with practical examples of successful research designs Û from single case designs to meta-analysis - and how to achieve them Addresses research implementation including regulatory issues and grant writing "