A Primer of Permutation Statistical Methods


Book Description

The primary purpose of this textbook is to introduce the reader to a wide variety of elementary permutation statistical methods. Permutation methods are optimal for small data sets and non-random samples, and are free of distributional assumptions. The book follows the conventional structure of most introductory books on statistical methods, and features chapters on central tendency and variability, one-sample tests, two-sample tests, matched-pairs tests, one-way fully-randomized analysis of variance, one-way randomized-blocks analysis of variance, simple regression and correlation, and the analysis of contingency tables. In addition, it introduces and describes a comparatively new permutation-based, chance-corrected measure of effect size. Because permutation tests and measures are distribution-free, do not assume normality, and do not rely on squared deviations among sample values, they are currently being applied in a wide variety of disciplines. This book presents permutation alternatives to existing classical statistics, and is intended as a textbook for undergraduate statistics courses or graduate courses in the natural, social, and physical sciences, while assuming only an elementary grasp of statistics.




Permutation Statistical Methods


Book Description

This research monograph provides a synthesis of a number of statistical tests and measures, which, at first consideration, appear disjoint and unrelated. Numerous comparisons of permutation and classical statistical methods are presented, and the two methods are compared via probability values and, where appropriate, measures of effect size. Permutation statistical methods, compared to classical statistical methods, do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity of variance, and depend only on the data at hand. This text takes a unique approach to explaining statistics by integrating a large variety of statistical methods, and establishing the rigor of a topic that to many may seem to be a nascent field in statistics. This topic is new in that it took modern computing power to make permutation methods available to people working in the mainstream of research. lly-informed="" audience,="" and="" can="" also="" easily="" serve="" as="" textbook="" in="" graduate="" course="" departments="" such="" statistics,="" psychology,="" or="" biology.="" particular,="" the="" audience="" for="" book="" is="" teachers="" of="" practicing="" statisticians,="" applied="" quantitative="" students="" fields="" medical="" research,="" epidemiology,="" public="" health,="" biology.




Permutation Statistical Methods with R


Book Description

This book takes a unique approach to explaining permutation statistics by integrating permutation statistical methods with a wide range of classical statistical methods and associated R programs. It opens by comparing and contrasting two models of statistical inference: the classical population model espoused by J. Neyman and E.S. Pearson and the permutation model first introduced by R.A. Fisher and E.J.G. Pitman. Numerous comparisons of permutation and classical statistical methods are presented, supplemented with a variety of R scripts for ease of computation. The text follows the general outline of an introductory textbook in statistics with chapters on central tendency and variability, one-sample tests, two-sample tests, matched-pairs tests, completely-randomized analysis of variance, randomized-blocks analysis of variance, simple linear regression and correlation, and the analysis of goodness of fit and contingency. Unlike classical statistical methods, permutation statistical methods do not rely on theoretical distributions, avoid the usual assumptions of normality and homogeneity, depend only on the observed data, and do not require random sampling. The methods are relatively new in that it took modern computing power to make them available to those working in mainstream research. Designed for an audience with a limited statistical background, the book can easily serve as a textbook for undergraduate or graduate courses in statistics, psychology, economics, political science or biology. No statistical training beyond a first course in statistics is required, but some knowledge of, or some interest in, the R programming language is assumed.




Statistical Methods: Connections, Equivalencies, and Relationships


Book Description

The primary purpose of this book is to introduce the reader to a wide variety of interesting and useful connections, relationships, and equivalencies between and among conventional and permutation statistical methods. There are approximately 320 statistical connections and relationships described in this book. For each connection or connections the tests are described, the connection is explained, and an example analysis illustrates both the tests and the connection(s). The emphasis is more on demonstrations than on proofs, so little mathematical expertise is assumed. While the book is intended as a stand-alone monograph, it can also be used as a supplement to a standard textbook such as might be used in a second- or third-term course in conventional statistical methods. Students, faculty, and researchers in the social, natural, or hard sciences will find an interesting collection of statistical connections and relationships - some well-known, some more obscure, and some presented here for the first time.




Permutation Methods


Book Description

This is the second edition of the comprehensive treatment of statistical inference using permutation techniques. It makes available to practitioners a variety of useful and powerful data analytic tools that rely on very few distributional assumptions. Although many of these procedures have appeared in journal articles, they are not readily available to practitioners. This new and updated edition places increased emphasis on the use of alternative permutation statistical tests based on metric Euclidean distance functions that have excellent robustness characteristics. These alternative permutation techniques provide many powerful multivariate tests including multivariate multiple regression analyses.




Information Processing in Medical Imaging


Book Description

This book constitutes the refeered proceedings of the 18th Interational Conference on Information Processing in Medical Imaging, IPMI 2003, held in UK, in July 2003. The 57 revised full papers presented were carefully reviewed and selected from submissions. The papers are organized in topical sections shape modeling, shape analysis, segmentation, color, performance characterization, registration and modeling similarity, registration and modeling deformation, cardiac motion, fMRI analysis, and diffusion imaging and tractography.




A Chronicle of Permutation Statistical Methods


Book Description

The focus of this book is on the birth and historical development of permutation statistical methods from the early 1920s to the near present. Beginning with the seminal contributions of R.A. Fisher, E.J.G. Pitman, and others in the 1920s and 1930s, permutation statistical methods were initially introduced to validate the assumptions of classical statistical methods. Permutation methods have advantages over classical methods in that they are optimal for small data sets and non-random samples, are data-dependent, and are free of distributional assumptions. Permutation probability values may be exact, or estimated via moment- or resampling-approximation procedures. Because permutation methods are inherently computationally-intensive, the evolution of computers and computing technology that made modern permutation methods possible accompanies the historical narrative. Permutation analogs of many well-known statistical tests are presented in a historical context, including multiple correlation and regression, analysis of variance, contingency table analysis, and measures of association and agreement. A non-mathematical approach makes the text accessible to readers of all levels.




The Evolution of Begging


Book Description

Begging by nestling birds has become the model system for investigating evolutionary conflicts of interest within families and their theoretical resolution provided by honest signals of offspring need. In response to the recent explosions of scientific papers on the revolution of begging; we have brought together twenty-four original contributions from major researchers in all areas of this dynamic field. Organised into six sections: I: Theoretical approaches; II: Begging as a signal; III: Nestling physiology; IV: Sibling competition; V: Brood parasitism; and VI: Statistical approaches; this book is primarily aimed at research scientists and those at the graduate student level. For the first time, the theoretical and empirical literature on begging is fully reviewed. New ideas and data are also presented from a wide range of natural systems, and each chapter ends with suggestions for future study.




Data Science and Machine Learning


Book Description

Focuses on mathematical understanding Presentation is self-contained, accessible, and comprehensive Full color throughout Extensive list of exercises and worked-out examples Many concrete algorithms with actual code




Analyzing the Large Number of Variables in Biomedical and Satellite Imagery


Book Description

This book grew out of an online interactive offered through statcourse.com, and it soon became apparent to the author that the course was too limited in terms of time and length in light of the broad backgrounds of the enrolled students. The statisticians who took the course needed to be brought up to speed both on the biological context as well as on the specialized statistical methods needed to handle large arrays. Biologists and physicians, even though fully knowledgeable concerning the procedures used to generate microaarrays, EEGs, or MRIs, needed a full introduction to the resampling methods—the bootstrap, decision trees, and permutation tests, before the specialized methods applicable to large arrays could be introduced. As the intended audience for this book consists both of statisticians and of medical and biological research workers as well as all those research workers who make use of satellite imagery including agronomists and meteorologists, the book provides a step-by-step approach to not only the specialized methods needed to analyze the data from microarrays and images, but also to the resampling methods, step-down multi-comparison procedures, multivariate analysis, as well as data collection and pre-processing. While many alternate techniques for analysis have been introduced in the past decade, the author has selected only those techniques for which software is available along with a list of the available links from which the software may be purchased or downloaded without charge. Topical coverage includes: very large arrays; permutation tests; applying permutation tests; gathering and preparing data for analysis; multiple tests; bootstrap; applying the bootstrap; classification methods; decision trees; and applying decision trees.