A Primer Of Permutation Statistical Methods
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A Primer of Permutation Statistical Methods
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 for Criminology and Criminal Justice
This book takes a unique approach to explaining permutation statistical methods for advanced undergraduate students, graduate students, faculty, researchers, and other professionals interested in the areas of criminology or criminal justice. The book integrates permutation statistical methods with a wide range of classical statistical methods. It opens with a comparison of two models of statistical inference: the classical population model espoused by J. Neyman and E. 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 illustrated with examples from criminology and criminal justice and 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, 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 solely on the observed data, and do not require random sampling, making permutation statistical methods ideal for analyzing criminology and criminal justice databases. Permutation methods are relatively new in that it took modern computing power to make them available to those working in criminology and criminal justice research. The book contains detailed examples of permutation analyses. Each analysis is paired with a conventional analysis; for example, a permutation test of the difference between experimental and control groups is contrasted with Student's two-sample $t$ test. An added feature is the inclusion of multiple historical notes on the origin and development of both parametric and conventional tests and measures. Designed for an audience with a basic statistical background and a strong interest in parametric and non-parametric statistics, the book can easily serve as a textbook for undergraduate and graduate students in criminology, criminal justice, or sociology, as well as serving as a research source for faculty, researchers, and other professionals in the area of criminology. No statistical training beyond a first course in statistics is required, but some knowledge of, or interest in, criminology or criminal justice is assumed.
Permutation Statistical Methods with R
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.