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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. This research monograph addresses a statistically-informed audience, and can also easily serve as a textbook in a graduate course in departments such as statistics, psychology, or biology. In particular, the audience for the book is teachers of statistics, practicing statisticians, applied statisticians, and quantitative graduate students in fields such as psychology, medical research, epidemiology, public health, and biology.

Statistics. --- History. --- Statistical Theory and Methods. --- Statistics for Life Sciences, Medicine, Health Sciences. --- History of Science. --- Mathematical statistics. --- Permutations. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistical methods --- Algebra --- Combinatorial analysis --- Statistics --- Probabilities --- Sampling (Statistics) --- Annals --- Auxiliary sciences of history --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Statistics .

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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.

Mathematical statistics. --- Statistics. --- Statistical methods. --- Combinatorics. --- Statistical Theory and Methods. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Biostatistics. --- History of Mathematical Sciences. --- Combinatorics --- Algebra --- Mathematical analysis --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistics . --- Mathematics. --- History. --- Annals --- Auxiliary sciences of history --- Math --- Science --- Biological statistics --- Biology --- Biometrics (Biology) --- Biostatistics --- Biomathematics

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This research monograph utilizes exact and Monte Carlo permutation statistical methods to generate probability values and measures of effect size for a variety of measures of association. Association is broadly defined to include measures of correlation for two interval-level variables, measures of association for two nominal-level variables or two ordinal-level variables, and measures of agreement for two nominal-level or two ordinal-level variables. Additionally, measures of association for mixtures of the three levels of measurement are considered: nominal-ordinal, nominal-interval, and ordinal-interval measures. Numerous comparisons of permutation and classical statistical methods are presented. Unlike classical statistical methods, permutation 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 book 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. This topic is relatively new in that it took modern computing power to make permutation methods available to those working in mainstream research. Written for a statistically informed audience, it is particularly useful for teachers of statistics, practicing statisticians, applied statisticians, and quantitative graduate students in fields such as psychology, medical research, epidemiology, public health, and biology. It can also serve as a textbook in graduate courses in subjects like statistics, psychology, and biology.

Statistical science --- Discrete mathematics --- Mathematical statistics --- Biomathematics. Biometry. Biostatistics --- Computer. Automation --- cyclohexanon --- medische statistiek --- discrete wiskunde --- biostatistiek --- informatica --- statistiek --- biometrie --- statistisch onderzoek --- Statistics. --- Combinatorial analysis. --- Biometry. --- Statistical Theory and Methods. --- Statistics and Computing/Statistics Programs. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Combinatorics. --- Biostatistics.