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Estadística matemàtica --- R (Llenguatge de programació) --- Permutacions --- Àlgebra --- Anàlisi combinatòria --- Grups de permutacions --- GNU-S (Llenguatge de programació) --- Llenguatges de programació --- Estadística descriptiva --- Inferència estadística --- Matemàtica estadística --- Mètodes estadístics --- Estadística --- Anàlisi d'error (Matemàtica) --- Anàlisi de regressió --- Anàlisi de sèries temporals --- Anàlisi de variància --- Anàlisi multivariable --- Anàlisi seqüencial --- Astronomia estadística --- Correlació (Estadística) --- Dependència (Estadística) --- Estadística no paramètrica --- Estadística robusta --- Física estadística --- Mètode dels moments (Estadística) --- Models lineals (Estadística) --- Models no lineals (Estadística) --- Teoria de l'estimació --- Teoria de la predicció --- Tests d'hipòtesi (Estadística) --- Biometria --- Mostreig (Estadística) --- Mathematical statistics. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- R (Computer program language). --- GNU-S (Computer program language) --- Domain-specific programming languages

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Most commonly-used parametric and permutation statistical tests, such as the matched-pairs t test and analysis of variance, are based on non-metric squared distance functions that have very poor robustness characteristics. This second 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. In addition to permutation techniques described in the first edition, this second edition also contains various new permutation statistical methods and studies that include resampling multiple contingency table analyses, analysis concerns involving log-linear models with small samples, an exact discrete analog of Fisher’s continuous method for combining P-values that arise from small data sets, multiple dichotomous response analyses, problems regarding Fisher’s Z transformation for correlation analyses, and multivariate similarity comparisons between corresponding multiple categories of two samples. Paul W. Mielke, Jr. is Professor of Statistics at Colorado State University, and a fellow of the American Statistical Association. Kenneth J. Berry is Professor of Sociology at Colorado State University.

Statistical hypothesis testing. --- Resampling (Statistics) --- Resampling methods (Statistics) --- Nonparametric statistics --- Hypothesis testing (Statistics) --- Significance testing (Statistics) --- Statistical significance testing --- Testing statistical hypotheses --- Distribution (Probability theory) --- Hypothesis --- Mathematical statistics --- Distribution (Probability theory. --- Mathematical statistics. --- Biometrics. --- Data mining. --- Psychometrics. --- Probability Theory and Stochastic Processes. --- Statistical Theory and Methods. --- Data Mining and Knowledge Discovery. --- Public Health. --- Measurement, Mental --- Measurement, Psychological --- Psychological measurement --- Psychological scaling --- Psychological statistics --- Psychology --- Psychometry (Psychophysics) --- Scaling, Psychological --- Psychological tests --- Scaling (Social sciences) --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Algorithmic knowledge discovery --- Factual data analysis --- KDD (Information retrieval) --- Knowledge discovery in data --- Knowledge discovery in databases --- Mining, Data --- Database searching --- Distribution functions --- Frequency distribution --- Characteristic functions --- Measurement --- Scaling --- Methodology --- Statistical methods --- Probabilities. --- Statistics . --- Biometrics (Biology). --- Public health. --- Biological statistics --- Biology --- Biometrics (Biology) --- Biostatistics --- Biomathematics --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Community health --- Health services --- Hygiene, Public --- Hygiene, Social --- Public health services --- Public hygiene --- Social hygiene --- Health --- Human services --- Biosecurity --- Health literacy --- Medicine, Preventive --- National health services --- Sanitation --- Probability --- Combinations --- Chance --- Least squares --- Risk --- Statistical hypothesis testing

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Statistical science --- statistisch onderzoek

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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.

Resampling (Statistics) --- Statistical hypothesis testing. --- Hypothesis testing (Statistics) --- Significance testing (Statistics) --- Statistical significance testing --- Testing statistical hypotheses --- Distribution (Probability theory) --- Hypothesis --- Mathematical statistics --- Resampling methods (Statistics) --- Nonparametric statistics --- Statistics. --- Statistics, general. --- History of Mathematical Sciences. --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Statistics . --- Mathematics. --- History. --- Annals --- Auxiliary sciences of history --- Math --- Science

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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.

Mathematical statistics. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Statistical methods --- Statistics. --- Combinatorics. --- Statistical methods. --- Statistical Theory and Methods. --- Statistics and Computing/Statistics Programs. --- Statistics for Life Sciences, Medicine, Health Sciences. --- Biostatistics. --- Combinatorics --- Algebra --- Mathematical analysis --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Statistics . --- Biological statistics --- Biology --- Biometrics (Biology) --- Biostatistics --- Biomathematics