Tables of the Ordinates and Probability Integral of the Distribution of the Correlation Coefficient in Small Samples PDF Download

Author: F. N. David
Publisher: Cambridge University Press
ISBN: 0521071690
Category : Mathematics
Languages : en
Pages : 114

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An examination of the theory of correlation and correlation tables.

Author: Erik Grafarend
Publisher: Springer Science & Business Media
ISBN: 3642222412
Category : Science
Languages : en
Pages : 1026

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Book Description
Here we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view as well as a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss-Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters we concentrate on underdetermined and overdeterimined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE and Total Least Squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann-Pluecker coordinates, criterion matrices of type Taylor-Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overdetermined system of nonlinear equations on curved manifolds. The von Mises-Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter eight is devoted to probabilistic regression, the special Gauss-Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four Appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger Algorithm, especially the C. F. Gauss combinatorial algorithm.

Author: Erik W. Grafarend
Publisher: Springer Nature
ISBN: 3030945987
Category : Science
Languages : en
Pages : 1127

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Book Description
This book provides numerous examples of linear and nonlinear model applications. Here, we present a nearly complete treatment of the Grand Universe of linear and weakly nonlinear regression models within the first 8 chapters. Our point of view is both an algebraic view and a stochastic one. For example, there is an equivalent lemma between a best, linear uniformly unbiased estimation (BLUUE) in a Gauss–Markov model and a least squares solution (LESS) in a system of linear equations. While BLUUE is a stochastic regression model, LESS is an algebraic solution. In the first six chapters, we concentrate on underdetermined and overdetermined linear systems as well as systems with a datum defect. We review estimators/algebraic solutions of type MINOLESS, BLIMBE, BLUMBE, BLUUE, BIQUE, BLE, BIQUE, and total least squares. The highlight is the simultaneous determination of the first moment and the second central moment of a probability distribution in an inhomogeneous multilinear estimation by the so-called E-D correspondence as well as its Bayes design. In addition, we discuss continuous networks versus discrete networks, use of Grassmann–Plucker coordinates, criterion matrices of type Taylor–Karman as well as FUZZY sets. Chapter seven is a speciality in the treatment of an overjet. This second edition adds three new chapters: (1) Chapter on integer least squares that covers (i) model for positioning as a mixed integer linear model which includes integer parameters. (ii) The general integer least squares problem is formulated, and the optimality of the least squares solution is shown. (iii) The relation to the closest vector problem is considered, and the notion of reduced lattice basis is introduced. (iv) The famous LLL algorithm for generating a Lovasz reduced basis is explained. (2) Bayes methods that covers (i) general principle of Bayesian modeling. Explain the notion of prior distribution and posterior distribution. Choose the pragmatic approach for exploring the advantages of iterative Bayesian calculations and hierarchical modeling. (ii) Present the Bayes methods for linear models with normal distributed errors, including noninformative priors, conjugate priors, normal gamma distributions and (iii) short outview to modern application of Bayesian modeling. Useful in case of nonlinear models or linear models with no normal distribution: Monte Carlo (MC), Markov chain Monte Carlo (MCMC), approximative Bayesian computation (ABC) methods. (3) Error-in-variables models, which cover: (i) Introduce the error-in-variables (EIV) model, discuss the difference to least squares estimators (LSE), (ii) calculate the total least squares (TLS) estimator. Summarize the properties of TLS, (iii) explain the idea of simulation extrapolation (SIMEX) estimators, (iv) introduce the symmetrized SIMEX (SYMEX) estimator and its relation to TLS, and (v) short outview to nonlinear EIV models. The chapter on algebraic solution of nonlinear system of equations has also been updated in line with the new emerging field of hybrid numeric-symbolic solutions to systems of nonlinear equations, ermined system of nonlinear equations on curved manifolds. The von Mises–Fisher distribution is characteristic for circular or (hyper) spherical data. Our last chapter is devoted to probabilistic regression, the special Gauss–Markov model with random effects leading to estimators of type BLIP and VIP including Bayesian estimation. A great part of the work is presented in four appendices. Appendix A is a treatment, of tensor algebra, namely linear algebra, matrix algebra, and multilinear algebra. Appendix B is devoted to sampling distributions and their use in terms of confidence intervals and confidence regions. Appendix C reviews the elementary notions of statistics, namely random events and stochastic processes. Appendix D introduces the basics of Groebner basis algebra, its careful definition, the Buchberger algorithm, especially the C. F. Gauss combinatorial algorithm.

Author: Florence Nightingale David
Publisher:
ISBN:
Category :
Languages : en
Pages : 55

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Author: D. V. Lindley
Publisher: Cambridge University Press
ISBN: 1107469457
Category : Mathematics
Languages : en
Pages : 100

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Book Description
The second edition of this very successful and authoritative set of tables still benefits from clear typesetting, which makes the figures easy to read and use. It has, however, been improved by the addition of new tables that provide Bayesian confidence limits for the binomial and Poisson distributions, and for the square of the multiple correlation coefficient, which have not been previously available. The intervals are the shortest possible, consistent with the requirement on probability. Great care has been taken to ensure that it is clear just what is being tabulated and how the values may be used; the tables are generally capable of easy interpolation. The book contains all the tables likely to be required for elementary statistical methods in the social, business and natural sciences. It will be an essential aid for teachers, researchers and students in those subjects where statistical analysis is not wholly carried out by computers.

Author: Y.L. Tong
Publisher: Springer Science & Business Media
ISBN: 1461396557
Category : Business & Economics
Languages : en
Pages : 281

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Book Description
The multivariate normal distribution has played a predominant role in the historical development of statistical theory, and has made its appearance in various areas of applications. Although many of the results concerning the multivariate normal distribution are classical, there are important new results which have been reported recently in the literature but cannot be found in most books on multivariate analysis. These results are often obtained by showing that the multivariate normal density function belongs to certain large families of density functions. Thus, useful properties of such families immedi ately hold for the multivariate normal distribution. This book attempts to provide a comprehensive and coherent treatment of the classical and new results related to the multivariate normal distribution. The material is organized in a unified modern approach, and the main themes are dependence, probability inequalities, and their roles in theory and applica tions. Some general properties of a multivariate normal density function are discussed, and results that follow from these properties are reviewed exten sively. The coverage is, to some extent, a matter of taste and is not intended to be exhaustive, thus more attention is focused on a systematic presentation of results rather than on a complete listing of them.

Author: Jerzy Neyman
Publisher: Univ of California Press
ISBN:
Category : Mathematical statistics
Languages : en
Pages : 784

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Author: Hoben Thomas
Publisher: Springer Science & Business Media
ISBN: 1468463667
Category : Social Science
Languages : en
Pages : 102

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Book Description
An important problem in personnel psychology, namely, the psychometric problem known as "validity generalization" is addressed in this volume. From a statistical point of view, the problem is how to make statements about a population correlation coefficient based on inferences from a collection of sample correlation coefficients. The first part of the book examines the largely ad hoc procedures which have been used to determine validity generalization. The second part develops a new model formulated from the perspective of finite mixture theory and, in addition, illustrates its use in several applications.

Author: Lothar Sachs
Publisher: Springer Science & Business Media
ISBN: 1461252466
Category : Mathematics
Languages : en
Pages : 737

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Book Description
This outline of statistics as an aid in decision making will introduce a reader with limited mathematical background to the most important modern statistical methods. This is a revised and enlarged version, with major extensions and additions, of my "Angewandte Statistik" (5th ed.), which has proved useful for research workers and for consulting statisticians. Applied statistics is at the same time a collection of applicable statistical methods and the application of these methods to measured and/or counted observations. Abstract mathematical concepts and derivations are avoided. Special emphasis is placed on the basic principles of statistical formulation, and on the explanation of the conditions under which a certain formula or a certain test is valid. Preference is given to consideration of the analysis of small sized samples and of distribution-free methods. As a text and reference this book is written for non-mathematicians, in particular for technicians, engineers, executives, students, physicians as well as researchers in other disciplines. It gives any mathematician interested in the practical uses of statistics a general account of the subject. Practical application is the main theme; thus an essential part of the book consists in the 440 fully worked-out numerical examples, some of which are very simple; the 57 exercises with solutions; a number of different compu tational aids; and an extensive bibliography and a very detailed index. In particular, a collection of 232 mathematical and mathematical-statistical tables serves to enable and to simplify the computations.

Author: Jacob Cohen
Publisher: Academic Press
ISBN: 1483276481
Category : Social Science
Languages : en
Pages : 459

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Book Description
Statistical Power Analysis for the Behavioral Sciences, Revised Edition emphasizes the importance of statistical power analysis. This edition discusses the concepts and types of power analysis, t test for means, significance of a product moment rs, and differences between correlation coefficients. The test that a proportion is .50 and sign test, differences between proportions, and chi-square tests for goodness of fit and contingency tables are also elaborated. This text likewise covers the F tests of variance proportions in multiple regression/correlation analysis and computational procedures. This publication is intended for behavioral and biosocial scientists who use statistical inference, but also serves as a supplementary textbook for intermediate level courses in applied statistics in behavioral/biosocial science.