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A Monte Carlo Study On The Robustness Of The Two Sample T Test For Discrete Dependent Distributions
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Book Synopsis A Monte Carlo Study on the Robustness of the Two-sample T-test for Discrete Dependent Distributions by : Margaret Elma Wilkinson
Download or read book A Monte Carlo Study on the Robustness of the Two-sample T-test for Discrete Dependent Distributions written by Margaret Elma Wilkinson and published by . This book was released on 1976 with total page 70 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Monte Carlo Study of the Properties of Selected Tests Based on Sample Spacings by : Kweku Ewusi-Mensah
Download or read book A Monte Carlo Study of the Properties of Selected Tests Based on Sample Spacings written by Kweku Ewusi-Mensah and published by . This book was released on 1972 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let X[subscript 1], X[subscript 2] ... X[subscript n] be n independent random variables each distributed uniformly over the interval (0,1) and let D[subscript 1], D[subscript 2] ... D[subscript n+1] respective spacings of the (n+1) intervals into which the unit interval is divided. There exists a class of statistical problems related to finding the distribution of certain functions of the D[subscript i]. A review of these statistical tests is given in Chapter II. In deriving the properties of the statistics, it is usually assumed that, because the underlying distribution of D[subscript i] is continuous, the problem of tied observations does not arise. However this is a problem the statistician has to face in actual data situations. We have, in this study evaluated the sensitivity of the test statistics to ties and grouping errors. We have also considered how robust the statistics are by evalua- ting their sensitivity under the X[2 over 2] normal (0,1) distributions. The result of this test for robustness will give the applied statistician a valid basis for using the statistics in tests of hypothesis other than those involving the uniform (0,1) distribution. For completeness we have also looked at ties and grouping errors under discrete distributions. In this case the sensitivity of the statistics to the different tie breaking rules is found to depend quite heavily on the number of ties occurring in the data. The Monte Carlo method was used in attacking the problem and results are given in Chapters IV and V.
Book Synopsis Abstracts of Theses for Masters' Degrees and Titles of Doctoral Dissertations by : Vanderbilt University
Download or read book Abstracts of Theses for Masters' Degrees and Titles of Doctoral Dissertations written by Vanderbilt University and published by . This book was released on 1973 with total page 800 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Robustness of Statistical Methods and Nonparametric Statistics by : Dieter Rasch
Download or read book Robustness of Statistical Methods and Nonparametric Statistics written by Dieter Rasch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains most of the invited and contributed papers presented at the Conference on Robustness of Statistical Methods and Nonparametric Statistics held in the castle oj'Schwerin, Mai 29 - June 4 1983. This conference was organized by the Mathematical Society of the GDR in cooperation with the Society of Physical and Mathematical Biology of the GDR, the GDR-Region of the International Biometric Society and the Academy of Agricultural Sciences of the GDR. All papers included were thoroughly reviewed by scientist listed under the heading "Editorial Collabora tories·'. Some contributions, we are sorry to report, were not recommended for publi cation by the rf'vif'wers and do not appear in these proceedings. The editors thank the reviewers for their valuable comments and suggestions. The conference was organizf'd bv a Programme Committee, its chairman was Prof. Dr. Dieter Rasch (Research Centre of Animal Production, Dummerstorf-Rostock). The members of the Programme Committee were Prof. Dr., Johannes Adam (Martin-Luther-University Halle) Prof. Dr. Heinz Ahrens (Academy of Sciences of the GDR, Berlin) Doz. Dr. Jana Jureckova (Charles University Praha) Prof. Dr. Moti Lal Tiku (McMaster University, Hamilton, Ontario) The aim of the conference was to discuss several aspects of robustness but mainly to present new results regarding the robustness of classical statistical methods especially tests, confidence estimations, and selection procedures, and to compare their perfor mance with nonparametric procedures. Robustness in this sens~ is understood as intensivity against. violation of the normal assumption.
Download or read book NBS Special Publication written by and published by . This book was released on 1970 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Monte Carlo Simulation Study of the Performance of Hypothesis Tests Under Assumption Violations by : Gareth Cleveland
Download or read book A Monte Carlo Simulation Study of the Performance of Hypothesis Tests Under Assumption Violations written by Gareth Cleveland and published by . This book was released on 2013 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hypothesis testing is frequently utilized in a wide range of disciplines as researchers attempt to draw inferences from data. Although most hypothesis tests theoretically require certain assumptions for their accuracy, these assumptions are often not known or simply ignored. The robustness of a test is defined as the ability of the test to withstand assumption violations with respect to its Type I error probability. This study seeks to empirically investigate the robustness of several two-sample hypothesis tests. Through Monte Carlo simulations, exact Type I error rates are calculated for five different tests under a wide range of simulation setups. Two of the five tests are parametric: Student's t-test and Welch's t-test. The remaining three tests are distribution free: the Mann-Whitney U test, a bootstrap-based test, and a permutation test. Results demonstrate that Welch's t-test, the bootstrap test, and the permutation test perform reasonably well under a variety of assumption violations.
Book Synopsis Introduction to Robust Estimation and Hypothesis Testing by : Rand R. Wilcox
Download or read book Introduction to Robust Estimation and Hypothesis Testing written by Rand R. Wilcox and published by Academic Press. This book was released on 2016-09-02 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Robust Estimating and Hypothesis Testing, 4th Editon, is a ‘how-to’ on the application of robust methods using available software. Modern robust methods provide improved techniques for dealing with outliers, skewed distribution curvature and heteroscedasticity that can provide substantial gains in power as well as a deeper, more accurate and more nuanced understanding of data. Since the last edition, there have been numerous advances and improvements. They include new techniques for comparing groups and measuring effect size as well as new methods for comparing quantiles. Many new regression methods have been added that include both parametric and nonparametric techniques. The methods related to ANCOVA have been expanded considerably. New perspectives related to discrete distributions with a relatively small sample space are described as well as new results relevant to the shift function. The practical importance of these methods is illustrated using data from real world studies. The R package written for this book now contains over 1200 functions. New to this edition 35% revised content Covers many new and improved R functions New techniques that deal with a wide range of situations Extensive revisions to cover the latest developments in robust regression Covers latest improvements in ANOVA Includes newest rank-based methods Describes and illustrated easy to use software
Book Synopsis Nonparametric Monte Carlo Tests and Their Applications by : Li-Xing Zhu
Download or read book Nonparametric Monte Carlo Tests and Their Applications written by Li-Xing Zhu and published by Springer Science & Business Media. This book was released on 2006-04-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: A fundamental issue in statistical analysis is testing the fit of a particular probability model to a set of observed data. Monte Carlo approximation to the null distribution of the test provides a convenient and powerful means of testing model fit. Nonparametric Monte Carlo Tests and Their Applications proposes a new Monte Carlo-based methodology to construct this type of approximation when the model is semistructured. When there are no nuisance parameters to be estimated, the nonparametric Monte Carlo test can exactly maintain the significance level, and when nuisance parameters exist, this method can allow the test to asymptotically maintain the level. The author addresses both applied and theoretical aspects of nonparametric Monte Carlo tests. The new methodology has been used for model checking in many fields of statistics, such as multivariate distribution theory, parametric and semiparametric regression models, multivariate regression models, varying-coefficient models with longitudinal data, heteroscedasticity, and homogeneity of covariance matrices. This book will be of interest to both practitioners and researchers investigating goodness-of-fit tests and resampling approximations. Every chapter of the book includes algorithms, simulations, and theoretical deductions. The prerequisites for a full appreciation of the book are a modest knowledge of mathematical statistics and limit theorems in probability/empirical process theory. The less mathematically sophisticated reader will find Chapters 1, 2 and 6 to be a comprehensible introduction on how and where the new method can apply and the rest of the book to be a valuable reference for Monte Carlo test approximation and goodness-of-fit tests. Lixing Zhu is Associate Professor of Statistics at the University of Hong Kong. He is a winner of the Humboldt Research Award at Alexander-von Humboldt Foundation of Germany and an elected Fellow of the Institute of Mathematical Statistics. From the reviews: "These lecture notes discuss several topics in goodness-of-fit testing, a classical area in statistical analysis. ... The mathematical part contains detailed proofs of the theoretical results. Simulation studies illustrate the quality of the Monte Carlo approximation. ... this book constitutes a recommendable contribution to an active area of current research." Winfried Stute for Mathematical Reviews, Issue 2006 "...Overall, this is an interesting book, which gives a nice introduction to this new and specific field of resampling methods." Dongsheng Tu for Biometrics, September 2006
Book Synopsis Master's Theses in the Arts and Social Sciences by :
Download or read book Master's Theses in the Arts and Social Sciences written by and published by . This book was released on 1978 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Author and Permuted Title Index to Selected Statistical Journals by : Brian L. Joiner
Download or read book An Author and Permuted Title Index to Selected Statistical Journals written by Brian L. Joiner and published by . This book was released on 1970 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: All articles, notes, queries, corrigenda, and obituaries appearing in the following journals during the indicated years are indexed: Annals of mathematical statistics, 1961-1969; Biometrics, 1965-1969#3; Biometrics, 1951-1969; Journal of the American Statistical Association, 1956-1969; Journal of the Royal Statistical Society, Series B, 1954-1969,#2; South African statistical journal, 1967-1969,#2; Technometrics, 1959-1969.--p.iv.
Book Synopsis A Monte Carlo Comparison of the Type I Error Rates of the Likelihood Ratio Chi-square Test Statistic and Hotelling's Two-sample T2 on Testing the Differences Between Group Means by : John R. Boulet
Download or read book A Monte Carlo Comparison of the Type I Error Rates of the Likelihood Ratio Chi-square Test Statistic and Hotelling's Two-sample T2 on Testing the Differences Between Group Means written by John R. Boulet and published by . This book was released on 1990 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present paper demonstrates how Structural Equation Modelling (SEM) can be used to formulate a test of the difference in means between groups on a number of dependent variables. A Monte Carlo study compared the Type I error rates of the Likelihood Ratio (LR) Chi-square ($\chi\sp2$) statistic (SEM test criterion) and Hotelling's two-sample T$\sp2$ statistic (MANOVA test criterion) in detecting differences in means between two independent samples. Seventy-two conditions pertaining to average sample size ((n$\sb1$ + n$\sb2$)/2), extent of inequality of sample sizes (n$\sb1$:n$\sb2$), number of variables (p), and degree of inequality of variance-covariance matrices ($\Sigma\sb1$:$\Sigma\sb2$) were modelled. Empirical sampling distributions of the LR $\chi\sp2$ statistic and Hotelling's T$\sp2$ statistic consisted fo 2000 samples drawn from multivariate normal parent populations. The actual proportion of values that exceeded the nominal levels are presented. The results indicated that, in terms of maintaining Type I error rates that were close to the nominal levels, the LR $\chi\sp2$ statistic and Hotelling's T$\sp2$ statistic were comparable when $\Sigma\sb1$ = $\Sigma\sb2$ and (n$\sb1$ + n$\sb2$)/2:p was relatively large (i.e., 30:1). However, when $\Sigma\sb1$ = $\Sigma\sb2$ and (n$\sb1$ + n$\sb2$)/2:p was small (i.e., 10:1) Hotelling's T$\sp2$ statistic was preferred. When $\Sigma\sb{1} \not=\Sigma\sb2$ the LR $\chi\sp2$ statistic provided more appropriate Type I error rates under all of the simulated conditions. The results are related to earlier findings, and implications for the appropriate use of the SEM method of testing for group mean differences are noted.
Book Synopsis Monte Carlo Methods by : Malvin H. Kalos
Download or read book Monte Carlo Methods written by Malvin H. Kalos and published by John Wiley & Sons. This book was released on 2009-06-10 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to Monte Carlo methods seeks to identify and study the unifying elements that underlie their effective application. Initial chapters provide a short treatment of the probability and statistics needed as background, enabling those without experience in Monte Carlo techniques to apply these ideas to their research. The book focuses on two basic themes: The first is the importance of random walks as they occur both in natural stochastic systems and in their relationship to integral and differential equations. The second theme is that of variance reduction in general and importance sampling in particular as a technique for efficient use of the methods. Random walks are introduced with an elementary example in which the modeling of radiation transport arises directly from a schematic probabilistic description of the interaction of radiation with matter. Building on this example, the relationship between random walks and integral equations is outlined. The applicability of these ideas to other problems is shown by a clear and elementary introduction to the solution of the Schrödinger equation by random walks. The text includes sample problems that readers can solve by themselves to illustrate the content of each chapter. This is the second, completely revised and extended edition of the successful monograph, which brings the treatment up to date and incorporates the many advances in Monte Carlo techniques and their applications, while retaining the original elementary but general approach.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1987 with total page 956 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Monte Carlo Study of the Robustness of Coefficient Alpha by : Sharon G. Shultz
Download or read book A Monte Carlo Study of the Robustness of Coefficient Alpha written by Sharon G. Shultz and published by . This book was released on 1993 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: The biasedness and efficiency of coefficient alpha were studied given various error score distribution, number of examinees, population reliability values, and number of subtests. A Monte Carlo methodology was used in which an additive true score matrix was constructed and an error score was added to each true score. The true scores were uniformly distributed while the error score distributions used were the normal, mixed normal, exponential, and the negative exponential. In addition, 1000 replications were used and the resulting sampling distributions were examined with respect to their skewness and kurtosis.
Book Synopsis Comparative Robustness and Power of the Wilcoxon Signed-rank Test, Sign Test, and T-test Under Distribution Asymmetry by : Bercedis L. Peterson
Download or read book Comparative Robustness and Power of the Wilcoxon Signed-rank Test, Sign Test, and T-test Under Distribution Asymmetry written by Bercedis L. Peterson and published by . This book was released on 1977 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Monte Carlo Statistical Methods by : Christian Robert
Download or read book Monte Carlo Statistical Methods written by Christian Robert and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 670 pages. Available in PDF, EPUB and Kindle. Book excerpt: We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.
Book Synopsis Lectures on Monte Carlo Methods by : Neal Noah Madras
Download or read book Lectures on Monte Carlo Methods written by Neal Noah Madras and published by Springer Science & Business. This book was released on 2002 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monte Carlo methods form an experimental branch of mathematics that employs simulations driven by random number generators. These methods are often used when others fail, since they are much less sensitive to the ``curse of dimensionality'', which plagues deterministic methods in problems with a large number of variables. Monte Carlo methods are used in many fields: mathematics, statistics, physics, chemistry, finance, computer science, and biology, for instance. This book is an introduction to Monte Carlo methods for anyone who would like to use these methods to study various kinds of mathematical models that arise in diverse areas of application. The book is based on lectures in a graduate course given by the author. It examines theoretical properties of Monte Carlo methods as well as practical issues concerning their computer implementation and statistical analysis. The only formal prerequisite is an undergraduate course in probability. The book is intended to be accessible to students from a wide range of scientific backgrounds. Rather than being a detailed treatise, it covers the key topics of Monte Carlo methods to the depth necessary for a researcher to design, implement, and analyze a full Monte Carlo study of a mathematical or scientific problem. The ideas are illustrated with diverse running examples. There are exercises sprinkled throughout the text. The topics covered include computer generation of random variables, techniques and examples for variance reduction of Monte Carlo estimates, Markov chain Monte Carlo, and statistical analysis of Monte Carlo output.
