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For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations. To develop these confidence bounds and test, we first establish that estimators based on Newton steps from [the square root of n]-consistent estimators may be used in place of efficient solutions of the likelihood equations in likelihood ratio, Wald, and Rao tests. Taking a quadratic mean differentiability approach, Lehmann and Romano have outlined proofs of similar results. We take a Cramér condition approach and make the conditions and their use explicit. Keywords: coefficient of variation, signal to noise ratio, risk to return ratio, one-step Newton estimators, Newton's method, [the square root of n]-consistent estimators, efficient likelihood estimators, Cramér conditions, quadratic mean differentiability, likelihood ratio test, Wald test, Rao test, asymptotics.
For normally distributed populations, we obtain confidence bounds on a ratio of two coefficients of variation, provide a test for the equality of k coefficients of variation, and provide confidence bounds on a coefficient of variation shared by k populations.
Introductory Statistics follows scope and sequence requirements of a one-semester introduction to statistics course and is geared toward students majoring in fields other than math or engineering. The text assumes some knowledge of intermediate algebra and focuses on statistics application over theory. Introductory Statistics includes innovative practical applications that make the text relevant and accessible, as well as collaborative exercises, technology integration problems, and statistics labs. Senior Contributing Authors Barbara Illowsky, De Anza College Susan Dean, De Anza College Contributing Authors Daniel Birmajer, Nazareth College Bryan Blount, Kentucky Wesleyan College Sheri Boyd, Rollins College Matthew Einsohn, Prescott College James Helmreich, Marist College Lynette Kenyon, Collin County Community College Sheldon Lee, Viterbo University Jeff Taub, Maine Maritime Academy
A Practical Guide to Implementing Nonparametric and Rank-Based Procedures Nonparametric Statistical Methods Using R covers traditional nonparametric methods and rank-based analyses, including estimation and inference for models ranging from simple location models to general linear and nonlinear models for uncorrelated and correlated responses. The authors emphasize applications and statistical computation. They illustrate the methods with many real and simulated data examples using R, including the packages Rfit and npsm. The book first gives an overview of the R language and basic statistical concepts before discussing nonparametrics. It presents rank-based methods for one- and two-sample problems, procedures for regression models, computation for general fixed-effects ANOVA and ANCOVA models, and time-to-event analyses. The last two chapters cover more advanced material, including high breakdown fits for general regression models and rank-based inference for cluster correlated data. The book can be used as a primary text or supplement in a course on applied nonparametric or robust procedures and as a reference for researchers who need to implement nonparametric and rank-based methods in practice. Through numerous examples, it shows readers how to apply these methods using R.
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This highly popular introduction to confidence intervals has been thoroughly updated and expanded. It includes methods for using confidence intervals, with illustrative worked examples and extensive guidelines and checklists to help the novice.
The third edition of Testing Statistical Hypotheses updates and expands upon the classic graduate text, emphasizing optimality theory for hypothesis testing and confidence sets. The principal additions include a rigorous treatment of large sample optimality, together with the requisite tools. In addition, an introduction to the theory of resampling methods such as the bootstrap is developed. The sections on multiple testing and goodness of fit testing are expanded. The text is suitable for Ph.D. students in statistics and includes over 300 new problems out of a total of more than 760.
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