This gracefully organized text reveals the rigorous theory of probability and statistical inference in the style of a tutorial, using worked examples, exercises, figures, tables, and computer simulations to develop and illustrate concepts. Drills and boxed summaries emphasize and reinforce important ideas and special techniques. Beginning with a review of the basic concepts and methods in probability theory, moments, and moment generating functions, the author moves to more intricate topics. Introductory Statistical Inference studies multivariate random variables, exponential families of distributions, and standard probability inequalities. It develops the Helmert transformation for normal distributions, introduces the notions of convergence, and spotlights the central limit theorems. Coverage highlights sampling distributions, Basu's theorem, Rao-Blackwellization and the Cramér-Rao inequality. The text also provides in-depth coverage of Lehmann-Scheffé theorems, focuses on tests of hypotheses, describes Bayesian methods and the Bayes' estimator, and develops large-sample inference. The author provides a historical context for statistics and statistical discoveries and answers to a majority of the end-of-chapter exercises. Designed primarily for a one-semester, first-year graduate course in probability and statistical inference, this text serves readers from varied backgrounds, ranging from engineering, economics, agriculture, and bioscience to finance, financial mathematics, operations and information management, and psychology.

This textbook covers the fundamentals of statistical inference and statistical theory including Bayesian and frequentist approaches and methodology possible without excessive emphasis on the underlying mathematics. This book is about some of the basic principles of statistics that are necessary to understand and evaluate methods for analyzing complex data sets. The likelihood function is used for pure likelihood inference throughout the book. There is also coverage of severity and finite population sampling. The material was developed from an introductory statistical theory course taught by the author at the Johns Hopkins University’s Department of Biostatistics. Students and instructors in public health programs will benefit from the likelihood modeling approach that is used throughout the text. This will also appeal to epidemiologists and psychometricians. After a brief introduction, there are chapters on estimation, hypothesis testing, and maximum likelihood modeling. The book concludes with sections on Bayesian computation and inference. An appendix contains unique coverage of the interpretation of probability, and coverage of probability and mathematical concepts.

This excellent text emphasizes the inferential and decision-making aspects of statistics. The first chapter is mainly concerned with the elements of the calculus of probability. Additional chapters cover the general properties of distributions, testing hypotheses, and more.

Based on the authors' lecture notes, this text presents concise yet complete coverage of statistical inference theory, focusing on the fundamental classical principles. Unlike related textbooks, it combines the theoretical basis of statistical inference with a useful applied toolbox that includes linear models. Suitable for a second semester undergraduate course on statistical inference, the text offers proofs to support the mathematics and does not require any use of measure theory. It illustrates core concepts using cartoons and provides solutions to all examples and problems.

A comprehensive, self-paced, step-by-step statistics course for tertiary students.

This textbook integrates traditional statistical data analysis with new computational experimentation capabilities and concepts of algorithmic complexity and chaotic behavior in nonlinear dynamic systems. This was the first advanced text/reference to bring together such a comprehensive variety of tools for the study of random phenomena occurring in engineering and the natural, life, and social sciences. The crucial computer experiments are conducted using the readily available computer program Mathematica® Uncertain Virtual WorldsTM software packages which optimize and facilitate the simulation environment. Brief tutorials are included that explain how to use the Mathematica® programs for effective simulation and computer experiments. Large and original real-life data sets are introduced and analyzed as a model for independent study. This is an excellent classroom tool and self-study guide. The material is presented in a clear and accessible style providing numerous exercises and bibliographical notes suggesting further reading. Topics and Features Comprehensive and integrated treatment of uncertainty arising in engineering and scientific phenomena – algorithmic complexity, statistical independence, and nonlinear chaotic behavior Extensive exercise sets, examples, and Mathematica® computer experiments that reinforce concepts and algorithmic methods Thorough presentation of methods of data compression and representation Algorithmic approach to model selection and design of experiments Large data sets and 13 Mathematica®-based Uncertain Virtual WorldsTM programs and code This text is an excellent resource for all applied statisticians, engineers, and scientists who need to use modern statistical analysis methods to investigate and model their data. The present, softcover reprint is designed to make this classic textbook available to a wider audience.

This comprehensive and uniquely organized text is aimed at undergraduate and graduate level statistics courses in education, psychology, and other social sciences. A conceptual approach, built around common issues and problems rather than statistical techniques, allows students to understand the conceptual nature of statistical procedures and to focus more on cases and examples of analysis. Wherever possible, presentations contain explanations of the underlying reasons behind a technique. Importantly, this is one of the first statistics texts in the social sciences using R as the principal statistical package. Key features include the following. Conceptual Focus – The focus throughout is more on conceptual understanding and attainment of statistical literacy and thinking than on learning a set of tools and procedures. Problems and Cases – Chapters and sections open with examples of situations related to the forthcoming issues, and major sections ends with a case study. For example, after the section on describing relationships between variables, there is a worked case that demonstrates the analyses, presents computer output, and leads the student through an interpretation of that output. Continuity of Examples – A master data set containing nearly all of the data used in the book’s examples is introduced at the beginning of the text. This ensures continuity in the examples used across the text. Companion Website – A companion website contains instructions on how to use R, SAS, and SPSS to solve the end-of-chapter exercises and offers additional exercises. Field Tested – The manuscript has been field tested for three years at two leading institutions.

Project-Based R Companion to Introductory Statistics is envisioned as a companion to a traditional statistics or biostatistics textbook, with each chapter covering traditional topics such as descriptive statistics, regression, and hypothesis testing. However, unlike a traditional textbook, each chapter will present its material using a complete step-by-step analysis of a real publicly available dataset, with an emphasis on the practical skills of testing assumptions, data exploration, and forming conclusions. The chapters in the main body of the book include a worked example showing the R code used at each step followed by a multi-part project for students to complete. These projects, which could serve as alternatives to traditional discrete homework problems, will illustrate how to "put the pieces together" and conduct a complete start-to-finish data analysis using the R statistical software package. At the end of the book, there are several projects that require the use of multiple statistical techniques that could be used as a take-home final exam or final project for a class. Key features of the text: Organized in chapters focusing on the same topics found in typical introductory statistics textbooks (descriptive statistics, regression, two-way tables, hypothesis testing for means and proportions, etc.) so instructors can easily pair this supplementary material with course plans Includes student projects for each chapter which can be assigned as laboratory exercises or homework assignments to supplement traditional homework Features real-world datasets from scientific publications in the fields of history, pop culture, business, medicine, and forensics for students to analyze Allows students to gain experience working through a variety of statistical analyses from start to finish The book is written at the undergraduate level to be used in an introductory statistical methods course or subject-specific research methods course such as biostatistics or research methods for psychology or business analytics. Author After a 10-year career as a research biostatistician in the Department of Ophthalmology and Visual Sciences at the University of Wisconsin-Madison, Chelsea Myers teaches statistics and biostatistics at Rollins College and Valencia College in Central Florida. She has authored or co-authored more than 30 scientific papers and presentations and is the creator of the MCAT preparation website MCATMath.com.

A fascinating investigation into the foundations of statistical inference This publication examines the distinct philosophical foundations of different statistical modes of parametric inference. Unlike many other texts that focus on methodology and applications, this book focuses on a rather unique combination of theoretical and foundational aspects that underlie the field of statistical inference. Readers gain a deeper understanding of the evolution and underlying logic of each mode as well as each mode's strengths and weaknesses. The book begins with fascinating highlights from the history of statistical inference. Readers are given historical examples of statistical reasoning used to address practical problems that arose throughout the centuries. Next, the book goes on to scrutinize four major modes of statistical inference: * Frequentist * Likelihood * Fiducial * Bayesian The author provides readers with specific examples and counterexamples of situations and datasets where the modes yield both similar and dissimilar results, including a violation of the likelihood principle in which Bayesian and likelihood methods differ from frequentist methods. Each example is followed by a detailed discussion of why the results may have varied from one mode to another, helping the reader to gain a greater understanding of each mode and how it works. Moreover, the author provides considerable mathematical detail on certain points to highlight key aspects of theoretical development. The author's writing style and use of examples make the text clear and engaging. This book is fundamental reading for graduate-level students in statistics as well as anyone with an interest in the foundations of statistics and the principles underlying statistical inference, including students in mathematics and the philosophy of science. Readers with a background in theoretical statistics will find the text both accessible and absorbing.

A multidisciplinary approach that emphasizes learning by analyzing real-world data sets This book is the result of the authors' hands-on classroom experience and is tailored to reflect how students best learn to analyze linear relationships. The text begins with the introduction of four simple examples of actual data sets. These examples are developed and analyzed throughout the text, and more complicated examples of data sets are introduced along the way. Taking a multidisciplinary approach, the book traces the conclusion of the analyses of data sets taken from geology, biology, economics, psychology, education, sociology, and environmental science. As students learn to analyze the data sets, they master increasingly sophisticated linear modeling techniques, including: * Simple linear models * Multivariate models * Model building * Analysis of variance (ANOVA) * Analysis of covariance (ANCOVA) * Logistic regression * Total least squares The basics of statistical analysis are developed and emphasized, particularly in testing the assumptions and drawing inferences from linear models. Exercises are included at the end of each chapter to test students' skills before moving on to more advanced techniques and models. These exercises are marked to indicate whether calculus, linear algebra, or computer skills are needed. Unlike other texts in the field, the mathematics underlying the models is carefully explained and accessible to students who may not have any background in calculus or linear algebra. Most chapters include an optional final section on linear algebra for students interested in developing a deeper understanding. The many data sets that appear in the text are available on the book's Web site. The MINITAB(r) software program is used to illustrate many of the examples. For students unfamiliar with MINITAB(r), an appendix introduces the key features needed to study linear models. With its multidisciplinary approach and use of real-world data sets that bring the subject alive, this is an excellent introduction to linear models for students in any of the natural or social sciences.