An Introduction to Statistical Inference and its Applications with R

About this book

With an emphasis on explaining how and why statistical methods are used to analyze data, An Introduction to Statistical Inference and its Applications with R introduces several important procedures: one and two sample location problems, one way analysis of variance, and simple linear regression. The book presents numerous applications and supporting datasets throughout along with historical background to illustrate the material. Offering a modern approach that focuses on the interpretation of data, it features an appendix that provides instruction on the use of R as well as datasets and simulation. In addition, R code is available for download on the web.

Contents

Experiments Examples Randomization The Importance of Probability Games of Chance Mathematical Preliminaries Sets Counting Functions Limits Probability Interpretations of Probability Axioms of Probability Finite Sample Spaces Conditional Probability Random Variables Case Study: Padrolling in Milton Murayama's All I asking for is my body Discrete Random Variables Basic Concepts Examples Expectation Binomial Distributions Continuous Random Variables A Motivating Example Basic Concepts Elementary Examples Normal Distributions Normal Sampling Distributions Quantifying Population Attributes Symmetry Quantiles The Method of Least Squares Data The Plug-In Principle Plug-In Estimates of Mean and Variance Plug-In Estimates of Quantiles Kernel Density Estimates Case Study: Are Forearm Lengths Normally Distributed? Transformations Lots of Data Averaging Decreases Variation The Weak Law of Large Numbers The Central Limit Theorem Inference A Motivating Example Point Estimation Heuristics of Hypothesis Testing Testing Hypotheses about a Population Mean Set Estimation 1-Sample Location Problems The Normal 1-Sample Location Problem The General 1-Sample Location Problem The Symmetric 1-Sample Location Problem Case Study: Deficit Unawareness in Alzheimer's Disease 2-Sample Location Problems The Normal 2-Sample Location Problem The Case of a General Shift Family Case Study: Etruscan versus Italian Head Breadth The Analysis of Variance The Fundamental Null Hypothesis Testing the Fundamental Null Hypothesis Planned Comparisons Post Hoc Comparisons Case Study: Treatments of Anorexia Goodness-of-Fit Partitions Test Statistics Testing Independence Association Bivariate Distributions Normal Random Variables Monotonic Association Explaining Association Case Study: Anorexia Treatments Revisited Simple Linear Regression The Regression Line The Method of Least Squares Computation The Simple Linear Regression Model Assessing Linearity Case Study: Are Thick Books More Valuable? Simulation-Based Inference Termite Foraging Revisited The Bootstrap Case Study: Adventure Racing R: A Statistical Programming Language Introduction Using R Functions That Accompany This Book Index Exercises appear at the end of each chapter.

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Biography

Michael W. Trosset is Professor of Statistics and Director of the Indiana Statistical Consulting Center at Indiana University.