An Introduction to Statistical Inference and Its Applications with R

An Introduction to Statistical Inference and Its Applications with R

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Description

Emphasizing concepts rather than recipes, An Introduction to Statistical Inference and Its Applications with R provides a clear exposition of the methods of statistical inference for students who are comfortable with mathematical notation. Numerous examples, case studies, and exercises are included. R is used to simplify computation, create figures, and draw pseudorandom samples-not to perform entire analyses. After discussing the importance of chance in experimentation, the text develops basic tools of probability. The plug-in principle then provides a transition from populations to samples, motivating a variety of summary statistics and diagnostic techniques. The heart of the text is a careful exposition of point estimation, hypothesis testing, and confidence intervals. The author then explains procedures for 1- and 2-sample location problems, analysis of variance, goodness-of-fit, and correlation and regression. He concludes by discussing the role of simulation in modern statistical inference. Focusing on the assumptions that underlie popular statistical methods, this textbook explains how and why these methods are used to analyze experimental data.show more

Product details

  • Electronic book text | 496 pages
  • Taylor & Francis Ltd
  • Chapman & Hall/CRC
  • London, United Kingdom
  • 30 Tables, black and white; 72 Illustrations, black and white
  • 1584889489
  • 9781584889489

About Michael W. Trosset

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

Table of contents

ExperimentsExamples 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 VariablesCase Study: Padrolling in Milton Murayama's All I asking for is my bodyDiscrete Random VariablesBasic Concepts Examples Expectation Binomial DistributionsContinuous Random Variables A Motivating Example Basic Concepts Elementary Examples Normal Distributions Normal Sampling DistributionsQuantifying Population Attributes Symmetry Quantiles The Method of Least SquaresData 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? TransformationsLots of Data Averaging Decreases Variation The Weak Law of Large Numbers The Central Limit TheoremInferenceA Motivating Example Point EstimationHeuristics of Hypothesis Testing Testing Hypotheses about a Population MeanSet Estimation1-Sample Location Problems The Normal 1-Sample Location Problem The General 1-Sample Location ProblemThe Symmetric 1-Sample Location Problem Case Study: Deficit Unawareness in Alzheimer's Disease2-Sample Location Problems The Normal 2-Sample Location ProblemThe Case of a General Shift FamilyCase Study: Etruscan versus Italian Head BreadthThe Analysis of Variance The Fundamental Null Hypothesis Testing the Fundamental Null Hypothesis Planned Comparisons Post Hoc Comparisons Case Study: Treatments of AnorexiaGoodness-of-Fit Partitions Test Statistics Testing IndependenceAssociation Bivariate Distributions Normal Random Variables Monotonic Association Explaining Association Case Study: Anorexia Treatments RevisitedSimple 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 RacingR: A Statistical Programming Language IntroductionUsing RFunctions That Accompany This BookIndexExercises appear at the end of each chapter.show more