An Introduction to Statistical Inference and Its Applications with R
Features
- Explains how statistical methods are used for data analysis
- Uses the elementary functions of R to perform the individual steps of statistical procedures
- Includes amusing anecdotes and trivia, such as Ambrose Bierce’s definition of insurance
- Introduces basic concepts of inference through a careful study of several important procedures, including parametric and nonparametric methods, analysis of variance, and regression
- Presents many applications along with supporting data sets
- Contains exercises at the end of each chapter
- Offers R code and data sets available for download online
Solutions manual available upon qualified course adoption
Summary
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.
Table of 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.
Author Bio(s)
Michael W. Trosset is Professor of Statistics and Director of the Indiana Statistical Consulting Center at Indiana University.
