An Introduction to Statistical Inference and Its Applications With R (Hardcover)

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.