Description of Samples and Populations
Data types
Visualizing categorical data
Visualizing quantitative data
Statistical summaries
What is a probability?
Linear Regression
Fitting a regression line
When is linear regression appropriate?
The correlation coefficient
Perspective
Comparison of Groups
Graphical and simple numerical comparison
Between-group variation and within-group variation
Populations, samples, and expected values
Least squares estimation and residuals
Paired and unpaired samples
Perspective
The Normal Distribution
Properties
One sample
Are the data (approximately) normally distributed?
The central limit theorem
Statistical Models, Estimation, and Confidence Intervals
Statistical models
Estimation
Confidence intervals
Unpaired samples with different standard deviations
Hypothesis Tests
Null hypotheses
t-tests
Tests in a one-way ANOVA
Hypothesis tests as comparison of nested models
Type I and type II errors
Model Validation and Prediction
Model validation
Prediction
Linear Normal Models
Multiple linear regression
Additive two-way analysis of variance
Linear models
Interactions between variables
Probabilities
Outcomes, events, and probabilities
Conditional probabilities
Independence
The Binomial Distribution
The independent trials model
The binomial distribution
Estimation, confidence intervals, and hypothesis tests
Differences between proportions
Analysis of Count Data
The chi-square test for goodness-of-fit
2 × 2 contingency table
Two-sided contingency tables
Logistic Regression
Odds and odds ratios
Logistic regression models
Estimation and confidence intervals
Hypothesis tests
Model validation and prediction
Case Exercises
Case 1: Linear modeling
Case 2: Data transformations
Case 3: Two sample comparisons
Case 4: Linear regression with and without intercept
Case 5: Analysis of variance and test for linear trend
Case 6: Regression modeling and transformations
Case 7: Linear models
Case 8: Binary variables
Case 9: Agreement
Case 10: Logistic regression
Appendix A: Summary of Inference Methods
Statistical concepts
Statistical analysis
Model selection
Appendix B: Introduction to R
Working with R
Data frames and reading data into R
Manipulating data
Graphics with R
Reproducible research
Installing R
Exercises
Appendix C: Statistical Tables
The x2 distribution
The normal distribution
The t distribution
The F distribution
Bibliography
Index