2.1 Basic Ideas
    2.1.1 Sample Spaces and Events
    2.1.2 Axioms of Probability and Basic Results
    2.1.3 How to Calculate Probabilities?
2.2 Conditional Probability and Independence
    2.2.1 Conditional Probability
    2.2.2 Independence
    2.2.3 Law of Total Probability
    2.2.4 Bayes' Theorem
2.3 Random Variables and Their Distributions
    2.3.1 Discrete Random Variables
    2.3.2 Continuous Random Variables
2.4 Expected Value, Variance, and Other Parameters of a Distribution
    2.4.1 Expected Value
    2.4.2 Variance and Standard Deviation
    2.4.3 *Skewness and Kurtosis
    2.4.4 *Moment Generating Function
    2.4.5 Quantiles and Percentiles
2.5 Jointly Distributed Random Variables
    2.5.1 Joint Probability Mass or Density Function
    2.5.2 Marginal Distribution
    2.5.3 Independent Random Variables
    2.5.4 Conditional Distribution
    2.5.5 Covariance
    2.5.6 Correlation Coefficient
    2.5.7 Multivariate Distributions
2.6 Chebyshev's Inequality and Weak Law of Large Numbers
2.7 Selected Discrete Distributions
    2.7.1 Bernoulli Distribution
    2.7.2 Binomial Distribution
    2.7.3 Hypergeometric Distribution
    2.7.4 Poisson Distribution
    2.7.5 Geometric Distribution
    2.7.6 Multinomial Distribution
2.8 Selected Continuous Distributions
    2.8.1 Uniform Distribution
    2.8.2 Exponential Distribution
    2.8.3 Gamma Distribution
    2.8.4 Beta Distribution
2.9 Normal Distribution
    2.9.1 Standard Normal Distribution
    2.9.2 Percentiles of the Normal Distribution
    2.9.3 Linear Combinations of Normal Random Variables
2.10 *Transformations of Random Variables
2.11 Chapter Summary
Exercises

Chapter 3 COLLECTING DATA

3.1 Types of Statistical Studies
    3.1.1 Importance of a Control Group in a Comparative Study
3.2 Observational Studies
    3.2.1 Sample Surveys
    3.2.2 Prospective and Retrospective Studies
3.3 Basic Sampling Designs
    3.3.1 Simple Random Sampling
    3.3.2 Stratified Random Sampling
    3.3.3 Multistage Cluster Sampling
    3.3.4 Systematic Sampling
3.4 Experimental Studies
    3.4.1 Terminology and Basic Concepts
    3.4.2 Strategies to Reduce Experimental Error Variation
    3.4.3 Basic Experimental Designs
3.4.4 Iterative Nature of Experimentation
3.5 Chapter Summary
Exercises

Chapter 4 SUMMARIZING AND EXPLORING DATA

4.1 Types of Data
4.2 Summarizing Categorical Data
4.3 Summarizing Numerical Data
    4.3.1 Summary Statistics: Measures of Location
    4.3.2 Summary Statistics: Measures of Dispersion
    4.3.3 *Summary Statistics: Skewness and Kurtosis
    4.3.4 Graphical Techniques
4.4 Summarizing Bivariate Data
    4.4.1 Summarizing Bivariate Categorical Data
    4.4.2 Summarizing Bivariate Numerical Data
4.5 Summarizing Time-Series Data
    4.5.1 Data Smoothing and Forecasting Techniques
    4.5.2 Autocorrelation Coefficients
4.6 Chapter Summary
Exercises

Chapter 5 SAMPLING DISTRIBUTIONS OF STATISTICS

5.1 Sampling Distribution of the Sample Mean
    5.1.1 Central Limit Theorem
    5.1.2 Normal Approximation to the Binomial Distribution
    5.1.3 Continuity Correction
5.2 Sampling Distribution of the Sample Variance
5.3 Student's t-Distribution
5.4 Snedecor-Fisher's F-Distribution
5.5 *Sampling Distributions of Order Statistics
    5.5.1 Distribution of the Sample Minimum and Maximum
    5.5.2 Distribution of the rth Order Statistic
5.6 Chapter Summary
Exercises

Chapter 6 BASIC CONCEPTS OF INFERENCE

6.1 Point Estimation
    6.1.1 Bias, Variance and Mean Square Error
    6.1.2 Methods of Estimation
6.2 Confidence Interval Estimation
    6.2.1 Two-Sided Confidence Intervals
    6.2.2 One-Sided Confidence Intervals
6.3 Hypothesis Testing
    6.3.1 Null and Alternative Hypotheses
    6.3.2 Hypothesis Tests
    6.3.3 Type I and Type II Error Probabilities
    6.3.4 *Operating Characteristic and Power Functions
    6.3.5 Level of Significance
    6.3.6 Observed Level of Significance or P-Value
    6.3.7 One-Sided and Two-Sided Tests
    6.3.8 Relation Between Confidence Intervals and Hypothesis Tests
    6.3.9 Use and Misuse of Hypothesis Tests in Practice
6.4 Chapter Summary
Exercises

Chapter 7 INFERENCES FOR SINGLE SAMPLES

7.1 Inferences on Mean (Large Samples)
    7.1.1 Confidence Intervals on Mean
    7.1.2 Hypothesis Tests on Mean
7.2 Inferences on Mean (Small Samples)
    7.2.1 Confidence Intervals on Mean
    7.2.2 Hypothesis Tests on Mean
7.3 Inferences on Variance
    7.3.1 Confidence Interval on Variance
    7.3.2 Hypothesis Tests on Variance
7.4 *Prediction and Tolerance Intervals
    7.4.1 Prediction Intervals
    7.4.2 Tolerance Intervals
7.5 Chapter Summary
Exercises

Chapter 8 INFERENCES FOR TWO SAMPLES

8.1 Independent Samples and Matched Pairs Designs
8.2 Graphical Methods for Comparing Two Samples
8.3 Comparing Means of Two Populations
8.3.1 Independent Samples Design
8.3.2 Matched Pairs Design
8.4 *Comparing Variances of Two Populations
8.5 Chapter Summary
Exercises

Chapter 9 INFERENCES FOR PROPORTIONS AND COUNT DATA

9.1 Inferences on Proportion
    9.1.1 Large Sample Confidence Interval for a Proportion
    9.1.2 Large Sample Hypothesis Tests on a Proportion
    9.1.3 *Small Sample Hypothesis Tests on a Proportion
9.2 Inferences for Comparing Two Proportions
    9.2.1 Independent Samples Design
    9.2.2 *Matched Pairs Design
9.3 Inferences for One-Way Count Data
    9.3.1 A Test for the Multinomial Distribution
    9.3.2 Chi-Square Goodness of Fit Test
9.4 Inferences for Two-Way Count Data
    9.4.1 Sampling Models
    9.4.2 Hypothesis Tests
    9.4.3 *Odds Ratio as a Measure of Association
9.5 Chapter Summary
Exercises

Chapter 10 SIMPLE LINEAR REGRESSION AND CORRELATION

10.1 A Probabilistic Model for Simple Linear Regression
10.2 Fitting the Simple Linear Regression Model
    10.2.1 Least Squares (LS) Fit
    10.2.2 Goodness of Fit of the LS Line
    10.2.3 Estimation of F²
10.3 Statistical Inference for Simple Linear Regression
    10.3.1 Statistical Inference on $₀ and $₁
    10.3.2 Analysis of Variance for Simple Linear Regression
    10.3.3 Prediction of Future Observations
    10.3.4 Calibration (Inverse Regression)
10.4 Regression Diagnostics
    10.4.1 Checking the Model Assumptions
    10.4.2 Checking for Outliers and Influential Observations
    10.4.3 Data Transformations
10.5 *Correlation Analysis
    10.5.1 Bivariate Normal Distribution
    10.5.2 Statistical Inference on the Correlation Coefficient
10.6 Pitfalls of Regression and Correlation Analyses
10.7 Chapter Summary
Exercises

Chapter 11 MULTIPLE LINEAR REGRESSION

11.1 A Probabilistic Model for Multiple Linear Regression
11.2 Fitting the Multiple Regression Model
    11.2.1 Least Squares (LS) Fit
    11.2.2 Goodness of Fit of the Model
11.3 *Multiple Regression Model in Matrix Notation
11.4 Statistical Inference for Multiple Regression
    11.4.1 Statistical Inference on $ 's
    11.4.2 Prediction of Future Observations
11.5 Regression Diagnostics
    11.5.1 Residual Analysis
    11.5.2 Data Transformations
11.6 Topics in Regression Modeling
    11.6.1 Multicollinearity
    11.6.2 Polynomial Regression
    11.6.3 Dummy Predictor Variables
    11.6.4 *Standardized Regression Coefficients
    11.6.5 *Logistic Regression Model
11.7 Variable Selection Methods
    11.7.1 Stepwise Regression
    11.7.2 Best Subsets Regression
11.8 A Strategy for Building a Multiple Regression Model
11.9 Chapter Summary
Exercises

Chapter 12 ANALYSIS OF SINGLE FACTOR EXPERIMENTS

12.1 Completely Randomized Design
    12.1.1 Model and Estimates of Its Parameters
    12.1.2 Analysis of Variance
    12.1.3 Model Diagnostics Using Residual Plots
12.2 Multiple Comparisons of Means
    12.2.1 Pairwise Comparisons of Means
    12.2.2 *Other Comparisons Among the Means
12.3 *Random Effects Model for a One-Way Layout
12.4 Randomized Block Design
    12.4.1 Model and Estimates of Its Parameters
    12.4.2 Analysis of Variance
    12.4.3 Model Diagnostics Using Residual Plots
    12.4.4 Multiple Comparisons of Treatment Effects
    12.4.5 Mixed-Effects Model for the RB Design
12.5 Chapter Summary
Exercises

Chapter 13 ANALYSIS OF MULTIFACTOR EXPERIMENTS

13.1 Two-Factor Experiments with Fixed Crossed Factors
    13.1.1 Model and Estimates of Its Parameters
    13.1.2 Analysis of Variance
    13.1.3 Model Diagnostics
    13.1.4 Multiple Comparisons Between Rows and/or Between Columns
    13.1.5 Unbalanced Two-Way Layouts
    13.1.6 Regression Approach to Two-Factor Experiments
13.2 2^k Factorial Experiments
    13.2.1 Main Effects and Interactions
    13.2.2 Statistical Inference for 2^k Experiments
    13.2.3 Regression Approach to 2^k Experiments
    13.2.4 Model Diagnostics
    13.2.5 Single Replicate Case
13.3 Other Selected Types of Two-Factor Experiments
    13.3.1 Two-Factor Experiments with Crossed and Mixed Factors
    13.3.2 Two-Factor Experiments with Nested and Mixed Factors
13.4 Chapter Summary
Exercises

Chapter 14 NONPARAMETRIC STATISTICAL METHODS

14.1 Inferences for Single Samples
    14.1.1 Sign Test and Confidence Interval
    14.1.2 Wilcoxon Signed Rank Test and Confidence Interval
14.2 Inferences for Two Independent Samples
    14.2.1 Wilcoxon-Mann-Whitney Test
    14.2.2 Wilcoxon-Mann-Whitney Confidence Interval
14.3 Inferences for Several Independent Samples
    14.3.1 Kruskal-Wallis Test
    14.3.2 *Pairwise Comparisons
14.4 Inferences for Several Matched Samples
    14.4.1 Friedman Test
    14.4.2 Pairwise Comparisons
14.5 Rank Correlation Methods
    14.5.1 Spearman's Rank Correlation Coefficient
    14.5.2 Kendall's Rank Correlation Coefficient
    14.5.3 *Kendall's Coefficient of Concordance
14.6 *Resampling Methods
    14.6.1 Permutation Tests
    14.6.2 Bootstrap Method
    14.6.3 Jackknife Method
14.7 Chapter Summary
Exercises

Chapter 15 LIKELIHOOD, BAYESIAN, AND DECISION THEORY METHODS

15.1 Maximum Likelihood Estimation
    15.1.1 Likelihood Function
    15.1.2 Calculation of Maximum Likelihood Estimators
    15.1.3 Properties of Maximum Likelihood Estimators
    15.1.4 Large Sample Inferences Based on the MLE's
    15.1.5 *Delta Method for Approximating the Variance of an Estimator
15.2 Likelihood Ratio Tests
    15.2.1 Neyman-Pearson Lemma
    15.2.2 *Generalized Likelihood Ratio Test
    15.2.3 *Wald Sequential Probability Ratio Test
15.3 Bayesian Inference
    15.3.1 Bayesian Estimation
    15.3.2 Bayesian Testing
15.4 Decision Theory
    15.4.1 Statistical Decision Problem
    15.4.2 Admissible, Minimax and Bayes Decision Rules
15.5 Chapter Summary
Exercises

Appendix A TABLES

Appendix B ABBREVIATED ANSWERS TOSELECTED ODD-NUMBERED EXERCISES

Index