## Table of Contents

Preface

**1. Introduction to Statistics and Data Analysis**

1.1 Overview: Statistical Inference, Samples, Populations, and the Role of Probability

1.2 Sampling Procedures; Collection of Data

1.3 Measures of Location: The Sample Mean and Median

Exercises

1.4 Measures of Variability

Exercises

1.5 Discrete and Continuous Data

1.6 Statistical Modeling, Scientific Inspection, and Graphical Methods 19

1.7 General Types of Statistical Studies: Designed Experiment,

Observational Study, and Retrospective Study

Exercises

**2. Probability**

2.1 Sample Space

2.2 Events

Exercises

2.3 Counting Sample Points

Exercises

2.4 Probability of an Event

2.5 Additive Rules

Exercises

2.6 Conditional Probability, Independence and Product Rules

Exercises

2.7 Bayes’ Rule

Exercises

Review Exercises

2.8 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**3. Random Variables and Probability Distributions**

3.1 Concept of a Random Variable

3.2 Discrete Probability Distributions

3.3 Continuous Probability Distributions

Exercises

3.4 Joint Probability Distributions

Exercises

Review Exercises

3.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**4. Mathematical Expectation**

4.1 Mean of a Random Variable

Exercises

4.2 Variance and Covariance of Random Variables

Exercises

4.3 Means and Variances of Linear Combinations of Random Variables 127

4.4 Chebyshev’s Theorem

Exercises

Review Exercises

4.5 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**5. Some Discrete Probability Distributions**

5.1 Introduction and Motivation

5.2 Binomial and Multinomial Distributions

Exercises

5.3 Hypergeometric Distribution

Exercises

5.4 Negative Binomial and Geometric Distributions

5.5 Poisson Distribution and the Poisson Process

Exercises

Review Exercises

5.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**6. Some Continuous Probability Distributions**

6.1 Continuous Uniform Distribution

6.2 Normal Distribution

6.3 Areas under the Normal Curve

6.4 Applications of the Normal Distribution

Exercises

6.5 Normal Approximation to the Binomial

Exercises

6.6 Gamma and Exponential Distributions

6.7 Chi-Squared Distribution

6.8 Beta Distribution

6.9 Lognormal Distribution (Optional)

6.10 Weibull Distribution (Optional)

Exercises

Review Exercises

6.11 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**7. Functions of Random Variables (Optional)**

7.1 Introduction

7.2 Transformations of Variables

7.3 Moments and Moment-Generating Functions

Exercises

**8. Sampling Distributions and More Graphical Tools**

8.1 Random Sampling and Sampling Distributions

8.2 Some Important Statistics

Exercises

8.3 Sampling Distributions

8.4 Sampling Distribution of Means and the Central Limit Theorem

Exercises

8.5 Sampling Distribution of *S*^{2}

8.6 *t*-Distribution

8.7 *F*-Distribution

8.8 Quantile and Probability Plots

Exercises

Review Exercises

8.9 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**9. One- and Two-Sample Estimation Problems**

9.1 Introduction

9.2 Statistical Inference

9.3 Classical Methods of Estimation

9.4 Single Sample: Estimating the Mean

9.5 Standard Error of a Point Estimate

9.6 Prediction Intervals

9.7 Tolerance Limits

Exercises

9.8 Two Samples: Estimating the Difference Between Two Means

9.9 Paired Observations

Exercises

9.10 Single Sample: Estimating a Proportion

9.11 Two Samples: Estimating the Difference between Two Proportions

Exercises

9.12 Single Sample: Estimating the Variance

9.13 Two Samples: Estimating the Ratio of Two Variances

Exercises

9.14 Maximum Likelihood Estimation (Optional)

Exercises

Review Exercises

9.15 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**10. One- and Two-Sample Tests of Hypotheses**

10.1 Statistical Hypotheses: General Concepts

10.2 Testing a Statistical Hypothesis

10.3 The Use of *P*-Values for Decision Making in Testing Hypotheses

Exercises

10.4 Single Sample: Tests Concerning a Single Mean

10.5 Two Samples: Tests on Two Means

10.6 Choice of Sample Size for Testing Means

10.7 Graphical Methods for Comparing Means

Exercises

10.8 One Sample: Test on a Single Proportion

10.9 Two Samples: Tests on Two Proportions

Exercises

10.10 One- and Two-Sample Tests Concerning Variances

Exercises

10.11 Goodness-of-Fit Test

10.12 Test for Independence (Categorical Data)

10.13 Test for Homogeneity

10.14 Two-Sample Case Study

Exercises

Review Exercises

10.15 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**11. Simple Linear Regression and Correlation**

11.1 Introduction to Linear Regression

11.2 The Simple Linear Regression Model

11.3 Least Squares and the Fitted Model

Exercises

11.4 Properties of the Least Squares Estimators

11.5 Inferences Concerning the Regression Coefficients

11.6 Prediction

Exercises

11.7 Choice of a Regression Model

11.8 Analysis-of-Variance Approach

11.9 Test for Linearity of Regression: Data with Repeated Observations 416

Exercises

11.10 Data Plots and Transformations

11.11 Simple Linear Regression Case Study

11.12 Correlation

Exercises

Review Exercises

11.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**12. Multiple Linear Regression and Certain Nonlinear Regression Models**

12.1 Introduction

12.2 Estimating the Coefficients

12.3 Linear Regression Model Using Matrices

Exercises

12.4 Properties of the Least Squares Estimators

12.5 Inferences in Multiple Linear Regression

Exercises

12.6 Choice of a Fitted Model through Hypothesis Testing

12.7 Special Case of Orthogonality (Optional)

Exercises

12.8 Categorical or Indicator Variables

Exercises

12.9 Sequential Methods for Model Selection

12.10 Study of Residuals and Violation of Assumptions

12.11 Cross Validation, *C*_{p}, and Other Criteria for Model Selection

Exercises

12.12 Special Nonlinear Models for Nonideal Conditions

Exercises

Review Exercises

12.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**13. One-Factor Experiments: General**

13.1 Analysis-of-Variance Technique

13.2 The Strategy of Experimental Design

13.3 One-Way Analysis of Variance: Completely Randomized Design (One-Way ANOVA)

13.4 Tests for the Equality of Several Variances

Exercises

13.5 Multiple Comparisons

Exercises

13.6 Comparing a Set of Treatments in Blocks

13.7 Randomized Complete Block Designs

13.8 Graphical Methods and Model Checking

13.9 Data Transformations In Analysis of Variance)

Exercises

13.10 Random Effects Models

13.11 Case Study

Exercises

Review Exercises

13.12 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**14. Factorial Experiments (Two or More Factors)**

14.1 Introduction

14.2 Interaction in the Two-Factor Experiment

14.3 Two-Factor Analysis of Variance

Exercises

14.4 Three-Factor Experiments

Exercises

14.5 Factorial Experiments for Random Effects and Mixed Models

Exercises

Review Exercises

14.6 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**15. 2**^{k} Factorial Experiments and Fractions

15.1 Introduction

15.2 The 2^{k} Factorial: Calculation of Effects and Analysis of Variance 598

15.3 Nonreplicated 2^{k} Factorial Experiment

Exercises

15.4 Factorial Experiments in a Regression Setting

15.5 The Orthogonal Design

Exercises

15.6 Fractional Factorial Experiments

15.7 Analysis of Fractional Factorial Experiments

Exercises

15.8 Higher Fractions and Screening Designs

15.9 Construction of Resolution III and IV Designs

15.10 Other Two-Level Resolution III Designs; The Plackett-Burman Designs

15.11 Introduction to Response Surface Methodology

15.12 Robust Parameter Design

Exercises

Review Exercises

15.13 Potential Misconceptions and Hazards; Relationship to Material in Other Chapters

**16. Nonparametric Statistics**

16.1 Nonparametric Tests

16.2 Signed-Rank Test

Exercises

16.3 Wilcoxon Rank-Sum Test

16.4 Kruskal-Wallis Test

Exercises

16.5 Runs Test

16.6 Tolerance Limits

16.7 Rank Correlation Coefficient

Exercises

Review Exercises

**17. Statistical Quality Control**

17.1 Introduction

17.2 Nature of the Control Limits

17.3 Purposes of the Control Chart

17.4 Control Charts for Variables

17.5 Control Charts for Attributes

17.6 Cusum Control Charts

Review Exercises

18 Bayesian Statistics

18.1 Bayesian Concepts

18.2 Bayesian Inferences

18.3 Bayes Estimates Using Decision Theory Framework

Exercises

Bibliography

A. Statistical Tables and Proofs

B. Answers to Odd-Numbered Non-Review Exercises

Index