Preface
1 Introduction
1.1 A Brief History
1.2 Some Examples
1.3 A Chapter Summary
2 Probability
2.1 Introduction...............
2.2 Sample Spaces and the Algebra of Sets
2.3 . The Probability Function .
2.4 Conditional Probability .
2.5 Independence . . . . . . .
2.6 Combinatorics.......
2.7 Combinatorial Probability
2.8 Taking a Second Look at Statistics (Enumeration and
Monte Carlo Techniques) ................
3 Random Variableli
3.1 Introduction..................
3.2 Binomial and Hypergeometric Probabilities
3.3 Discrete Random Variables . .
3.4 Continuous Random Variables
3.5 Expected Values.
3.6 The Variance. . . . . . . . . . .
3.7 Joint Densities . . . . . . . . . .
3.8 Combining Random Variables.
3.9 Further Properties of the Mean and Variance
3.10 Order Statistics .........
3.11 Conditional Densities. . . . . . . . . . . . . .
3.12 Moment-Generating Functions ........
3.13 Taking a Second Look at Statistics (Intotpreting Means)
Appendix 3.A.1 MINIT AB Applications . . . . . . . . . . . .
4 Special Distributions
4.1 Introduction.......
4.2 The Poisson Distribution
4.3 The Normal Distribution
4.4 The Geometric Distribution
4.5 The Negative Binomial Distribution.
4.6 The Gamma Distribution
4.7 Taking a Second Look at Statistics (Monte Carlo
Simulations)
Appendix 4.A.l MINITAB Applications.
Appendix 4.A.2 A Proof of the Central Limit Theorem
5 Estimation
5.1 Introduction
5.2 Estimating Parameters: The Method of Maximum Likelihood
and the Method of Moments
5.3 Interval Estimation
5.4 Properties of Estimators
5.5 Minimum-Variance Estimators: The Cramer-Rao Lower Bound . 394
5.6 Sufficient Estimators
5.7 Consistency
5.8 Bayesian Estimation
5.9 Taking a Second Look at Statistics (Revisiting the Margin of Error) . 423
Appendix 5.A.1 MINIT AB Applications
6 Hypothesis Testing
6.1 Introduction .
6.2 The Decision Rule.
6.3 Testing Binomial Data-Ho: P = Po
6.4 Type I and Type IT Errors
6.5 A Notion of Optimality: The Generalized Likelihood Ratio
6.6 Taking a Second Look at Statistics (Statistical Significance
versus "Practical" Significance)
7 The Normal Distribution
7.1 Introduction
7.2 Comparing In and J; In
7.3 Deriving the Distribution of %/
7.4 Drawing Inferences About J1
7.5 Drawing Inferences About a 2
7.6 Taking a Second Look at Statistics ("Bad" Estimators) .
Appendix 7.Al MINIT AB Applications
Appendix 7.A2 Some Distribution Results for Y and S2 . . .
Appendix 7.A3 A Proof of Theorem 7.5.2
Appendix 7.A4 A Proof that the One-Sample t Test Is a GLRT
8 Types of Data: A Brief Overview
8.1 Introduction
8.2 Classifying Data
8.3 Taking a Second Look at Statistics (Samples Are Not "Valid")
9 Two-Sample Problems
9.1 Introduction
9.2 Testing Ho: fLx = fLy-The Two-Sample t Test.
9.3 Testing Ho: a = ai-The FTest
9.4 Binomial Data: Testing Ho: px = py
9.5 Confidence Intervals for the Two-Sample Problem
9.6 Taking a Second Look at Statistics (Choosing Samples)
Appendix 9.A.l A Derivation of the Two-Sample t Test
(A Proof of Theorem 9.2.2)
Appendix 9.A.2 MINITAB Applications
10 Goodness-of-Fit Tests
10.1 Introduction
10.2 The Multinomial Distribution
10.3 Goodness-of-Fit Tests: All Parameters Known
10.4 Goodness-of-Fit Tests: Parameters Unknown
10.5 Contingency Tables
10.6 Taking a Second Look at Statistics (Outliers) .
Appendix 1O.A.l MINITAB Applications
U Regression
11.1 Introduction
11.2 The Method of Least Squares
11.3 TheLinearModel
11.4 Covariance and Correlation
11.5 The Bivariate Normal Distribution
11.6 Taking a Second Look at Statistics (How Not to Interpret the Sample
Correlation Coefficient)
Appendix 11.A.l MINITAB Applications
Appendix 11.A.2 A Proof of Theorem
12 The Analysis of Variance
12.1 Introduction
12.2 The F Test
12.3 Multiple Comparisons: Tukey's Method
12.4 Testing Subhypotheses with Contrasts
12.5 Data Transformations
12.6 Taking a Second Look at Statistics (Putting the Subject of Statistics
Together-The Contributions of Ronald A. Fisher)
Appendix 12.A.l MINITAB Applications
Appendix 12.A.2 A Proof of Theorem
Appendix 12.A.3
13 Randomized Block Designs
13.1 Introduction
13.2 The FTest for a Randomized Block Design
13.3 The Paired t Test
13.4 Taking a Second Look at Statistics (Choosing Between a Two-Sample
t Test and a Paired t Test)
Appendix 13.A.l MINITAB Applications .
14 Nonparametric Statistics
14.1 Introduction
14.2 The Sign Test
14.3 Wilcoxon Tests.
14.4 The Kruskal-Wallis Test
14.5 The Friedman Test
14.6 Testing for Randomness
14.7 Taking a Second Look at Statistics (Comparing Parametric and Nonparametric Procedures)
Appendix 14.A.1 MINITAB Applications
Appendix: Statistical Tables
Answers to Selected Odd-Numbered Questions
Bibliography
Index
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