| Preface | xiii |
Part 1 | Introduction and Fundamental Ideas | 1 |
Chapter 1 | Statistics as Science | 2 |
1.1 | What You Will Learn in This Chapter | 2 |
1.2 | Introduction | 2 |
1.3 | Statistics: A Framework for Decision Making | 3 |
1.4 | Statistics and the Methodology of Science | 7 |
1.5 | Statistics as a Science | 9 |
| The Subject Matter of Statistics | 9 |
| Statistics and Science Interwined | 10 |
1.6 | Summary | 12 |
| Case Study: Was There Age Discrimination in a Public Utility? | 13 |
1.7 | Addendum for the Reader | 14 |
| Exercises | 17 |
Chapter 2 | Types of Variables, Measurements, and Explanation | 20 |
2.1 | What You Will Learn in This Chapter | 20 |
2.2 | Introduction | 20 |
2.3 | Types of Variables | 21 |
| Cardinal Measurement | 23 |
| Ordinal Measurement | 24 |
| Categorical Variables | 25 |
| Indices | 25 |
| Time Series | 26 |
2.4 | Random and Deterministic Variables | 26 |
2.5 | Summary | 32 |
| Case Study: Was There Age Discrimination in a Public Utility? | 32 |
| Exercises | 33 |
Part 2 | Descriptive Statistics | 37 |
Chapter 3 | How to Describe and Summarize Random Data by Graphical Procedures | 38 |
3.1 | What You Will Learn in This Chapter | 38 |
3.2 | Introduction | 38 |
3.3 | Describing Data by Box-and-Whisker Plots | 40 |
| The Median | 41 |
| The Range | 43 |
| Quartiles | 44 |
| Box-and-Whisker Plots | 45 |
3.4 | Plotting Relative Frequencies | 48 |
3.5 | Cumulative Frequencies | 51 |
3.6 | Histogram | 53 |
3.7 | Summary | 63 |
| Case Study: Was There Age Discrimination in a Public Utility? | 65 |
| Exercises | 69 |
Chapter 4 | Moments and the Shape of Histograms | 77 |
4.1 | What You Will Learn in This Chapter | 77 |
4.2 | Introduction | 77 |
4.3 | The Mean, a Measure of Location | 77 |
| An Aside on Notation | 79 |
| Averaging Grouped Data | 81 |
| Interpreting the Mean | 83 |
4.4 | The Second Moment as a Measure of Spread | 85 |
4.5 | General Definition of Moments | 88 |
| The Third Moment as a Measure of Skewness | 90 |
| The Fourth Moment as a Measure of Peakedness, or "Fat Tails" | 92 |
4.6 | Standardized Moments | 93 |
| Some Practical Uses for Higher Moments | 99 |
4.7 | Standardization of Variables | 104 |
| The Higher Moments about the Origin | 105 |
| Higher Moments and Grouped Data | 106 |
4.8 | Summary | 106 |
| Case Study: Was There Age Discrimination in a Public Utility? | 107 |
| Exercises | 110 |
Chapter 5 | The Description of Bivariate Data | 120 |
5.1 | What You Will Learn in This Chapter | 120 |
5.2 | Introduction | 120 |
5.3 | Three-Dimensional Histograms | 121 |
5.4 | Scatter Plots | 122 |
5.5 | Standardization for Pairs of Random Variables | 125 |
5.6 | Covariation and m[subscript 11], the First Cross Product Moment | 126 |
5.7 | Linear Statistical Relationships and the Correlation Coefficient | 135 |
5.8 | The Correlation Coefficient and Slope | 140 |
5.9 | Rank Correlation | 142 |
5.10 | Bivariate Categorical Data | 144 |
| Row Comparisons | 145 |
| Column Comparisons | 147 |
| Joint Comparisons | 148 |
5.11 | Summary | 152 |
| Case Study: Was There Age Discrimination in a Public Utility? | 153 |
| Exercises | 159 |
Part 3 | Probability and Distribution Theory | 169 |
Chapter 6 | The Theory of Statistics: An Introduction | 170 |
6.1 | What You Will Learn in This Chapter | 170 |
6.2 | Introduction | 171 |
6.3 | The Theory: First Steps | 173 |
| The Sample Space | 173 |
| Introducing Probabilities | 175 |
| Probabilities of Unions and Joint Events | 177 |
| A Mathematical Digression | 180 |
| Calculating the Probabilities of the Union of Events | 182 |
| The Definition of Probability for Sample Spaces of Discrete Events | 184 |
6.4 | Conditional Probability | 185 |
| Summing Up the Many Definitions of Probability | 190 |
6.5 | Random Variables: Intuition Made Formal | 191 |
| An Example Using Two Random Variables | 193 |
6.6 | Statistical Independence | 197 |
| Application of the Results to Continuous Random Variables | 199 |
| Consequences of the Equally Likely Principle | 200 |
6.7 | Summary | 202 |
| Case Study: Was There Age Discrimination in a Public Utility? | 203 |
| Excercises | 205 |
Chapter 7 | The Generation and Description of Discrete Probability Distributions | 214 |
7.1 | What You Will Learn in This Chapter | 214 |
7.2 | Introduction | 215 |
7.3 | Combinations and Permutations | 215 |
7.4 | Generating Binomial Probabilities | 220 |
| The Convolution Sum | 222 |
| Deriving the Binomial Distribution | 222 |
| Parameters and the Shape of the Probability Distribution | 228 |
| Theoretical Moments and the Shape of the Probability Distribution | 230 |
7.5 | Expectation | 236 |
| Moment-Generating Functions for Discrete Variables | 242 |
7.6 | The Cumulative Distribution Function | 246 |
7.7 | The Poisson Probability Distribution | 246 |
7.8 | Summary | 253 |
| Case Study: Was There Age Discrimination in a Public Utility? | 254 |
| Exercises | 254 |
Chapter 8 | The Generation of Some Continuous Probability Distributions | 267 |
8.1 | What You Will Learn in This Chapter | 267 |
8.2 | Introduction | 267 |
8.3 | How to Express Probability in Terms of Continuous Random Variables | 268 |
8.4 | Theoretical Moments and Density Functions | 277 |
8.5 | The Uniform Distribution | 278 |
8.6 | The Normal, or Gaussian, Density Function and the Central Limit Theorem | 281 |
| Standard Deviation and the Nonstandard Gaussian | 286 |
| The Gaussian, or Normal, Distribution as an Approximation to the Binomial Distribution | 288 |
| Moment-Generating Functions for Continuous Variables | 296 |
| The Chebyshev Inequality | 299 |
| Terminology | 301 |
8.7 | Summary | 302 |
| Case Study: Was There Age Discrimination in a Public Utility? | 303 |
| Exercises | 303 |
Part 4 | Basic Principles of Inference | 313 |
Chapter 9 | Elementary Sampling Theory | 314 |
9.1 | What You Will Learn in This Chapter | 314 |
9.2 | Introduction | 314 |
9.3 | An Illustrative Example | 316 |
9.4 | An Introduction to the Theory of Simple Random Sampling | 320 |
9.5 | Stratified Random Sampling | 325 |
9.6 | Summary | 329 |
| Case Study: Was There Age Discrimination in a Public Utility? | 330 |
| Exercises | 332 |
Chapter 10 | Estimation of Theoretical Moments and the Parameters of Probability Distributions | 337 |
10.1 | What You Will Learn in This Chapter | 337 |
10.2 | Introduction | 337 |
10.3 | Estimating Theoretical Moments: Large Sample Results | 339 |
10.4 | Estimating Moments and Parameters: Confidence Intervals and Small Sample Results | 347 |
| Estimating a Binomial Probability | 356 |
| Estimating the Poisson Parameter | 360 |
| The Student's T Distribution | 363 |
| The Chi-square Distribution and Confidence Intervals for the Variance | 372 |
10.5 | Maximum Likelihood Estimators | 375 |
10.6 | Summary | 379 |
| Case Study: Was There Age Discrimination in a Public Utility? | 380 |
| Exercises | 381 |
Chapter 11 | Hypothesis Testing: How to Discriminate between Two Alternatives | 393 |
11.1 | What You Will Learn in This Chapter | 393 |
11.2 | Introduction | 393 |
11.3 | The Basic Idea of Hypotheses Tests | 394 |
| A Digression on the Interpretation of Rejection Regions | 399 |
| How to Choose an Optimal Decision Rule | 399 |
| Why Type I Error Is Usually Small | 407 |
| The Special Rofe of the Null Hypothesis | 409 |
11.4 | Simple and Composite Hypotheses Tests | 411 |
11.5 | Two-Sided Hypotheses Tests | 415 |
11.6 | Tests of Proportions | 417 |
11.7 | Hypotheses Tests When the Variance Is Unknown | 418 |
| Testing the Difference between Two Means | 421 |
| An Aside on Statistical Significance | 425 |
| P Values | 426 |
11.8 | Some Practical Examples | 428 |
11.9 | Summary | 433 |
| Case Study: Was There Age Discrimination in a Public Utility? | 435 |
| Exercises | 436 |
Part 5 | Bivariate Distributions, Regression, and ANOVA | 449 |
Chapter 12 | The Generation of Bivariate and Conditional Probability Distributions | 450 |
12.1 | What You Will Learn in This Chapter | 450 |
12.2 | Introduction | 450 |
12.3 | Some Pragmatic Examples | 454 |
12.4 | The Generation of a Bivariate Discrete Distribution | 457 |
12.5 | The Generation of a Bivariate Continuous Distribution | 458 |
| The Conditional Normal Density Function | 468 |
| Moments of Joint and Conditional Density Functions | 470 |
12.6 | Bivariate and Conditional Distributions Obtained by Sampling | 474 |
12.7 | Summary | 476 |
| Case Study: Was There Age Discrimination in a Public Unility? | 476 |
| Exercises | 477 |
Chapter 13 | The Theory and Practice of Regression Analysis | 481 |
13.1 | What You Will Learn in This Chapter | 481 |
13.2 | Introduction | 481 |
13.3 | The Regression Model | 483 |
13.4 | Estimation and Inference: The Basics | 489 |
| The Coefficient of Determination and the Degree of Fit | 500 |
13.5 | Estimation and Inference: Confidence Intervals and Hypotheses Tests | 505 |
| Confidence Intervals for the Regression Parameters | 506 |
| Predicting the Dependent Variable | 508 |
| Confidence Intervals for the Error Term Standard Deviation | 515 |
| The F Distribution and Measuring the Goodness of Fit | 516 |
| Testing Hypotheses in Regression Equations | 520 |
| Calculations | 522 |
13.6 | The "Regression" in Regression Analysis | 524 |
13.7 | Summary | 527 |
| Case Study: Was There Age Discrimination in a Public Utility? | 528 |
| Exercises | 531 |
Chapter 14 | Comparing Populations through the Analysis of Variance | 541 |
14.1 | What You Will Learn in This Chapter | 541 |
14.2 | Introduction | 541 |
14.3 | An Introduction to One-Way Analysis of Variance | 543 |
| For Multiple Treatments, Which Is Best? | 550 |
| The Link to Regression Analysis | 555 |
14.4 | Summary | 558 |
| Case Study: Was There Age Discrimination in a Public Utility? | 559 |
| Exercises | 561 |
Part 6 | Retrospective | 567 |
Chapter 15 | Retrospective | 568 |
15.1 | What You Will Learn in This Chapter | 568 |
15.2 | Introduction | 568 |
15.3 | A Schematic Review of What You Have Learned | 568 |
15.4 | The Role of Statistics in Everyday Life | 572 |
| Case Study: Was There Age Discrimination in a Public Utility? | 574 |
15.5 | The Relationship between Science and Statistics | 575 |
15.6 | What Might You Learn Next in Statistics? | 576 |
| Exercises | 577 |
Part 7 | Appendixes | 581 |
Appendix A | Mathematical Appendix: Review of Concepts and Conventions | 582 |
A.1 | Notational Conventions | 583 |
A.2 | Indexing | 586 |
A.3 | Sigma Notation | 587 |
A.4 | Elementary Set Theory | 593 |
A.5 | Elements of Calculus | 596 |
| Exercises | 616 |
Appendix B | Directions for Using the Student Version of S-Plus 4.5 | 620 |
B.1 | Installing, Starting, and Closing S-Plus | 620 |
B.2 | Using S-Plus in This Text | 621 |
B.3 | General Notes about S-Plus | 621 |
B.4 | Data Files | 622 |
B.5 | Windows in S-Plus | 622 |
B.6 | Menu Bar Commands | 624 |
B.7 | Probability and Density Calculations | 628 |
B.8 | Statistical Tables | 636 |
| Supplemental Material | |
Supplement C | Nonparametric Measures | |
Supplement D | Bayesian Inference | |
| Index | 643 |