For Introductory Computer courses in Microsoft Office 2003 or courses in Computer Concepts with a lab component for Microsoft Office 2003 applications.
Designed for readers who want to stress the understanding of basic concepts and the development of "statistical intuition," this book demonstrates that statistical reasoning is everywhere and that statistical concepts are as important to readers' personal lives as they are to their future professional careers. Ramsey aims to develop statistically literacyfrom the ability to read and think critically about statistics published in popular media to the ability to analyze and act upon statistics gathered in the business world. The underlying philosophy of this book is that given a reasonable level of depth in the analysis, the reader can later acquire a much more extensive, and even more intensive, exposure to statistics on their own or in the context of the work environment. Some use of calculus is included. Use of the computer is integrated throughout.
Written for sophomore-level undergraduates, this textbook provides an introduction to statistics, especially as they are used in the social sciences. It explains fundamental ideas and principles, including descriptive statistics, probability, distribution, inference, bivariate distributions, regression, and ANOVA. Appendixes review basic mathematical concepts and conventions, offer directions for the student version of S-Plus 4.5, and provide supplementary information on nonparametric measures and Bayesian inference. Ramsey teaches at New York University. Annotation c. Book News, Inc., Portland, OR (booknews.com)
| 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 |