The elements of statistics : with applications to economics and the social sciences

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Designed for instructors 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 students' personal lives as they are to their future professional careers. Ramsey aims to develop statistically literacy - from 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 student 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.

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

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