简介
Summary:
Publisher Summary 1
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)
Publisher Summary 2
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 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 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.
Publisher Summary 3
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.
目录
Preface p. xiii
Introduction and Fundamental Ideas p. 1
Statistics as Science p. 2
What You Will Learn in This Chapter p. 2
Introduction p. 2
Statistics: A Framework for Decision Making p. 3
Statistics and the Methodology of Science p. 7
Statistics as a Science p. 9
The Subject Matter of Statistics p. 9
Statistics and Science Interwined p. 10
Summary p. 12
Case Study: Was There Age Discrimination in a Public Utility? p. 13
Addendum for the Reader p. 14
Exercises p. 17
Types of Variables, Measurements, and Explanation p. 20
What You Will Learn in This Chapter p. 20
Introduction p. 20
Types of Variables p. 21
Cardinal Measurement p. 23
Ordinal Measurement p. 24
Categorical Variables p. 25
Indices p. 25
Time Series p. 26
Random and Deterministic Variables p. 26
Summary p. 32
Case Study: Was There Age Discrimination in a Public Utility? p. 32
Exercises p. 33
Descriptive Statistics p. 37
How to Describe and Summarize Random Data by Graphical Procedures p. 38
What You Will Learn in This Chapter p. 38
Introduction p. 38
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
Plotting Relative Frequencies p. 48
Cumulative Frequencies p. 51
Histogram p. 53
Summary p. 63
Case Study: Was There Age Discrimination in a Public Utility? p. 65
Exercises p. 69
Moments and the Shape of Histograms p. 77
What You Will Learn in This Chapter p. 77
Introduction p. 77
The Mean, a Measure of Location p. 77
An Aside on Notation p. 79
Averaging Grouped Data p. 81
Interpreting the Mean p. 83
The Second Moment as a Measure of Spread p. 85
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
Standardized Moments p. 93
Some Practical Uses for Higher Moments p. 99
Standardization of Variables p. 104
The Higher Moments about the Origin p. 105
Higher Moments and Grouped Data p. 106
Summary p. 106
Case Study: Was There Age Discrimination in a Public Utility? p. 107
Exercises p. 110
The Description of Bivariate Data p. 120
What You Will Learn in This Chapter p. 120
Introduction p. 120
Three-Dimensional Histograms p. 121
Scatter Plots p. 122
Standardization for Pairs of Random Variables p. 125
Covariation and m[subscript 11], the First Cross Product Moment p. 126
Linear Statistical Relationships and the Correlation Coefficient p. 135
The Correlation Coefficient and Slope p. 140
Rank Correlation p. 142
Bivariate Categorical Data p. 144
Row Comparisons p. 145
Column Comparisons p. 147
Joint Comparisons p. 148
Summary p. 152
Case Study: Was There Age Discrimination in a Public Utility? p. 153
Exercises p. 159
Probability and Distribution Theory p. 169
The Theory of Statistics: An Introduction p. 170
What You Will Learn in This Chapter p. 170
Introduction p. 171
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
Conditional Probability p. 185
Summing Up the Many Definitions of Probability p. 190
Random Variables: Intuition Made Formal p. 191
An Example Using Two Random Variables p. 193
Statistical Independence p. 197
Application of the Results to Continuous Random Variables p. 199
Consequences of the Equally Likely Principle p. 200
Summary p. 202
Case Study: Was There Age Discrimination in a Public Utility? p. 203
Excercises p. 205
The Generation and Description of Discrete Probability Distributions p. 214
What You Will Learn in This Chapter p. 214
Introduction p. 215
Combinations and Permutations p. 215
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
Expectation p. 236
Moment-Generating Functions for Discrete Variables p. 242
The Cumulative Distribution Function p. 246
The Poisson Probability Distribution p. 246
Summary p. 253
Case Study: Was There Age Discrimination in a Public Utility? p. 254
Exercises p. 254
The Generation of Some Continuous Probability Distributions p. 267
What You Will Learn in This Chapter p. 267
Introduction p. 267
How to Express Probability in Terms of Continuous Random Variables p. 268
Theoretical Moments and Density Functions p. 277
The Uniform Distribution p. 278
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
Summary p. 302
Case Study: Was There Age Discrimination in a Public Utility? p. 303
Exercises p. 303
Basic Principles of Inference p. 313
Elementary Sampling Theory p. 314
What You Will Learn in This Chapter p. 314
Introduction p. 314
An Illustrative Example p. 316
An Introduction to the Theory of Simple Random Sampling p. 320
Stratified Random Sampling p. 325
Summary p. 329
Case Study: Was There Age Discrimination in a Public Utility? p. 330
Exercises p. 332
Estimation of Theoretical Moments and the Parameters of Probability Distributions p. 337
What You Will Learn in This Chapter p. 337
Introduction p. 337
Estimating Theoretical Moments: Large Sample Results p. 339
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
Maximum Likelihood Estimators p. 375
Summary p. 379
Case Study: Was There Age Discrimination in a Public Utility? p. 380
Exercises p. 381
Hypothesis Testing: How to Discriminate between Two Alternatives p. 393
What You Will Learn in This Chapter p. 393
Introduction p. 393
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
Simple and Composite Hypotheses Tests p. 411
Two-Sided Hypotheses Tests p. 415
Tests of Proportions p. 417
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
Some Practical Examples p. 428
Summary p. 433
Case Study: Was There Age Discrimination in a Public Utility? p. 435
Exercises p. 436
Bivariate Distributions, Regression, and ANOVA p. 449
The Generation of Bivariate and Conditional Probability Distributions p. 450
What You Will Learn in This Chapter p. 450
Introduction p. 450
Some Pragmatic Examples p. 454
The Generation of a Bivariate Discrete Distribution p. 457
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
Bivariate and Conditional Distributions Obtained by Sampling p. 474
Summary p. 476
Case Study: Was There Age Discrimination in a Public Unility? p. 476
Exercises p. 477
The Theory and Practice of Regression Analysis p. 481
What You Will Learn in This Chapter p. 481
Introduction p. 481
The Regression Model p. 483
Estimation and Inference: The Basics p. 489
The Coefficient of Determination and the Degree of Fit p. 500
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
The "Regression" in Regression Analysis p. 524
Summary p. 527
Case Study: Was There Age Discrimination in a Public Utility? p. 528
Exercises p. 531
Comparing Populations through the Analysis of Variance p. 541
What You Will Learn in This Chapter p. 541
Introduction p. 541
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
Summary p. 558
Case Study: Was There Age Discrimination in a Public Utility? p. 559
Exercises p. 561
Retrospective p. 567
Retrospective p. 568
What You Will Learn in This Chapter p. 568
Introduction p. 568
A Schematic Review of What You Have Learned p. 568
The Role of Statistics in Everyday Life p. 572
Case Study: Was There Age Discrimination in a Public Utility? p. 574
The Relationship between Science and Statistics p. 575
What Might You Learn Next in Statistics? p. 576
Exercises p. 577
Appendixes p. 581
Mathematical Appendix: Review of Concepts and Conventions p. 582
Notational Conventions p. 583
Indexing p. 586
Sigma Notation p. 587
Elementary Set Theory p. 593
Elements of Calculus p. 596
Exercises p. 616
Directions for Using the Student Version of S-Plus 4.5 p. 620
Installing, Starting, and Closing S-Plus p. 620
Using S-Plus in This Text p. 621
General Notes about S-Plus p. 621
Data Files p. 622
Windows in S-Plus p. 622
Menu Bar Commands p. 624
Probability and Density Calculations p. 628
Statistical Tables p. 636
Supplemental Material
Nonparametric Measures
Bayesian Inference
Index p. 643
Introduction and Fundamental Ideas p. 1
Statistics as Science p. 2
What You Will Learn in This Chapter p. 2
Introduction p. 2
Statistics: A Framework for Decision Making p. 3
Statistics and the Methodology of Science p. 7
Statistics as a Science p. 9
The Subject Matter of Statistics p. 9
Statistics and Science Interwined p. 10
Summary p. 12
Case Study: Was There Age Discrimination in a Public Utility? p. 13
Addendum for the Reader p. 14
Exercises p. 17
Types of Variables, Measurements, and Explanation p. 20
What You Will Learn in This Chapter p. 20
Introduction p. 20
Types of Variables p. 21
Cardinal Measurement p. 23
Ordinal Measurement p. 24
Categorical Variables p. 25
Indices p. 25
Time Series p. 26
Random and Deterministic Variables p. 26
Summary p. 32
Case Study: Was There Age Discrimination in a Public Utility? p. 32
Exercises p. 33
Descriptive Statistics p. 37
How to Describe and Summarize Random Data by Graphical Procedures p. 38
What You Will Learn in This Chapter p. 38
Introduction p. 38
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
Plotting Relative Frequencies p. 48
Cumulative Frequencies p. 51
Histogram p. 53
Summary p. 63
Case Study: Was There Age Discrimination in a Public Utility? p. 65
Exercises p. 69
Moments and the Shape of Histograms p. 77
What You Will Learn in This Chapter p. 77
Introduction p. 77
The Mean, a Measure of Location p. 77
An Aside on Notation p. 79
Averaging Grouped Data p. 81
Interpreting the Mean p. 83
The Second Moment as a Measure of Spread p. 85
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
Standardized Moments p. 93
Some Practical Uses for Higher Moments p. 99
Standardization of Variables p. 104
The Higher Moments about the Origin p. 105
Higher Moments and Grouped Data p. 106
Summary p. 106
Case Study: Was There Age Discrimination in a Public Utility? p. 107
Exercises p. 110
The Description of Bivariate Data p. 120
What You Will Learn in This Chapter p. 120
Introduction p. 120
Three-Dimensional Histograms p. 121
Scatter Plots p. 122
Standardization for Pairs of Random Variables p. 125
Covariation and m[subscript 11], the First Cross Product Moment p. 126
Linear Statistical Relationships and the Correlation Coefficient p. 135
The Correlation Coefficient and Slope p. 140
Rank Correlation p. 142
Bivariate Categorical Data p. 144
Row Comparisons p. 145
Column Comparisons p. 147
Joint Comparisons p. 148
Summary p. 152
Case Study: Was There Age Discrimination in a Public Utility? p. 153
Exercises p. 159
Probability and Distribution Theory p. 169
The Theory of Statistics: An Introduction p. 170
What You Will Learn in This Chapter p. 170
Introduction p. 171
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
Conditional Probability p. 185
Summing Up the Many Definitions of Probability p. 190
Random Variables: Intuition Made Formal p. 191
An Example Using Two Random Variables p. 193
Statistical Independence p. 197
Application of the Results to Continuous Random Variables p. 199
Consequences of the Equally Likely Principle p. 200
Summary p. 202
Case Study: Was There Age Discrimination in a Public Utility? p. 203
Excercises p. 205
The Generation and Description of Discrete Probability Distributions p. 214
What You Will Learn in This Chapter p. 214
Introduction p. 215
Combinations and Permutations p. 215
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
Expectation p. 236
Moment-Generating Functions for Discrete Variables p. 242
The Cumulative Distribution Function p. 246
The Poisson Probability Distribution p. 246
Summary p. 253
Case Study: Was There Age Discrimination in a Public Utility? p. 254
Exercises p. 254
The Generation of Some Continuous Probability Distributions p. 267
What You Will Learn in This Chapter p. 267
Introduction p. 267
How to Express Probability in Terms of Continuous Random Variables p. 268
Theoretical Moments and Density Functions p. 277
The Uniform Distribution p. 278
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
Summary p. 302
Case Study: Was There Age Discrimination in a Public Utility? p. 303
Exercises p. 303
Basic Principles of Inference p. 313
Elementary Sampling Theory p. 314
What You Will Learn in This Chapter p. 314
Introduction p. 314
An Illustrative Example p. 316
An Introduction to the Theory of Simple Random Sampling p. 320
Stratified Random Sampling p. 325
Summary p. 329
Case Study: Was There Age Discrimination in a Public Utility? p. 330
Exercises p. 332
Estimation of Theoretical Moments and the Parameters of Probability Distributions p. 337
What You Will Learn in This Chapter p. 337
Introduction p. 337
Estimating Theoretical Moments: Large Sample Results p. 339
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
Maximum Likelihood Estimators p. 375
Summary p. 379
Case Study: Was There Age Discrimination in a Public Utility? p. 380
Exercises p. 381
Hypothesis Testing: How to Discriminate between Two Alternatives p. 393
What You Will Learn in This Chapter p. 393
Introduction p. 393
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
Simple and Composite Hypotheses Tests p. 411
Two-Sided Hypotheses Tests p. 415
Tests of Proportions p. 417
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
Some Practical Examples p. 428
Summary p. 433
Case Study: Was There Age Discrimination in a Public Utility? p. 435
Exercises p. 436
Bivariate Distributions, Regression, and ANOVA p. 449
The Generation of Bivariate and Conditional Probability Distributions p. 450
What You Will Learn in This Chapter p. 450
Introduction p. 450
Some Pragmatic Examples p. 454
The Generation of a Bivariate Discrete Distribution p. 457
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
Bivariate and Conditional Distributions Obtained by Sampling p. 474
Summary p. 476
Case Study: Was There Age Discrimination in a Public Unility? p. 476
Exercises p. 477
The Theory and Practice of Regression Analysis p. 481
What You Will Learn in This Chapter p. 481
Introduction p. 481
The Regression Model p. 483
Estimation and Inference: The Basics p. 489
The Coefficient of Determination and the Degree of Fit p. 500
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
The "Regression" in Regression Analysis p. 524
Summary p. 527
Case Study: Was There Age Discrimination in a Public Utility? p. 528
Exercises p. 531
Comparing Populations through the Analysis of Variance p. 541
What You Will Learn in This Chapter p. 541
Introduction p. 541
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
Summary p. 558
Case Study: Was There Age Discrimination in a Public Utility? p. 559
Exercises p. 561
Retrospective p. 567
Retrospective p. 568
What You Will Learn in This Chapter p. 568
Introduction p. 568
A Schematic Review of What You Have Learned p. 568
The Role of Statistics in Everyday Life p. 572
Case Study: Was There Age Discrimination in a Public Utility? p. 574
The Relationship between Science and Statistics p. 575
What Might You Learn Next in Statistics? p. 576
Exercises p. 577
Appendixes p. 581
Mathematical Appendix: Review of Concepts and Conventions p. 582
Notational Conventions p. 583
Indexing p. 586
Sigma Notation p. 587
Elementary Set Theory p. 593
Elements of Calculus p. 596
Exercises p. 616
Directions for Using the Student Version of S-Plus 4.5 p. 620
Installing, Starting, and Closing S-Plus p. 620
Using S-Plus in This Text p. 621
General Notes about S-Plus p. 621
Data Files p. 622
Windows in S-Plus p. 622
Menu Bar Commands p. 624
Probability and Density Calculations p. 628
Statistical Tables p. 636
Supplemental Material
Nonparametric Measures
Bayesian Inference
Index p. 643
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