DAVID FREEDMANROBERT PISANIROGER PURVES

StatisticsFourth Edition

W • W • NORTON & COMPANY

NEW YORK • LONDON

ContentsPreface xv

PART I. DESIGN OF EXPERIMENTS

Chapter 1. Controlled Experiments

1. The Salk Vaccine Field Trial 32. The Portacaval Shunt 73. Historical Controls 84. Summary 10

Chapter 2. Observational Studies

1. Introduction 122. The Clofibrate Trial 133. More Examples 154. Sex Bias in Graduate Admissions5. Confounding 206. Review Exercises 247. Summary and Overview 27

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PART II. DESCRIPTIVE STATISTICS

Chapter 3. The Histogram

1. Introduction 312. Drawing a Histogram 353. The Density Scale 384. Variables 425. Controlling for a Variable 456. Cross-Tabulation 477. Selective Breeding 488. Review Exercises 509. Summary 56

Chapter 4. The Average and the Standard Deviation

1. Introduction 572. The Average 583. The Average and the Histogram 614. The Root-Mean-Square 665. The Standard Deviation 676. Computing the Standard Deviation 717. Using a Statistical Calculator 748. Review Exercises 749. Summary 76

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Chapter 5. The Normal Approximation for Data

1. The Normal Curve 782. Finding Areas under the Normal Curve 823. The Normal Approximation for Data 854. Percentiles 885. Percentiles and the Normal Curve 906. Change of Scale 927. Review Exercises 938. Summary 96

Chapter 6. Measurement Error

1. Introduction 972. Chance Error 973. Outliers 1024. Bias * 1035. Review Exercises 1046. Special Review Exercises 1057. Summary and Overview 108

Chapter 7. Plotting Points and Lines

1. Reading Points off a Graph 1102. Plotting Points 1123. Slope and Intercept 1134. Plotting Lines 1145. The Algebraic Equation for a Line 115

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PART HI. CORRELATION AND REGRESSION

Chapter 8. Correlation

1. The Scatter Diagram 1192. The Correlation Coefficient 1253. The SD Line 1304. Computing the Correlation Coefficient 1325. Review Exercises 1346. Summary 139

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Chapter 9. More about Correlation

1. Features of the Correlation Coefficient2. Changing SDs 1443. Some Exceptional Cases 1474. Ecological Correlations 1485. Association is Not Causation 1506. Review Exercises 1537. Summary 157

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Chapter 10. Regression

1. Introduction 1582. The Graph of Averages

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3. The Regression Method for Individuals 1654. The Regression Fallacy 1695. There Are Two Regression Lines 1746. Review Exercises 1767. Summary 178

Chapter 11. The R.M.S. Error for Regression

1. Introduction 1802. Computing the R.M.S. Error 1853. Plotting the Residuals 1874. Looking at Vertical Strips 1905. Using the Normal Curve Inside a Vertical Strip6. Review Exercises 1987. Summary 201

Chapter 12. The Regression Line

1. Slope and Intercept 2022. The Method of Least Squares 2083. Does the Regression Make Sense? 2114. Review Exercises 2135. Summary and Overview 216

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PART IV. PROBABILITY

Chapter 13. What Are the Chances?

1. Introduction 2212. Conditional Probabilities 2263. The Multiplication Rule 2284. Independence 2305. The Collins Case 2336. Review Exercises 2347. Summary 236

Chapter 14. More about Chance

1. Listing the Ways 2372. The Addition Rule 2413. Two FAQs (Frequently Asked Questions) 2434. The Paradox of the Chevalier De Mere 2485. Are Real Dice Fair? 2526. Review Exercises 2527. Summary 254

Chapter 15. The Binomial Formula

1. Introduction 2552. The Binomial Formula 2593. Review Exercises 2614. Special Review Exercises 2635. Summary and Overview 268

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PARTV. CHANCE VARIABILITY

Chapter 16. The Law of Averages

1. What Does the Law of Averages Say? 2732. Chance Processes 2783. The Sum of Draws 2794. Making a Box Model 2815. Review Exercises 2856. Summary 287

Chapter 17. The Expected Value and Standard Error

1. The Expected Value 2882. The Standard Error 2903. Using the Normal Curve 2944. AShort-Cut 2985. Classifying and Counting 2996. Review Exercises 3047. Postscript 3078. Summary 307

Chapter 18. The Normal Approximation for Probability Histograms

1. Introduction 3082. Probability Histograms 3103. Probability Histograms and the Normal Curve 3154. The Normal Approximation 3175. The Scope of the Normal Approximation 3196. Conclusion 3257. Review Exercises 3278. Summary 329

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PART VI. SAMPLING

Chapter 19. Sample Surveys

1. Introduction 3332. The Literary Digest Poll 3343. The Year the Polls Elected Dewey 3374. Using Chance in Survey Work 3395. How Well Do Probability Methods Work? 3426. A Closer Look at the Gallup Poll 3437. Telephone Surveys 3468. Chance Error and Bias 3489. Review Exercises 35110. Summary 353

Chapter 20. Chance Errors in Sampling

1. Introduction 3552. The Expected Value and Standard Error 3593. Using the Normal Curve 362

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4. The Correction Factor 3675. The Gallup Poll 3706. Review Exercises 3717. Summary 373

Chapter 21. The Accuracy of Percentages

1. Introduction 3752. Confidence Intervals 3813. Interpreting a Confidence Interval 3834. Caveat Emptor 3875. The Gallup Poll 3896. Review Exercises 3917. Summary 394

Chapter 22. Measuring Employment and Unemployment

1. Introduction 3952. The Design of the Current Population Survey 3963. Carrying out the Survey 3984. Weighting the Sample 4015. Standard Errors 4026. The Quality of the Data 4047. Bias 4048. Review Exercises 4059. Summary 407

Chapter 23. The Accuracy of Averages

1. -introduction 4092. The Sample Average 4153. Which SE? 4224. A Reminder 4245. Review Exercises 4256. Special Review Exercises 4287. Summary and Overview 436

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PARTVH. CHANCE MODELS

Chapter 24. A Model for Measurement Error

1. Estimating the Accuracy of an Average 4412. Chance Models 4453. The Gauss Model 4504. Conclusion 4545. Review Exercises 4556. Summary 457

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Chapter 25. Chance Models in Genetics

1. How Mendel Discovered Genes2. Did Mendel's Facts Fit His Model?3. The Law of Regression 465

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4. An Appreciation of the Model5. Review Exercises 4706. Summary and Overview 471

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PART VIII. TESTS OF SIGNIFICANCE

Chapter 26. Tests of Significance

1. Introduction 4752. The Null and the Alternative 4773. Test Statistics and Significance Levels 4784. Making a Test of Significance 4825. Zero-One Boxes 4836. Ther-Test 4887. Review Exercises 4958. Summary 500

Chapter 27. More Tests for Averages

1. The Standard Error for a Difference 5012. Comparing Two Sample Averages 5033. Experiments 5084. More on Experiments 5125. When Does the z-Test Apply? 5176. Review Exercises 5187. Summary 521

Chapter 28. The ChhStjuare Test

1. Introduction 5232. The Structure of the x2-Test 5303. How Fisher Used the x2-Test 5334. Testing Independence 5355. Review Exercises 5406. Summary 544

Chapter 29. A Closer Look at Tests of Significance

1. Was the Result Significant? 5452. Data Snooping 5473. Was the Result Important? 5524. The Role of the Model 5555. Does the Difference Prove the Point? 5606. Conclusion 5627. Review Exercises 5638. Special Review Exercises 5659. Summary and Overview 576

NotesAnswers to Exercises

TablesIndex

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501

523

545

A3A43

A104

A107