Biostatistics

PREFACE vii

1 INTRODUCTION TO BIOSTATISTICS 1

1.1 Introduction, 2

1.2 Basic Concepts and Definitions, 2

1.3 Measurement and Measurement Scales, 5

1.4 Sampling and Statistical Inference, 7
Exercises, 12

1.5 The Scientific Method, 13
Exercises, 15

1.6 Computers and Technology, 15

1.7 Summary, 16

Review Questions and Exercises, 16

References, 17

2 DESCRIPTIVE STATISTICS 18

2.1 Introduction, 19

2.2 The Ordered Array, 19

2.3 Frequency Tables, 21
Exercises, 25

2.4 Measures of Central Tendency, 29

2.5 Measures of Dispersion, 34
Exercises, 41

2.6 Visualizing Data, 43
Exercises, 51

2.7 Summary, 51

Summary of Formulas for Chapter 2, 51

Review Questions and Exercises, 53

References, 56

3 SOME BASIC PROBABILITY CONCEPTS 57

3.1 Introduction, 57

3.2 Two Views of Probability: Objective and Subjective, 58

3.3 Elementary Properties of Probability, 60

3.4 Calculating the Probability of an Event, 61
Exercises, 68

3.5 Bayes' Theorem, Screening Tests, Sensitivity, Specificity, and Predictive Value Positive and Negative, 69
Exercises, 73

3.6 Summary, 74

Summary of Formulas for Chapter 3, 75

Review Questions and Exercises, 76

References, 79

4 PROBABILITY DISTRIBUTIONS 80

4.1 Introduction, 81

4.2 Probability Distributions of Discrete Variables, 81
Exercises, 86

4.3 The Binomial Distribution, 87
Exercises, 95

4.4 The Poisson Distribution, 96

Exercises, 100
4.5 Continuous Probability Distributions, 101

4.6 The Normal Distribution, 103
Exercises, 109

4.7 Normal Distribution Applications, 109
Exercises, 113

4.8 Summary, 114

Summary of Formulas for Chapter 4, 114

Review Questions and Exercises, 115

References, 117

5 SOME IMPORTANT SAMPLING DISTRIBUTIONS 119

5.1 Introduction, 119

5.2 Sampling Distributions, 120

5.3 Distribution of the Sample Mean, 121
Exercises, 128

5.4 Distribution of the Difference between Two Sample Means, 129
Exercises, 133

5.5 Distribution of the Sample Proportion, 134
Exercises, 136

5.6 Distribution of the Difference between Two Sample Proportions, 137
Exercises, 139

5.7 Summary, 139

Summary of Formulas for Chapter 5, 140

Review Questions and Exercises, 140

References, 141

6 ESTIMATION 143

6.1 Introduction, 144

6.2 Confidence Interval for a Population Mean, 147
Exercises, 152

6.3 The t Distribution, 153
Exercises, 157

6.4 Confidence Interval for the Difference between Two Population Means, 158
Exercises, 164

6.5 Confidence Interval for a Population Proportion, 165
Exercises, 166

6.6 Confidence Interval for the Difference between Two Population Proportions, 167
Exercises, 168

6.7 Determination of Sample Size for Estimating Means, 169
Exercises, 171

6.8 Determination of Sample Size for Estimating Proportions, 171
Exercises, 172

6.9 The Chi-Square Distribution and the Confidence Interval for the Variance of a Normally Distributed Population, 173
Exercises, 177

6.10 The F-Distribution and the Confidence Interval for the Ratio of the Variances of Two Normally Distributed Populations, 177
Exercises, 180

6.11 Summary, 181

Summary of Formulas for Chapter 6, 182

Review Questions and Exercises, 183

References, 186

7 HYPOTHESIS TESTING 189

7.1 Introduction, 190

7.2 Hypothesis Testing: A Single Population Mean, 200
Exercises, 211

7.3 Hypothesis Testing: The Difference between Two Population Means, 213
Exercises, 221

7.4 Paired Comparisons, 224
Exercises, 229

7.5 Hypothesis Testing: A Single Population Proportion, 232
Exercises, 234

7.6 Hypothesis Testing: The Difference between Two Population Proportions, 235
Exercises, 236

7.7 Hypothesis Testing: A Single Population Variance, 238
Exercises, 240

7.8 Hypothesis Testing: The Ratio of Two Population Variances, 241
Exercises, 244

7.9 The Type II Error and the Power of a Test, 245
Exercises, 249

7.10 Determining Sample Size to Control Type II Errors, 249
Exercises, 251

7.11 Summary, 251

Summary of Formulas for Chapter 7, 252

Review Questions and Exercises, 254

References, 264

8 ANALYSIS OF VARIANCE 267

8.1 Introduction, 268

8.2 The Completely Randomized Design, 271
Exercises, 289

8.3 The Randomized Complete Block Design, 294
Exercises, 301

8.4 The Repeated Measures Design, 305
Exercises, 313

8.5 The Factorial Experiment, 315
Exercises, 326

8.6 Summary, 329

Summary of Formulas for Chapter 8, 329

Review Questions and Exercises, 331

References, 350

9 SIMPLE LINEAR REGRESSION AND CORRELATION 354

9.1 Introduction, 355

9.2 The Regression Model, 355

9.3 The Sample Regression Equation, 357
Exercises, 364

9.4 Evaluating the Regression Equation, 366
Exercises, 380

9.5 Using the Regression Equation, 380
Exercises, 384

9.6 The Correlation Model, 384

9.7 The Correlation Coefficient, 386
Exercises, 394

9.8 Some Precautions, 397

9.9 Summary, 398

Summary of Formulas for Chapter 9, 399

Review Questions and Exercises, 401

References, 413

10 MULTIPLE REGRESSION AND CORRELATION 416

10.1 Introduction, 417

10.2 The Multiple Linear Regression Model, 417

10.3 Obtaining the Multiple Regression Equation, 418
Exercises, 423

10.4 Evaluating the Multiple Regression Equation, 427
Exercises, 433

10.5 Using the Multiple Regression Equation, 433
Exercises, 435

10.6 The Multiple Correlation Model, 435
Exercises, 443

10.7 Summary, 446

Summary of Formulas for Chapter 10, 447

Review Questions and Exercises, 448

References, 454

11 REGRESSION ANALYSIS: SOME ADDITIONAL TECHNIQUES 455

11.1 Introduction, 455

11.2 Qualitative Independent Variables, 459
Exercises, 472

11.3 Variable Selection Procedures, 474
Exercises, 478

11.4 Logistic Regression, 485
Exercises, 495

11.5 Poisson Regression, 497
Exercises, 503

11.6 Summary, 504

Summary of Formulas for Chapter 11, 505

Review Questions and Exercises, 506

References, 517

12 ThE CHI-SQUARE DISTRIBUTION AND THE ANALYSIS OF FREQUENCIES 519

12.1 Introduction, 520

12.2 The Mathematical Properties of the Chi-Square Distribution, 520

12.3 Tests of Goodness-of-Fit, 523
Exercises, 533

12.4 Tests of Independence, 535
Exercises, 544

12.5 Tests of Homogeneity, 545
Exercises, 551

12.6 The Fisher's Exact Test, 552
Exercises, 557

12.7 Relative Risk, Odds Ratio, and the Mantel-Haenszel Statistic, 557
Exercises, 567

12.8 Summary, 569

Summary of Formulas for Chapter 12, 570

Review Questions and Exercises, 571

References, 576

13 NONPARAMETRIC AND DISTRIBUTION-FREE STATISTICS 579

13.1 Introduction, 580

13.2 Measurement Scales, 581

13.3 The Sign Test, 581
Exercises, 588

13.4 The Wilcoxon Signed-Rank Test for Location, 589
Exercises, 593

13.5 The Median Test, 594
Exercises, 596

13.6 The Mann–Whitney Test, 597
Exercises, 602

13.7 The Kolmogorov–Smirnov Goodness-of-Fit Test, 604
Exercises, 610

13.8 The Kruskal–Wallis One-Way Analysis of Variance by Ranks, 610
Exercises, 615

13.9 The Friedman Two-Way Analysis of Variance by Ranks, 618
Exercises, 622

13.10 The Spearman Rank Correlation Coefficient, 623
Exercises, 629

13.11 Nonparametric Regression Analysis, 631
Exercises, 634

13.12 Summary, 634

Summary of Formulas for Chapter 13, 635

Review Questions and Exercises, 636

References, 644

14 SURVIVAL ANALYSIS 646

14.1 Introduction, 647

14.2 Time-to-Event Data and Censoring, 647

14.3 The Kaplan–Meier Procedure, 651
Exercises, 656

14.4 Comparing Survival Curves, 658
Exercises, 661

14.5 Cox Regression: The Proportional Hazards Model, 663
Exercises, 666

14.6 Summary, 667

Summary of Formulas for Chapter 14, 667

Review Questions and Exercises, 668

References, 669

15 VITAL STATISTICS 671

15.1 Introduction, 671

15.2 Death Rates and Ratios, 672
Exercises, 677

15.3 Measures of Fertility, 679
Exercises, 681

15.4 Measures of Morbidity, 682
Exercises, 683

15.5 Summary, 683

Summary of Formulas for Chapter 15, 684

Review Questions and Exercises, 685

References, 686

INDEX 689

The following supplements are available through your instructor

APPENDIX: STATISTICAL TABLES

ANSWERS TO SELECTED PROBLEMS