Introduction to Biostatistics (eBook)

Front Cover 1
Introduction to Biostatistics: A Guide to Design, Analysis, and Discovery 4
Copyright Page 5
Table of Contents 8
Dedication 6
Preface 18
CHAPTER 1. Introduction 20
I. DATA: THE KEY COMPONENT OF A STUDY 21
II. REPLICATION: PART OF THE SCIENTIFIC METHOD 24
III. CONTENTS 24
EXERCISES 26
REFERENCES 26
CHAPTER 2. Data and Numbers 28
I. DATA: NUMERICAL REPRESENTATION 28
II. OBSERVATIONS AND VARIABLES 29
III. SCALES USED WITH VARIABLES 30
IV. RELIABILITY AND VALIDITY 31
V. RANDOMIZED RESPONSE TECHNIQUE 33
VI. COMMON DATA PROBLEMS 35
VII. CONCLUDING REMARKS 38
EXERCISES 38
REFERENCES 40
CHAPTER 3. Sampling 42
I. WHAT AND WHY SAMPLING 42
II. SAMPLING AND SELECTION BIAS 44
III. IMPORTANCE OF PROBABILITY SAMPLING 46
IV. SIMPLE RANDOM SAMPLING 46
V. COMPLEX SAMPLING DESIGNS 49
VI. PROBLEMS CAUSED BY UNINTENDED SAMPLING 50
VII. CONCLUDING REMARKS 54
EXERCISES 54
REFERENCES 57
CHAPTER 4. Descriptive Tools 58
I. USE OF THE COMPUTER: MINITAB 58
II. TABULAR AND GRAPHICAL PRESENTATION 61
III. MEASURES OF CENTRAL TENDENCY 80
IV. MEASURES OF VARIABILITY 87
V. RATES: CRUDE, SPECIFIC, AND ADJUSTED 96
VI. CORRELATION COEFFICIENTS 101
VII. CONCLUDING REMARKS 105
EXERCISES 106
REFERENCES 111
CHAPTER 5. Probability and Life Tables 112
I. A DEFINITION OF PROBABILITY 112
II. RULES FOR CALCULATING PROBABILITIES 114
III. DEFINITIONS FROM EPIDEMIOLOGY 121
IV. BAYES' THEOREM 124
V. PROBABILITY IN SAMPLING 126
VI. ESTIMATING PROBABILITIES BY SIMULATION 128
VII. PROBABILITY AND THE LIFE TABLE 131
VIII. CONCLUDING REMARKS 140
EXERCISES 140
REFERENCES 143
CHAPTER 6. Probability Distributions 144
I. THE BINOMIAL DISTRIBUTION 144
II. THE POISSON DISTRIBUTION 155
III. THE NORMAL DISTRIBUTION 162
IV. THE CENTRAL LIMIT THEOREM 176
V. APPROXIMATIONS TO THE BINOMIAL AND POISSON DISTRIBUTIONS 180
VI. CONCLUDING REMARKS 192
EXERCISES 193
REFERENCES 195
CHAPTER 7. Interval Estimation 196
I. PREDICTION, CONFIDENCE, AND TOLERANCE INTERVALS 197
II. DISTRIBUTION-FREE INTERVALS 197
III. INTERVALS BASED ON THE NORMAL DISTRIBUTION 205
IV. CONCLUDING REMARKS 243
EXERCISES 243
REFERENCES 249
CHAPTER 8. Designed Experiments 252
I. SAMPLE SURVEYS AND EXPERIMENTS 252
II. EXAMPLE OF AN EXPERIMENT 253
III. COMPARISON GROUPS AND RANDOMIZATION 254
IV. RANDOM ASSIGNMENT AND SAMPLE SIZE 255
V. SINGLE- AND DOUBLE-BLIND EXPERIMENTS 259
VI. BLOCKING AND EXTRANEOUS VARIABLES 261
VII. LIMITATIONS OF EXPERIMENTS 262
VIII. CONCLUDING REMARKS 264
EXERCISES 264
REFERENCES 268
CHAPTER 9. Tests of Hypotheses 270
I. DEFINITIONS OF TERMS USED IN HYPOTHESIS TESTING 271
II. DETERMINATION OF THE DECISION RULE 273
III. RELATIONSHIP OF THE DECISION RULE, a AND ß 276
IV. CONDUCTING THE TEST 280
V. TESTS OF HYPOTHESES AND CONFIDENCE INTERVALS 282
VI. CONCLUDING REMARKS 283
EXERCISES 283
REFERENCE 284
CHAPTER 10. Nonparametric Tests 286
I. THE SIGN TEST 286
II. WILCOXON SIGNED RANK TEST 291
III. WILCOXON RANK SUM TEST 296
IV. KRUSKAL–WALLIS TEST 302
V. CONCLUDING REMARKS 305
EXERCISES 305
REFERENCES 309
CHAPTER 11. Analysis of Categorical Data 310
I. GOODNESS-OF-FIT TEST 311
II. 2 BY 2 CONTINGENCY TABLE 315
III. r BY c CONTINGENCY TABLE 322
IV. MULTIPLE 2 BY 2 CONTINGENCY TABLES 327
V. CONCLUDING REMARKS 332
EXERCISES 333
REFERENCES 337
CHAPTER 12. Analysis of Survival Data 338
I. DATA COLLECTION IN FOLLOW-UP STUDIES 339
II. THE LIFE-TABLE METHOD 341
III. PRODUCT-LIMIT METHOD 349
IV. COMPARISON OF TWO SURVIVAL DISTRIBUTIONS 356
V. CONCLUDING REMARKS 361
EXERCISES 361
REFERENCES 364
CHAPTER 13. Tests of Hypotheses Based on the Normal Distribution 366
I. TESTING HYPOTHESES ABOUT THE MEAN 367
II. TESTING HYPOTHESES ABOUT THE PROPORTION 377
III. TESTING CRUDE AND ADJUSTED RATES 378
IV. TESTING HYPOTHESES ABOUT THE VARIANCE 379
V. TESTING HYPOTHESES ABOUT THE PEARSON CORRELATION COEFFICIENT 381
VI. TESTING HYPOTHESES ABOUT THE DIFFERENCE OF TWO MEANS 383
VII. TESTING HYPOTHESES ABOUT THE DIFFERENCE OF TWO PROPORTIONS 390
VIII. CONCLUDING REMARKS 392
EXERCISES 392
REFERENCES 396
CHAPTER 14. Analysis of Variance 398
I. ASSUMPTIONS FOR THE USE OF THE ANOVA 399
II. ONE-WAY ANOVA 399
III. MULTIPLE COMPARISONS 405
IV. TWO-WAY ANOVA FOR THE RANDOMIZED BLOCK DESIGN WITH m REPLICATES 410
V. TWO-WAY ANOVA WITH INTERACTION 414
VI. LINEAR MODEL REPRESENTATION OF THE ANOVA 420
VII. CONCLUDING REMARKS 423
EXERCISES 423
REFERENCES 425
CHAPTER 15. Linear and Logistic Regression 428
I. SIMPLE LINEAR REGRESSION 429
II. ESTIMATION OF THE COEFFICIENTS 431
III. VARIANCE OF Y|X 433
IV. R2, THE COEFFICIENT OF DETERMINATION 436
V. INFERENCE ABOUT THE COEFFICIENTS 437
VI. INTERVAL ESTIMATION FOR µ.|. and .|. 446
VII. INTRODUCTION TO MULTIPLE LINEAR REGRESSION 453
VIII. INTRODUCTION TO LOGISTIC REGRESSION 459
IX. CONCLUDING REMARKS 463
EXERCISES 464
REFERENCES 468
APPENDIX A: SAS and Stata Commands 470
I. SAS COMMANDS 471
II. STATA COMMANDS 500
References 522
APPENDIX B: Statistical Tables 524
List of Tables 524
APPENDIX C: Selected Governmental Sources of Biostatistical Data 558
I. POPULATION CENSUS DATA 558
II. VITAL STATISTICS 559
III. SAMPLE SURVEYS 560
IV. LIFE TABLES 562
APPENDIX D: Solutions to Selected Exercises 564
Index 572