Biostatistics

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1 Introduction to Biostatistics 1 1.1 Introduction 2 1.2 Some Basic Concepts 2 1.3 Measurement and Measurement Scales 5 1.4 Sampling and Statistical Inference 7 1.5 The Scientific Method and the Design of Experiments 13 1.6 Computers and Biostatistical Analysis 15 1.7 Summary 16 Review Questions and Exercises 17 References 18 2 Descriptive Statistics 19 2.1 Introduction 20 2.2 The Ordered Array 20 2.3 Grouped Data: The Frequency Distribution 22 2.4 Descriptive Statistics: Measures of Central Tendency 38 2.5 Descriptive Statistics: Measures of Dispersion 43 2.6 Summary 55 Review Questions and Exercises 57 References 63 3 Some Basic Probability Concepts 65 3.1 Introduction 65 3.2 Two Views of Probability: Objective and Subjective 66 3.3 Elementary Properties of Probability 68 3.4 Calculating the Probability of an Event 69 3.5 Bayes' Theorem, Screening Tests, Sensitivity, Specificity, and Predictive Value Positive and Negative 78 3.6 Summary 84 Review Questions and Exercises 85 References 90 4 Probability Distributions 92 4.1 Introduction 93 4.2 Probability Distributions of Discrete Variables 93 4.3 The Binomial Distribution 99 4.4 The Poisson Distribution 108 4.5 Continuous Probability Distributions 113 4.6 The Normal Distribution 116 4.7 Normal Distribution Applications 122 4.8 Summary 128 Review Questions and Exercises 130 References 133 5 Some Important Sampling Distributions 134 5.1 Introduction 134 5.2 Sampling Distributions 135 5.3 Distribution of the Sample Mean 136 5.4 Distribution of the Difference Between Two Sample Means 145 5.5 Distribution of the Sample Proportion 150 5.6 Distribution of the Difference Between Two Sample Proportions 154 5.7 Summary 157 Review Questions and Exercises 158 References 160 6 Estimation 161 6.1 Introduction 162 6.2 Confidence Interval for a Population Mean 165 6.3 The t Distribution 171 6.4 Confidence Interval for the Difference Between Two Population Means 177 6.5 Confidence Interval for a Population Proportion 185 6.6 Confidence Interval for the Difference Between Two Population Proportions 187 6.7 Determination of Sample Size for Estimating Means 189 6.8 Determination of Sample Size for Estimating Proportions 191 6.9 Confidence Interval for the Variance of a Normally Distributed Population 193 6.10 Confidence Interval for the Ratio of the Variances of Two Normally Distributed Populations 198 6.11 Summary 203 Review Questions and Exercises 205 References 210 7 Hypothesis Testing 214 7.1 Introduction 215 7.2 Hypothesis Testing: A Single Population Mean 222 7.3 Hypothesis Testing: The Difference Between Two Population Means 236 7.4 Paired Comparisons 249 7.5 Hypothesis Testing: A Single Population Proportion 257 7.6 Hypothesis Testing: The Difference Between Two Population Proportions 261 7.7 Hypothesis Testing: A Single Population Variance 264 7.8 Hypothesis Testing: The Ratio of Two Population Variances 267 7.9 The Type II Error and the Power of a Test 272 7.10 Determining Sample Size to Control Type II Errors 277 7.11 Summary 280 Review Questions and Exercises 282 References 300 8 Analysis of Variance 304 8.1 Introduction 305 8.2 The Completely Randomized Design 308 8.3 The Randomized Complete Block Design 334 8.4 The Repeated Measures Design 346 8.5 The Factorial Experiment 358 8.6 Summary 373 Review Questions and Exercises 376 References 408 9 Simple Linear Regression and Correlation 413 9.1 Introduction 414 9.2 The Regression Model 414 9.3 The Sample Regression Equation 417 9.4 Evaluating the Regression Equation 427 9.5 Using the Regression Equation 441 9.6 The Correlation Model 445 9.7 The Correlation Coefficient 446 9.8 Some Precautions 459 9.9 Summary 460 Review Questions and Exercises 464 References 486 10 Multiple Regression and Correlation 489 10.1 Introduction 490 10.2 The Multiple Linear Regression Model 490 10.3 Obtaining the Multiple Regression Equation 492 10.4 Evaluating the Multiple Regression Equation 501 10.5 Using the Multiple Regression Equation 507 10.6 The Multiple Correlation Model 510 10.7 Summary 523 Review Questions and Exercises 525 References 537 11 Regression Analysis: Some Additional Techniques 539 11.1 Introduction 540 11.2 Qualitative Independent Variables 543 11.3 Variable Selection Procedures 560 11.4 Logistic Regression 569 11.5 Summary 582 Review Questions and Exercises 583 References 597 12 The Chi-Square Distribution and the Analysis of Frequencies 600 12.1 Introduction 601 12.2 The Mathematical Properties of the Chi-Square Distribution 601 12.3 Tests of Goodness-of-Fit 604 12.4 Tests of Independence 619 12.5 Tests of Homogeneity 630 12.6 The Fisher Exact Test 636 12.7 Relative Risk, Odds Ratio, and the Mantel-Haenszel Statistic 641 12.8 Summary 655 Review Questions and Exercises 657 References 666 13 Nonparametric and Distribution-Free Statistics 670 13.1 Introduction 671 13.2 Measurement Scales 672 13.3 The Sign Test 673 13.4 The Wilcoxon Signed-Rank Test for Location 681 13.5 The Median Test 686 13.6 The Mann-Whitney Test 690 13.7 The Kolmogorov-Smirnov Goodness-of-Fit Test 698 13.8 The Kruskal-Wallis One-Way Analysis of Variance by Ranks 704 13.9 The Friedman Two-Way Analysis of Variance by Ranks 712 13.10 The Spearman Rank Correlation Coefficient 718 13.11 Nonparametric Regression Analysis 727 13.12 Summary 730 Review Questions and Exercises 732 References 747 14 Survival Analysis 750 14.1 Introduction 750 14.2 Time-to-Event Data and Censoring 751 14.3 The Kaplan-Meier Procedure 756 14.4 Comparing Survival Curves 763 14.5 Cox Regression: The Proportional Hazards Model 768 14.6 Summary 773 Review Questions and Exercises 774 References 777 15 Vital Statistics (Online) www.wiley.com/college/daniel 15.1 Introduction 15.2 Death Rates and Ratios 15.3 Measures of Fertility 15.4 Measures of Morbidity 15.5 Summary Review Questions and Exercises References Appendix: Statistical Tables A-1 Answers to Odd-Numbered Exercises A-107 Index I-1

Professor Emeritus, Georgia State University, Dr. Wayne W. Daniel taught statistics in the College of Business and the College of Allied Health Sciences for thirty years. Prior to joining the Georgia State University faculty, he was employed as a biostatistician at the Georgia Department of Public Health. Professor Daniel received his undergraduate degree from the University of Georgia, a Master of Public Health degree with biostatistics concentration from the University of North Carolina, Chapel Hill, and a Ph. D. in Public Health with concentration in biostatistics from the University of Oklahoma. During his academic career he served as a statistical consultant and authored and co-authored statistics related articles published in several scientific journals. Professor Daniel is the author of five statistics textbooks, including Biostatistics. Dr. Chad L. Cross is trained as a multidisciplinary scientist and holds advanced degrees in statistics, the life sciences, and the social sciences. He works primarily as a biostatistician, where he specializes in multivariate and nonparametric statistics, sampling and experimental design, and the application of novel techniques to nonstandard data sets. He has worked extensively with state and federal governments, academic scientists, and private consultancies. He is skilled and experienced in all aspects of research design and analysis. Dr. Cross actively pursues furthering his statistical knowledge and expertise by engaging in several professional and learned societies, including the American Statistical Association, with whom he carries the Accredited Professional Statistician credential.

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