CONTENTS Preface ... xvii 1 Introduction Ⅰ. Data : The Key Component of Study ... 2 Ⅱ. Replication : Part of the Scientific method ... 5 Ⅲ. Contents ... 5 Exercises ... 7 References ... 7 2 Data and Numbers Ⅰ. Data : Numerical Representation ... 9 Ⅱ. Observations and Variables ... 10 Ⅲ. Scales Used with Variables ... 11 Ⅳ. Reliability and Validity ... 12 Ⅴ. Randomized Response Technique ... 14 Ⅵ. Common Data Problems ... 16 Ⅶ. Concluding Remarks ... 19 Exercises ... 19 References ... 21 3 Sampling Ⅰ. What and Why sampling ... 23 Ⅱ. Sampling and Selection Bias ... 25 Ⅲ. Importance of Probability Sampling ... 27 Ⅳ. Simple Random Sampling ... 27 Ⅴ. Complex Sampling Designs ... 30 Ⅵ. Problems Caused by Unintended Sampling ... 31 Ⅶ. Concluding Remarks ... 35 Exercises ... 35 References ... 38 4 Descriptive Tools Ⅰ. Use of the Computer : MINITAB ... 39 Ⅱ. Tabular and Graphical Presentation ... 42 A. Frequency Tables ... 42 B. Line Graphs ... 45 C. Bar Charts ... 49 D. Histograms ... 51 E. Stem-and-Leaf Plot ... 57 F. Scatter Plot ... 60 Ⅲ. Measures of Central Tendency ... 61 A. Mean, Median, and Mode ... 62 B. Use of the measures of Central Tendency ... 64 C. The Geometric Mean ... 64 Ⅳ. Measures of Variability ... 68 A. Range and Percentiles ... 68 B. Box Plot ... 70 C. Variance and Standard Deviation ... 71 Ⅴ. Rates : Crude, Specific, and Adjusted ... 77 A. Crude and Specific Rates ... 78 B. Adjusted Rates ... 79 Ⅵ. Correlation Coefficients ... 82 A. Pearson Correlation Coefficient ... 83 B. Spearman Rank Correlation Coefficient ... 85 Ⅶ. Concluding Remarks ... 86 Exercises ... 87 References ... 92 5 Probability and Life Tables Ⅰ. A Definition of Probability ... 93 Ⅱ. Rules for Calculating Probabilities ... 95 A. Addition Rule for Probabilities ... 96 B. Conditional Probabilities ... 97 C. Independent Events ... 101 Ⅲ. Definitions from Epidemiology ... 102 A. Prevalence and Incidence ... 102 B. Sensitivity, Specificity, and Predicted Value Positive and Negative ... 104 Ⅳ. Bayes Theorem ... 105 Ⅴ. Probability in Sampling ... 107 Ⅵ. Estimating Probabilities by Simulation ... 109 Ⅶ. Probability and the Life Table ... 112 A. The first Four Columns in the Life Table ... 114 B. Some Uses of the Life Table ... 116 C. Expected Values in the Life Table ... 118 D. Columns 5, 6 and 7 in the Life Table ... 119 Ⅷ. Concluding Remarks ... 121 Exercises ... 121 References ... 124 6 Probability Distributions Ⅰ. The Binomial Distribution ... 125 A. Mean and Variance of the Binomial Distribution ... 132 B. Example : Use of the Binomial Distribution ... 133 C. Shapes of the Binomial Distribution ... 134 Ⅱ. The Poisson Distribution ... 136 A. Mean and Variance of the Poisson Distribution ... 139 B. Example 1 : Finding Poisson Probabilities ... 139 C. Cxample 2 : Use of the Poisson Distribution ... 141 Ⅲ. The Normal Distribution ... 143 A. Transforming Normally Distributed Data to the Standard Normal Distribution ... 146 B. Calculation of Normal Probabilities ... 147 C. The Normal Probability Plot ... 154 Ⅳ. The Central Limit theorem ... 157 Ⅴ. Approximations to the Binomial and Poisson Distribution ... 161 A. Normal Approximations to the Binomial Distribution ... 162 B. Poisson Approximations to the Binomial Distribution ... 167 C. Normal Approximations to the Binomial Distribution ... 168 Ⅵ. Concluding Remarks ... 173 Exercises ... 174 References ... 176 7 Interval Estimation Ⅰ. Prediction, Confidence, and Tolerance Intervals ... 178 Ⅱ. Distribution-Free Intervals ... 178 A. Prediction Interval ... 178 B. Confidence Interval ... 180 C. Tolerance Interval ... 184 Ⅲ. Intervals Based on the Normal distribution ... 186 A. Confidence Interval for the Mean ... 186 B. Confidence Interval for Proportion ... 195 C. Confidence Interval for Crude and Adjusted Rates ... 199 D. Confidence Interval for Variance ... 203 E. Confidence Interval for Pearson Correlation Coefficient ... 209 F. Confidence Interval for Difference of Two Mean ... 212 G. Confidence Interval for Difference of Two Proportions ... 221 H. Prediction and Tolerance Intervals Bassed on the Normal Distribution ... 223 Ⅳ. Concluding Remarks ... 224 Exercises ... 224 References ... 230 8 Designed Experiments Ⅰ. Sample Survey and Experiments ... 233 Ⅱ. Example of an Experiment ... 234 Ⅲ. Comparison Croups and Randomization ... 235 Ⅳ. Random Assignment and Sample Size ... 236 Ⅴ. Single-and Double-Blind Experiments ... 240 Ⅵ. Blocking and Extraneous Variables ... 242 Ⅶ. Limitations of Experiments ... 243 Ⅷ. Concluding Remarks ... 245 Exercises ... 245 References ... 249 9 Tests of Hypotheses Ⅰ. Definitions of Terms Used in Hypothesis testing ... 252 A. Null and Alternative Hypotheses ... 253 B. Type Ⅰ and Type Ⅱ Errors ... 253 C. The Test Statistic ... 254 Ⅱ. Determination of the Decision Rule ... 254 A. One-and Two-sided Tests ... 255 B. Calculation of the Probabilities of Type Ⅰ and Type Ⅱ Errors ... 256 Ⅲ. Relationship of the Decision Rule, α and β ... 257 A. What Are Reasonable Values for α and β ? ... 257 B. Ways to Decrease β Without Increasing α ... 258 Ⅳ. Conducting the Test ... 261 A. The p Value ... 262 B. Statistical and Practical Significance ... 263 Ⅴ. Tests of Hypotheses and Confidence Intervals ... 263 Ⅵ. Concluding Remarks ... 264 Exercises ... 264 References ... 265 10 Nonparametric Tests Ⅰ. The Sign Test ... 267 A. Descriptive Statistics ... 268 B. Hypothesis of Interest ... 269 C. Population ... 270 D. Conducting the Test ... 270 E. Power of the Test ... 271 F. The STEST Command ... 271 Ⅱ. Wilcoxon Signed Rank Test ... 272 A. Expected Value of the Signed Rank sum under the Null Hypothesis ... 273 B. Determination of the Critical Region ... 274 C. Conduction the Test ... 275 D. The WTEST Command ... 275 E. The Sign Test and the WSR Test ... 276 F. Ties in the data ... 276 G. The Normal Approximation ... 276 Ⅲ. Wilcoxon Rank Sum Test ... 277 A. Expected Value of the Rank Sum under the Null Hypothesis ... 278 B. Determination of the Critical Region ... 279 C. Conduction the Test ... 281 D. Mann-Whitney Command ... 281 E. The Normal Approximation ... 282 Ⅳ. Kruskal-Wallis Test ... 283 A. The Test Statistic and its Distribution ... 284 B. Conducting the Test ... 284 C. Kruskal-Wallis Command ... 284 Ⅴ. Concluding Remarks ... 286 Exercises ... 286 References ... 290 11 Analysis of Categorical Data Ⅰ. Goodness-of-Fie Test ... 292 A. No Parameter Estimation Required ... 293 B. Parameter Estimation Required ... 294 Ⅱ. 2 by 2 Contingency Table ... 296 A. Comparing Two Independent Binomial Proportions ... 297 B. Expected Cell counts Assuming No Association ... 297 C. The Odds Ratio : A Measure of Association ... 298 D. Data Collection ... 299 E. Calculation of the Confidence Interval for the difference in Proportions ... 299 F. The test Statistic and Its Calculation ... 300 G. Confidence interval for the Odds Ratio ... 301 Ⅲ. r by c Contingency Table ... 303 A. Hypothessis of No Association ... 303 B. Hypothessis of No Trend ... 306 Ⅳ. Multiple 2 by 2 Contigency Table ... 308 A. Analyzing the Tables Separately ... 308 B. The Cochran-Mantel-Haenszel Test ... 310 C. The Mantel-Haenszel Common Odds Ratio ... 313 Ⅴ. Concluding Remarks ... 313 Exercises ... 314 References ... 318 12 Analysis of Survival Data Ⅰ. Data Collection in Follow-Up Studies ... 320 Ⅱ. The Life Table method ... 322 Ⅲ. Product-Limit Method ... 330 Ⅳ. Comparison of Two Survival Distributions ... 337 Ⅴ. Concluding Remarks ... 342 Exercises ... 342 References ... 345 13 Tests of Hypotheses Based on the Normal Distribution Ⅰ. Testing Hypotheses about the Mean ... 348 A. Known Variance ... 348 B. UnKnown Variance ... 357 Ⅱ. Testing Hypotheses about the Proportion ... 358 Ⅲ. Testing Crude and Adjusted Rates ... 359 Ⅳ. Testing Hypotheses about the Variance ... 360 Ⅴ. Testing Hypotheses about the Pearson Correlation Coefficient ... 362 Ⅵ. Testing Hypotheses about the Differences of Two Means ... 364 A. Independent Means ... 364 B. Test about the Difference of Two dependent Means ... 370 Ⅶ. Testing Hypotheses about the Differences of Two Proportions ... 371 Ⅷ. Concluding Remarks ... 373 Exercises ... 373 References ... 377 14 Analysis of Variance Ⅰ. Assumptions for the Use of the ANOVA ... 380 Ⅱ. One-Way ANOVA ... 380 A. Sums of Squares and Mean Squares ... 382 B. The F Statistic ... 383 C. The ANOVA Table ... 384 D. Analysis of the Ages ... 385 Ⅲ. Multiple Comparisons ... 386 A. Error Rates : individual and Family ... 387 B. Tukey-Kramer Method ... 387 C. Fishers Least Significant difference Method ... 388 D. Dunnetts Method ... 389 E. Analysis by Computer ... 390 Ⅳ. Two-Way ANOVA for the Randomized Block Design with m Replicates ... 391 Ⅴ. Two-Way ANOVA with Interaction ... 395 Ⅵ. Linear Model Representation of the ANOVA ... 401 A. Linear Model for the Completely Randomized Design ... 401 B. Linear Model for the Randomized Block Design with m Replicates ... 402 C. Two-Way ANOVA with Interaction ... 403 Ⅶ. Concluding Remarks ... 404 Exercises ... 404 References ... 406 15 Linear and Logistic Regression Ⅰ. Simple Linear Regression ... 410 Ⅱ. Estimation of the Coefficients ... 412 Ⅲ. The variance of γ ∣ X ... 414 Ⅳ. R 2 the Confficient of determination ... 417 Ⅴ. Inference about the Coefficients ... 418 A. Assumptions for Inference in Linear Regression ... 419 B. Regression Deagnostics ... 420 C. Slope Coefficient ... 423 D. Y-Intercept Coefficient ... 425 E. An ANOVA Table Summary ... 426 Ⅵ. Interval Estimation for μ Y∣ X and Y ∣ X ... 427 A. Confidence Interval for μ Y∣ X ... 427 B. Prediction Interval for Y ∣ X ... 429 Ⅶ. Introduction to Multiple Linear Regression ... 434 Ⅷ. Introduction to Logistic Regression ... 440 Ⅸ. Concluding Remarks ... 444 Exercises ... 445 References ... 449 APPENDIX A SAS and Stata Commands Ⅰ. SAS Commands ... 452 Ⅱ. Stata Commands ... 481 References ... 503 APPENDIX B Statistical Tables List of Tables ... 505 APPENDIX C Selected Governmental Biostatistical data Ⅰ. Population Census Data ... 539 Ⅱ. Vital Statistics ... 540 Ⅲ. Sample Surveys ... 541 Ⅳ. Life Tables ... 543 APPENDIX D Solutions to Selected Exercises Chapter 1 ... 545 Chapter 2 ... 546 Chapter 3 ... 546 Chapter 4 ... 547 Chapter 5 ... 547 Chapter 6 ... 547 Chapter 7 ... 548 Chapter 8 ... 548 Chapter 9 ... 549 Chapter 10 ... 549 Chapter 11 ... 549 Chapter 12 ... 550 Chapter 13 ... 550 Chapter 14 ... 551 Chapter 15 ... 551 Index ... 553