Sample Size Determination and Power

THOMAS P. RYAN, PhD, teaches online advanced statistics courses for Northwestern University and The Institute for Statistics Education in sample size determination, design of experiments, engineering statistics, and regression analysis.

• Preface xv1 Brief Review of Hypothesis Testing Concepts/Issues and Confidence Intervals 11.1 Basic Concepts of Hypothesis Testing, 11.2 Review of Confidence Intervals and Their Relationship to Hypothesis Tests, 51.3 Sports Applications, 91.4 Observed Power, Retrospective Power, Conditional Power, and Predictive Power, 91.5 Testing for Equality, Equivalence, Noninferiority, or Superiority, 101.5.1 Software, 11References, 12Exercises, 142 Methods of Determining Sample Sizes 172.1 Internal Pilot Study Versus External Pilot Study, 202.2 Examples: Frequentist and Bayesian, 242.2.1 Bayesian Approaches, 302.2.2 Probability Assessment Approach, 312.2.3 Reproducibility Probability Approach, 322.2.4 Competing Probability Approach, 322.2.5 Evidential Approach, 322.3 Finite Populations, 322.4 Sample Sizes for Confidence Intervals, 332.4.1 Using the Finite Population Correction Factor, 362.4.1.1 Estimating Population Totals, 382.5 Confidence Intervals on Sample Size and Power, 392.6 Specification of Power, 392.7 Cost of Sampling, 402.8 Ethical Considerations, 402.9 Standardization and Specification of Effect Sizes, 422.10 Equivalence Tests, 432.11 Software and Applets, 452.12 Summary, 47References, 47Exercises, 533 Means and Variances 573.1 One Mean, Normality, and Known Standard Deviation, 583.1.1 Using the Coefficient of Variation, 653.2 One Mean, Standard Deviation Unknown, Normality Assumed, 663.3 Confidence Intervals on Power and/or Sample Size, 673.4 One Mean, Standard Deviation Unknown, Nonnormality Assumed, 703.5 One Mean, Exponential Distribution, 713.6 Two Means, Known Standard Deviations—Independent Samples, 713.6.1 Unequal Sample Sizes, 743.7 Two Means, Unknown but Equal Standard Deviations—Independent Samples, 743.7.1 Unequal Sample Sizes, 763.8 Two Means, Unequal Variances and Sample Sizes—Independent Samples, 773.9 Two Means, Unknown and Unequal Standard Deviations—Independent Samples, 773.10 Two Means, Known and Unknown Standard Deviations—Dependent Samples, 783.11 Bayesian Methods for Comparing Means, 813.12 One Variance or Standard Deviation, 813.13 Two Variances, 833.14 More Than Two Variances, 843.15 Confidence Intervals, 843.15.1 Adaptive Confidence Intervals, 853.15.2 One Mean, Standard Deviation Unknown—With Tolerance Probability, 853.15.3 Difference Between Two Independent Means, Standard Deviations Known and Unknown—With and Without Tolerance Probability, 883.15.4 Difference Between Two Paired Means, 903.15.5 One Variance, 913.15.6 One-Sided Confidence Bounds, 923.16 Relative Precision, 933.17 Computing Aids, 943.18 Software, 943.19 Summary, 95Appendix, 95References, 96Exercises, 994 Proportions and Rates 1034.1 One Proportion, 1034.1.1 One Proportion—With Continuity Correction, 1074.1.2 Software Disagreement and Rectification, 1084.1.3 Equivalence Tests and Noninferiority Tests for One Proportion, 1094.1.4 Confidence Interval and Error of Estimation, 1104.1.5 One Proportion—Exact Approach, 1134.1.6 Bayesian Approaches, 1154.2 Two Proportions, 1154.2.1 Two Proportions—With Continuity Correction, 1194.2.2 Two Proportions—Fisher’s Exact Test, 1214.2.3 What Approach Is Recommended?, 1224.2.4 Correlated Proportions, 1234.2.5 Equivalence Tests for Two Proportions, 1244.2.6 Noninferiority Tests for Two Proportions, 1254.2.7 Need for Pilot Study?, 1254.2.8 Linear Trend in Proportions, 1254.2.9 Bayesian Method for Estimating the Difference of Two Binomial Proportions, 1264.3 Multiple Proportions, 1264.4 Multinomial Probabilities and Distributions, 1294.5 One Rate, 1304.5.1 Pilot Study Needed?, 1324.6 Two Rates, 1324.7 Bayesian Sample Size Determination Methods for Rates, 1354.8 Software, 1354.9 Summary, 136Appendix, 136References, 140Exercises, 1445 Regression Methods and Correlation 1455.1 Linear Regression, 1455.1.1 Simple Linear Regression, 1465.1.2 Multiple Linear Regression, 1505.1.2.1 Application: Predicting College Freshman Grade Point Average, 1555.2 Logistic Regression, 1555.2.1 Simple Logistic Regression, 1565.2.1.1 Normally Distributed Covariate, 1585.2.1.2 Binary Covariate, 1625.2.2 Multiple Logistic Regression, 1635.2.2.1 Measurement Error, 1655.2.3 Polytomous Logistic Regression, 1655.2.4 Ordinal Logistic Regression, 1665.2.5 Exact Logistic Regression, 1675.3 Cox Regression, 1675.4 Poisson Regression, 1695.5 Nonlinear Regression, 1725.6 Other Types of Regression Models, 1725.7 Correlation, 1725.7.1 Confidence Intervals, 1745.7.2 Intraclass Correlation, 1755.7.3 Two Correlations, 1755.8 Software, 1765.9 Summary, 177References, 177Exercises, 1806 Experimental Designs 1836.1 One Factor—Two Fixed Levels, 1846.1.1 Unequal Sample Sizes, 1866.2 One Factor—More Than Two Fixed Levels, 1876.2.1 Multiple Comparisons and Dunnett’s Test, 1926.2.2 Analysis of Means (ANOM), 1936.2.3 Unequal Sample Sizes, 1956.2.4 Analysis of Covariance, 1966.2.5 Randomized Complete Block Designs, 1976.2.6 Incomplete Block Designs, 1986.2.7 Latin Square Designs, 1996.2.7.1 Graeco-Latin Square Designs, 2026.3 Two Factors, 2036.4 2k Designs, 2056.4.1 22 Design with Equal and Unequal Variances, 2066.4.2 Unreplicated 2k Designs, 2066.4.3 Software for 2k Designs, 2086.5 2k − p Designs, 2096.6 Detecting Conditional Effects, 2106.7 General Factorial Designs, 2116.8 Repeated Measures Designs, 2126.8.1 Crossover Designs, 2156.8.1.1 Software, 2176.9 Response Surface Designs, 2186.10 Microarray Experiments, 2196.10.1 Software, 2206.11 Other Designs, 2206.11.1 Plackett–Burman Designs, 2206.11.2 Split-Plot and Strip-Plot Designs, 2226.11.3 Nested Designs, 2246.11.4 Ray designs, 2256.12 Designs for Nonnormal Responses, 2256.13 Designs with Random Factors, 2276.14 Zero Patient Design, 2286.15 Computer Experiments, 2286.16 Noninferiority and Equivalence Designs, 2296.17 Pharmacokinetic Experiments, 2296.18 Bayesian Experimental Design, 2296.19 Software, 2306.20 Summary, 232Appendix, 233References, 234Exercises, 2397 Clinical Trials 2437.1 Clinical Trials, 2457.1.1 Cluster Randomized Trials, 2477.1.2 Phase II Trials, 2477.1.2.1 Phase II Cancer Trials, 2477.1.3 Phase III Trials, 2477.1.4 Longitudinal Clinical Trials, 2487.1.5 Fixed Versus Adaptive Clinical Trials, 2487.1.6 Noninferiority Trials, 2497.1.7 Repeated Measurements, 2497.1.8 Multiple Tests, 2507.1.9 Use of Internal Pilot Studies for Clinical Trials, 2507.1.10 Using Historical Controls, 2507.1.11 Trials with Combination Treatments, 2517.1.12 Group Sequential Trials, 2517.1.13 Vaccine Efficacy Studies, 2517.2 Bioequivalence Studies, 2517.3 Ethical Considerations, 2527.4 The Use of Power in Clinical Studies, 2527.5 Preclinical Experimentation, 2537.6 Pharmacodynamic, Pharmacokinetic, and Pharmacogenetic Experiments, 2537.7 Method of Competing Probability, 2547.8 Bayesian Methods, 2557.9 Cost and Other Sample Size Determination Methods for Clinical Trials, 2567.10 Meta-Analyses of Clinical Trials, 2567.11 Miscellaneous, 2577.12 Survey Results of Published Articles, 2597.13 Software, 2607.14 Summary, 263References, 263Exercises, 2758 Quality Improvement 2778.1 Control Charts, 2778.1.1 Shewhart Measurement Control Charts, 2788.1.2 Using Software to Determine Subgroup Size, 2818.1.2.1 ¯X -Chart, 2828.1.2.2 S-Chart and S2-Chart, 2848.1.3 Attribute Control Charts, 2868.1.4 CUSUM and EWMA Charts, 2898.1.4.1 Subgroup Size Considerations for CUSUM Charts, 2908.1.4.2 CUSUM and EWMA Variations, 2918.1.4.3 Subgroup Size Determination for CUSUM and EWMA Charts and Their Variations, 2918.1.4.4 EWMA Applied to Autocorrelated Data, 2938.1.5 Adaptive Control Charts, 2938.1.6 Regression and Cause-Selecting Control Charts, 2938.1.7 Multivariate Control Charts, 2958.2 Medical Applications, 2968.3 Process Capability Indices, 2978.4 Tolerance Intervals, 2988.5 Measurement System Appraisal, 3008.6 Acceptance Sampling, 3008.7 Reliability and Life Testing, 3018.8 Software, 3018.9 Summary, 302References, 302Exercises, 3059 Survival Analysis and Reliability 3079.1 Survival Analysis, 3079.1.1 Logrank Test, 3089.1.1.1 Freedman Method, 3119.1.1.2 Other Methods, 3129.1.2 Wilcoxon–Breslow–Gehan Test, 3139.1.3 Tarone–Ware Test, 3139.1.4 Other Tests, 3149.1.5 Cox Proportional Hazards Model, 3149.1.6 Joint Modeling of Longitudinal and Survival Data, 3159.1.7 Multistage Designs, 3169.1.8 Comparison of Software and Freeware, 3169.2 Reliability Analysis, 3179.3 Summary, 318References, 319Exercise, 32110 Nonparametric Methods 32310.1 Wilcoxon One-Sample Test, 32410.1.1 Wilcoxon Test for Paired Data, 32710.2 Wilcoxon Two–Sample Test (Mann–Whitney Test), 32710.2.1 van Elteren Test—A Stratified Mann–Whitney Test, 33110.3 Kruskal–Wallis One-Way ANOVA, 33110.4 Sign Test, 33110.5 McNemar’s Test, 33410.6 Contingency Tables, 33410.7 Quasi-Likelihood Method, 33410.8 Rank Correlation Coefficients, 33510.9 Software, 33510.10 Summary, 336References, 336Exercises, 33911 Miscellaneous Topics 34111.1 Case–Control Studies, 34111.2 Epidemiology, 34211.3 Longitudinal Studies, 34211.4 Microarray Studies, 34311.5 Receiver Operating Characteristic ROC Curves, 34311.6 Meta-Analyses, 34311.7 Sequential Sample Sizes, 34311.8 Sample Surveys, 34411.8.1 Vegetation Surveys, 34411.9 Cluster Sampling, 34511.10 Factor Analysis, 34611.11 Multivariate Analysis of Variance and Other Multivariate Methods, 34611.12 Structural Equation Modeling, 34811.13 Multilevel Modeling, 34911.14 Prediction Intervals, 34911.15 Measures of Agreement, 35011.16 Spatial Statistics, 35011.17 Agricultural Applications, 35011.18 Estimating the Number of Unseen Species, 35111.19 Test Reliability, 35111.20 Agreement Studies, 35111.21 Genome-wide Association Studies, 35111.22 National Security, 35211.23 Miscellaneous, 35211.24 Summary, 353References, 354Answers to Selected Exercises 363Index 369

“This very comprehensive book is well structured.”  (International Statistical Review, 1 October 2015)“In summary, this book succeeds in the author’s aim of providing a general purpose text for readers interested in methodology without much technical fuss. In general, the book focuses on providing wealth of discussions and reviews for sample size and power and is an excellent source for up-to-date software and references for a wide range of topics related to sample size determination.”  (International Statistical Review, 1 March 2015)