Introduction to Statistics Through Resampling Methods and R

PHILLIP I. GOOD, PhD, is Operations Manager of Information Research, a consulting firm specializing in statistical solutions for private and public organizations. He has published over thirty scholarly works, more than 600 articles, and forty-four books, including Common Errors in Statistics (and How to Avoid Them) and A Manager's Guide to the Design and Conduct of Clinical Trials, both published by Wiley.

• Preface xi1. Variation 11.1 Variation 11.2 Collecting Data 21.2.1 A Worked-Through Example 31.3 Summarizing Your Data 41.3.1 Learning to Use R 51.4 Reporting Your Results 71.4.1 Picturing Data 81.4.2 Better Graphics 101.5 Types of Data 111.5.1 Depicting Categorical Data 121.6 Displaying Multiple Variables 121.6.1 Entering Multiple Variables 131.6.2 From Observations to Questions 141.7 Measures of Location 151.7.1 Which Measure of Location? 171.7.2 The Geometric Mean 181.7.3 Estimating Precision 181.7.4 Estimating with the Bootstrap 191.8 Samples and Populations 201.8.1 Drawing a Random Sample 221.8.2 Using Data That Are Already in Spreadsheet Form 231.8.3 Ensuring the Sample Is Representative 231.9 Summary and Review 232. Probability 252.1 Probability 252.1.1 Events and Outcomes 272.1.2 Venn Diagrams 272.2 Binomial Trials 292.2.1 Permutations and Rearrangements 302.2.2 Programming Your Own Functions in R 322.2.3 Back to the Binomial 332.2.4 The Problem Jury 332.3 Conditional Probability 342.3.1 Market Basket Analysis 362.3.2 Negative Results 362.4 Independence 382.5 Applications to Genetics 392.6 Summary and Review 403. Two Naturally Occurring Probability Distributions 433.1 Distribution of Values 433.1.1 Cumulative Distribution Function 443.1.2 Empirical Distribution Function 453.2 Discrete Distributions 463.3 The Binomial Distribution 473.3.1 Expected Number of Successes in n Binomial Trials 473.3.2 Properties of the Binomial 483.4 Measuring Population Dispersion and Sample Precision 513.5 Poisson: Events Rare in Time and Space 533.5.1 Applying the Poisson 533.5.2 Comparing Empirical and Theoretical Poisson Distributions 543.5.3 Comparing Two Poisson Processes 553.6 Continuous Distributions 553.6.1 The Exponential Distribution 563.7 Summary and Review 574. Estimation and the Normal Distribution 594.1 Point Estimates 594.2 Properties of the Normal Distribution 614.2.1 Student’s t-Distribution 634.2.2 Mixtures of Normal Distributions 644.3 Using Confidence Intervals to Test Hypotheses 654.3.1 Should We Have Used the Bootstrap? 654.3.2 The Bias-Corrected and Accelerated Nonparametric Bootstrap 664.3.3 The Parametric Bootstrap 684.4 Properties of Independent Observations 694.5 Summary and Review 705. Testing Hypotheses 715.1 Testing a Hypothesis 715.1.1 Analyzing the Experiment 725.1.2 Two Types of Errors 745.2 Estimating Effect Size 765.2.1 Effect Size and Correlation 765.2.2 Using Confidence Intervals to Test Hypotheses 785.3 Applying the t-Test to Measurements 795.3.1 Two-Sample Comparison 805.3.2 Paired t-Test 805.4 Comparing Two Samples 815.4.1 What Should We Measure? 815.4.2 Permutation Monte Carlo 825.4.3 One- vs. Two-Sided Tests 835.4.4 Bias-Corrected Nonparametric Bootstrap 835.5 Which Test Should We Use? 845.5.1 p-Values and Significance Levels 855.5.2 Test Assumptions 855.5.3 Robustness 865.5.4 Power of a Test Procedure 875.6 Summary and Review 896. Designing an Experiment or Survey 916.1 The Hawthorne Effect 916.1.1 Crafting an Experiment 926.2 Designing an Experiment or Survey 946.2.1 Objectives 946.2.2 Sample from the Right Population 956.2.3 Coping with Variation 976.2.4 Matched Pairs 986.2.5 The Experimental Unit 996.2.6 Formulate Your Hypotheses 996.2.7 What Are You Going to Measure? 1006.2.8 Random Representative Samples 1016.2.9 Treatment Allocation 1026.2.10 Choosing a Random Sample 1036.2.11 Ensuring Your Observations Are Independent 1036.3 How Large a Sample? 1046.3.1 Samples of Fixed Size 1066.3.1.1 Known Distribution 1066.3.1.2 Almost Normal Data 1086.3.1.3 Bootstrap 1106.3.2 Sequential Sampling 1126.3.2.1 Stein’s Two-Stage Sampling Procedure 1126.3.2.2 Wald Sequential Sampling 1126.3.2.3 Adaptive Sampling 1156.4 Meta-Analysis 1166.5 Summary and Review 1167. Guide to Entering, Editing, Saving, and Retrieving Large Quantities of Data Using R 1197.1 Creating and Editing a Data File 1207.2 Storing and Retrieving Files from within R 1207.3 Retrieving Data Created by Other Programs 1217.3.1 The Tabular Format 1217.3.2 Comma-Separated Values 1217.3.3 Data from Microsoft Excel 1227.3.4 Data from Minitab, SAS, SPSS, or Stata Data Files 1227.4 Using R to Draw a Random Sample 1228. Analyzing Complex Experiments 1258.1 Changes Measured in Percentages 1258.2 Comparing More Than Two Samples 1268.2.1 Programming the Multi-Sample Comparison in R 1278.2.2 Reusing Your R Functions 1288.2.3 What Is the Alternative? 1298.2.4 Testing for a Dose Response or Other Ordered Alternative 1298.3 Equalizing Variability 1318.4 Categorical Data 1328.4.1 Making Decisions with R 1348.4.2 One-Sided Fisher’s Exact Test 1358.4.3 The Two-Sided Test 1368.4.4 Testing for Goodness of Fit 1378.4.5 Multinomial Tables 1378.5 Multivariate Analysis 1398.5.1 Manipulating Multivariate Data in R 1408.5.2 Hotelling’s T2 1418.5.3 Pesarin–Fisher Omnibus Statistic 1428.6 R Programming Guidelines 1448.7 Summary and Review 1489. Developing Models 1499.1 Models 1499.1.1 Why Build Models? 1509.1.2 Caveats 1529.2 Classification and Regression Trees 1529.2.1 Example: Consumer Survey 1539.2.2 How Trees Are Grown 1569.2.3 Incorporating Existing Knowledge 1589.2.4 Prior Probabilities 1589.2.5 Misclassification Costs 1599.3 Regression 1609.3.1 Linear Regression 1619.4 Fitting a Regression Equation 1629.4.1 Ordinary Least Squares 1629.4.2 Types of Data 1659.4.3 Least Absolute Deviation Regression 1669.4.4 Errors-in-Variables Regression 1679.4.5 Assumptions 1689.5 Problems with Regression 1699.5.1 Goodness of Fit versus Prediction 1699.5.2 Which Model? 1709.5.3 Measures of Predictive Success 1719.5.4 Multivariable Regression 1719.6 Quantile Regression 1749.7 Validation 1769.7.1 Independent Verification 1769.7.2 Splitting the Sample 1779.7.3 Cross-Validation with the Bootstrap 1789.8 Summary and Review 17810. Reporting Your Findings 18110.1 What to Report 18110.1.1 Study Objectives 18210.1.2 Hypotheses 18210.1.3 Power and Sample Size Calculations 18210.1.4 Data Collection Methods 18310.1.5 Clusters 18310.1.6 Validation Methods 18410.2 Text, Table, or Graph? 18510.3 Summarizing Your Results 18610.3.1 Center of the Distribution 18910.3.2 Dispersion 18910.3.3 Categorical Data 19010.4 Reporting Analysis Results 19110.4.1 p-Values? Or Confidence Intervals? 19210.5 Exceptions Are the Real Story 19310.5.1 Nonresponders 19310.5.2 The Missing Holes 19410.5.3 Missing Data 19410.5.4 Recognize and Report Biases 19410.6 Summary and Review 19511. Problem Solving 19711.1 The Problems 19711.2 Solving Practical Problems 20111.2.1 Provenance of the Data 20111.2.2 Inspect the Data 20211.2.3 Validate the Data Collection Methods 20211.2.4 Formulate Hypotheses 20311.2.5 Choosing a Statistical Methodology 20311.2.6 Be Aware of What You Don’t Know 20411.2.7 Qualify Your Conclusions 204Answers to Selected Exercises 205Index 207