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<p><b>1 Data and Case Studies 1</b></p> <p>1.1 Case Study: Flight Delays 1</p> <p>1.2 Case Study: BirthWeights of Babies 2</p> <p>1.3 Case Study: Verizon Repair Times 3</p> <p>1.4 Case Study: Iowa Recidivism 4</p> <p>1.5 Sampling 5</p> <p>1.6 Parameters and Statistics 6</p> <p>1.7 Case Study: General Social Survey 7</p> <p>1.8 Sample Surveys 8</p> <p>1.9 Case Study: Beer and HotWings 9</p> <p>1.10 Case Study: Black Spruce Seedlings 10</p> <p>1.11 Studies 10</p> <p>1.12 Google Interview Question: Mobile Ads Optimization 12</p> <p>Exercises 16</p> <p><b>2 Exploratory Data Analysis 21</b></p> <p>2.1 Basic Plots 21</p> <p>2.2 Numeric Summaries 25</p> <p>2.2.1 Center 25</p> <p>2.2.2 Spread 26</p> <p>2.2.3 Shape 27</p> <p>2.3 Boxplots 28</p> <p>2.4 Quantiles and Normal Quantile Plots 29</p> <p>2.5 Empirical Cumulative Distribution Functions 35</p> <p>2.6 Scatter Plots 38</p> <p>2.7 Skewness and Kurtosis 40</p> <p><b>3 Introduction to Hypothesis Testing: Permutation Tests 47</b></p> <p>3.1 Introduction to Hypothesis Testing 47</p> <p>3.2 Hypotheses 48</p> <p>3.3 Permutation Tests 50</p> <p>3.3.1 Implementation Issues 55</p> <p>3.3.2 One-sided and Two-sided Tests 61</p> <p>3.3.3 Other Statistics 62</p> <p>3.3.4 Assumptions 64</p> <p>3.3.5 Remark on Terminology 68</p> <p>3.4 Matched Pairs 68</p> <p>Exercises 70</p> <p><b>4 Sampling Distributions 75</b></p> <p>4.1 Sampling Distributions 75</p> <p>4.2 Calculating Sampling Distributions 80</p> <p>4.3 The Central LimitTheorem 84</p> <p>4.3.1 CLT for Binomial Data 86</p> <p>4.3.2 Continuity Correction for Discrete Random Variables 89</p> <p>4.3.3 Accuracy of the Central Limit Theorem∗ 91</p> <p>4.3.4 CLT for SamplingWithout Replacement 92</p> <p>Exercises 93</p> <p><b>5 Introduction to Confidence Intervals: The Bootstrap 103</b></p> <p>5.1 Introduction to the Bootstrap 103</p> <p>5.2 The Plug-in Principle 110</p> <p>5.2.1 Estimating the Population Distribution 112</p> <p>5.2.2 How Useful Is the Bootstrap Distribution? 113</p> <p>5.3 Bootstrap Percentile Intervals 118</p> <p>5.4 Two-Sample Bootstrap 119</p> <p>5.4.1 Matched Pairs 124</p> <p>5.5 Other Statistics 128</p> <p>5.6 Bias 131</p> <p>5.7 Monte Carlo Sampling: The “Second Bootstrap Principle” 134</p> <p>5.8 Accuracy of Bootstrap Distributions 135</p> <p>5.8.1 Sample Mean: Large Sample Size 135</p> <p>5.8.2 Sample Mean: Small Sample Size 137</p> <p>5.8.3 Sample Median 138</p> <p>5.8.4 Mean–Variance Relationship 138</p> <p>5.9 HowMany Bootstrap Samples Are Needed? 140</p> <p>Exercises 141</p> <p><b>6 Estimation 149</b></p> <p>6.1 Maximum Likelihood Estimation 149</p> <p>6.1.1 Maximum Likelihood for Discrete Distributions 150</p> <p>6.1.2 Maximum Likelihood for Continuous Distributions 153</p> <p>6.1.3 Maximum Likelihood for Multiple Parameters 157</p> <p>6.2 Method of Moments 161</p> <p>6.3 Properties of Estimators 163</p> <p>6.3.1 Unbiasedness 164</p> <p>6.3.2 Efficiency 167</p> <p>6.3.3 Mean Square Error 171</p> <p>6.3.4 Consistency 173</p> <p>6.3.5 Transformation Invariance∗ 175</p> <p>6.3.6 Asymptotic Normality of MLE∗ 177</p> <p>6.4 Statistical Practice 178</p> <p>6.4.1 Are You Asking the Right Question? 179</p> <p>6.4.2 Weights 179</p> <p>Exercises 180</p> <p><b>7 More Confidence Intervals 187</b></p> <p>7.1 Confidence Intervals for Means 187</p> <p>7.1.1 Confidence Intervals for a Mean, Variance Known 187</p> <p>7.1.2 Confidence Intervals for a Mean, Variance Unknown 192</p> <p>7.1.3 Confidence Intervals for a Difference in Means 198</p> <p>7.1.4 Matched Pairs, Revisited 204</p> <p>7.2 Confidence Intervals in General 204</p> <p>7.2.1 Location and Scale Parameters∗ 208</p> <p>7.3 One-sided Confidence Intervals 212</p> <p>7.4 Confidence Intervals for Proportions 214</p> <p>7.4.1 Agresti–Coull Intervals for a Proportion 217</p> <p>7.4.2 Confidence Intervals for a Difference of Proportions 218</p> <p>7.5 Bootstrap Confidence Intervals 219</p> <p>7.5.1 <i>t </i>Confidence Intervals Using Bootstrap Standard Errors 219</p> <p>7.5.2 Bootstrap <i>t</i> Confidence Intervals 220</p> <p>7.5.3 Comparing Bootstrap <i>t</i> and Formula <i>t</i> Confidence Intervals 224</p> <p>7.6 Confidence Interval Properties 226</p> <p>7.6.1 Confidence Interval Accuracy 226</p> <p>7.6.2 Confidence Interval Length 227</p> <p>7.6.3 Transformation Invariance 227</p> <p>7.6.4 Ease of Use and Interpretation 227</p> <p>7.6.5 Research Needed 228</p> <p>Exercises 228</p> <p><b>8 More Hypothesis Testing 241</b></p> <p>8.1 Hypothesis Tests for Means and Proportions: One Population 241</p> <p>8.1.1 A Single Mean 241</p> <p>8.1.2 One Proportion 244</p> <p>8.2 Bootstrap t-Tests 246</p> <p>8.3 Hypothesis Tests for Means and Proportions: Two Populations 248</p> <p>8.3.1 Comparing Two Means 248</p> <p>8.3.2 Comparing Two Proportions 251</p> <p>8.3.3 Matched Pairs for Proportions 254</p> <p>8.4 Type I and Type II Errors 255</p> <p>8.4.1 Type I Errors 257</p> <p>8.4.2 Type II Errors and Power 261</p> <p>8.4.3 P-Values versus Critical Regions 266</p> <p>8.5 Interpreting Test Results 267</p> <p>8.5.1 P-Values 267</p> <p>8.5.2 On Significance 268</p> <p>8.5.3 Adjustments for Multiple Testing 269</p> <p>8.6 Likelihood Ratio Tests 271</p> <p>8.6.1 Simple Hypotheses and the Neyman–Pearson Lemma 271</p> <p>8.6.2 Likelihood Ratio Tests for Composite Hypotheses 275</p> <p>8.7 Statistical Practice 279</p> <p>8.7.1 More Campaigns with No Clicks and No Conversions 284</p> <p>Exercises 285</p> <p><b>9 Regression 297</b></p> <p>9.1 Covariance 297</p> <p>9.2 Correlation 301</p> <p>9.3 Least-Squares Regression 304</p> <p>9.3.1 Regression Toward the Mean 308</p> <p>9.3.2 Variation 310</p> <p>9.3.3 Diagnostics 311</p> <p>9.3.4 Multiple Regression 317</p> <p>9.4 The Simple LinearModel 317</p> <p>9.4.1 Inference for 𝛼 and 𝛽 322</p> <p>9.4.2 Inference for the Response 326</p> <p>9.4.3 Comments about Assumptions for the Linear Model 330</p> <p>9.5 Resampling Correlation and Regression 332</p> <p>9.5.1 Permutation Tests 335</p> <p>9.5.2 Bootstrap Case Study: Bushmeat 336</p> <p>9.6 Logistic Regression 340</p> <p>9.6.1 Inference for Logistic Regression 346</p> <p>Exercises 350</p> <p><b>10 Categorical Data 359</b></p> <p>10.1 Independence in Contingency Tables 359</p> <p>10.2 Permutation Test of Independence 361</p> <p>10.3 Chi-square Test of Independence 365</p> <p>10.3.1 Model for Chi-square Test of Independence 366</p> <p>10.3.2 2 × 2 Tables 368</p> <p>10.3.3 Fisher’s Exact Test 370</p> <p>10.3.4 Conditioning 371</p> <p>10.4 Chi-square Test of Homogeneity 372</p> <p>10.5 Goodness-of-fit Tests 374</p> <p>10.5.1 All Parameters Known 374</p> <p>10.5.2 Some Parameters Estimated 377</p> <p>10.6 Chi-square and the Likelihood Ratio∗ 379</p> <p>Exercises 380</p> <p><b>11 Bayesian Methods 391</b></p> <p>11.1 Bayes Theorem 392</p> <p>11.2 Binomial Data: Discrete Prior Distributions 392</p> <p>11.3 Binomial Data: Continuous Prior Distributions 400</p> <p>11.4 Continuous Data 406</p> <p>11.5 Sequential Data 409</p> <p>Exercises 414</p> <p><b>12 One-way ANOVA 419</b></p> <p>12.1 Comparing Three or More Populations 419</p> <p>12.1.1 The ANOVA F-test 419</p> <p>12.1.2 A Permutation Test Approach 428</p> <p>Exercises 429</p> <p><b>13 Additional Topics 433</b></p> <p>13.1 Smoothed Bootstrap 433</p> <p>13.1.1 Kernel Density Estimate 435</p> <p>13.2 Parametric Bootstrap 437</p> <p>13.3 The Delta Method 441</p> <p>13.4 Stratified Sampling 445</p> <p>13.5 Computational Issues in Bayesian Analysis 446</p> <p>13.6 Monte Carlo Integration 448</p> <p>13.7 Importance Sampling 452</p> <p>13.7.1 Ratio Estimate for Importance Sampling 458</p> <p>13.7.2 Importance Sampling in Bayesian Applications 461</p> <p>13.8 The EM Algorithm 467</p> <p>13.8.1 General Background 469</p> <p>Exercises 472</p> <p><b>Appendix A Review of Probability 477</b></p> <p>A.1 Basic Probability 477</p> <p>A.2 Mean and Variance 478</p> <p>A.3 The Normal Distribution 480</p> <p>A.4 The Mean of a Sample of RandomVariables 481</p> <p>A.5 Sums of Normal Random Variables 482</p> <p>A.6 The Law of Averages 483</p> <p>A.7 Higher Moments and the Moment-generating Function 484</p> <p><b>Appendix B Probability Distributions 487</b></p> <p>B.1 The Bernoulli and Binomial Distributions 487</p> <p>B.2 The Multinomial Distribution 488</p> <p>B.3 The Geometric Distribution 490</p> <p>B.4 The Negative Binomial Distribution 491</p> <p>B.5 The Hypergeometric Distribution 492</p> <p>B.6 The Poisson Distribution 493</p> <p>B.7 The Uniform Distribution 495</p> <p>B.8 The Exponential Distribution 495</p> <p>B.9 The Gamma Distribution 497</p> <p>B.10 The Chi-square Distribution 499</p> <p>B.11 The Student’s t Distribution 502</p> <p>B.12 The Beta Distribution 504</p> <p>B.13 The F Distribution 505</p> <p>Exercises 507</p> <p><b>Appendix C Distributions Quick Reference 509</b></p> <p>Solutions to Selected Exercises 513</p> <p>References 525</p> <p>Index 531</p>

<p><b>John R. Bradley,</b> CBE MA DM FRCP, Consultant Physician and Honorary Professor of Experimental Medicine, University of Cambridge School of Clinical Medicine, Cambridge University Hospitals, Cambridge <p><b>Mark Gurnell,</b> MA (MedEd) PhD FAcadMEd FRCP, Clinical SubDean, Senior Lecturer and Honorary Consultant Physician, University of Cambridge School of Clinical Medicine, Cambridge University Hospitals, Cambridge <p><b>Diana F. Wood,</b> MA MD FRCP, Director of Medical Education, Clinical Dean and Honorary Consultant Physician, University of Cambridge School of Clinical Medicine, Cambridge University Hospitals, Cambridge

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