Preface |
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xi | |
1 Introduction |
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1 | (7) |
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1 | (2) |
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1.2 Science, Reproducibility, and Statistical Inferences |
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3 | (2) |
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5 | (1) |
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6 | (1) |
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6 | (2) |
2 Theory of Tests, p-Values, and Confidence Intervals |
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8 | (15) |
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8 | (1) |
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2.2 Components of a Hypothesis Test |
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8 | (5) |
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2.3 Confidence Sets: Inverting a Series of Hypothesis Tests |
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13 | (4) |
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2.4 Properties of Hypothesis Tests |
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17 | (2) |
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19 | (1) |
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2.6 Extensions and Bibliographic Notes |
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20 | (1) |
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20 | (2) |
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22 | (1) |
3 From Scientific Theory to Statistical Hypothesis Test |
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23 | (26) |
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3.1 The Statistician's Role |
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23 | (1) |
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3.2 Causality versus Association |
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23 | (5) |
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28 | (5) |
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3.4 Designing an Experimental Study |
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33 | (3) |
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3.5 Designing an Observational Study |
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36 | (4) |
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3.6 A Probability Model for the Study |
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40 | (3) |
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3.7 Statistics Methods Overview |
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43 | (2) |
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45 | (1) |
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3.9 Extensions and Bibliographic Notes |
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46 | (1) |
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47 | (1) |
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48 | (1) |
4 One-Sample Studies with Binary Responses |
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49 | (18) |
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49 | (1) |
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4.2 Key Method: Exact Central Method (Clopper-Pearson) |
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50 | (1) |
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4.3 Other Methods for Independent Binary Responses |
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51 | (9) |
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4.4 Designing a One-Sample Binary Response Study |
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60 | (2) |
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62 | (1) |
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4.6 Extensions and Bibliographic Notes |
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63 | (1) |
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4.7 R Functions and Packages |
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64 | (1) |
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65 | (1) |
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66 | (1) |
5 One-Sample Studies with Ordinal or Numeric Responses |
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67 | (17) |
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67 | (2) |
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5.2 Exact Test on the Median or Other Quantiles |
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69 | (1) |
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70 | (7) |
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5.4 Testing Other Parameters from One-Sample Numeric Data |
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77 | (2) |
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5.5 Designing a One-Sample Study |
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79 | (1) |
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79 | (1) |
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5.7 Extensions and Bibliographic Notes |
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80 | (1) |
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5.8 R Functions and Packages |
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80 | (1) |
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80 | (3) |
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83 | (1) |
6 Paired Data |
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84 | (20) |
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84 | (1) |
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85 | (1) |
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6.3 Wilcoxon Signed-Rank Test |
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86 | (4) |
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6.4 Choosing a Paired-Difference Test under Symmetry |
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90 | (4) |
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6.5 Correlation and Related Types of Association |
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94 | (4) |
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6.6 Agreement Coefficients |
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98 | (2) |
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100 | (1) |
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6.8 Extensions and Bibliographic Notes |
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101 | (1) |
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6.9 R Functions and Packages |
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101 | (1) |
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102 | (1) |
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103 | (1) |
7 Two-Sample Studies with Binary Responses |
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104 | (20) |
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104 | (2) |
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7.2 Parameters to Measure Effects |
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106 | (2) |
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108 | (7) |
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115 | (1) |
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7.6 Asymptotic Approximations |
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116 | (1) |
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7.7 Comparison of Binomial Methods |
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117 | (2) |
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119 | (1) |
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120 | (1) |
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7.10 Extensions and Bibliographic Notes |
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121 | (1) |
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7.11 R Functions and Packages |
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122 | (1) |
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122 | (1) |
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122 | (2) |
8 Assumptions and Hypothesis Tests |
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124 | (5) |
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124 | (1) |
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8.2 Which Test Is More Restrictive? |
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124 | (2) |
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8.3 Multiple Perspective Decision Rules |
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126 | (2) |
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128 | (1) |
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8.5 Extensions and Bibliographic Notes |
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128 | (1) |
9 Two-Sample Studies with Ordinal or Numeric Responses |
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129 | (32) |
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129 | (4) |
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9.2 Inferences on Proportional Odds |
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133 | (1) |
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133 | (8) |
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9.4 Differences in Medians |
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141 | (2) |
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9.5 Mann-Whitney Parameter |
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143 | (8) |
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9.6 Choosing a Test when Power Concerns Dominate |
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151 | (4) |
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155 | (2) |
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9.8 Extensions and Bibliographic Notes |
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157 | (1) |
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9.9 R Functions and Packages |
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157 | (1) |
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158 | (1) |
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158 | (3) |
10 General Methods for Frequentist Inferences |
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161 | (34) |
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161 | (1) |
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10.2 One-Dimensional Parameter |
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161 | (3) |
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164 | (1) |
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10.4 Multivariate Normal Inferences |
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165 | (1) |
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10.5 Asymptotic Normality and the Central Limit Theorem |
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166 | (2) |
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168 | (1) |
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10.7 Wald, Score, and Likelihood Ratio Tests |
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169 | (5) |
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174 | (2) |
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176 | (5) |
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181 | (4) |
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10.11 Melding: Combining Confidence Intervals in the Two-Sample Case |
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185 | (2) |
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10.12 Within-Cluster Resampling |
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187 | (1) |
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188 | (1) |
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188 | (2) |
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10.15 Extensions and Bibliographic Notes |
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190 | (1) |
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10.16 R Functions and Packages |
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190 | (1) |
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190 | (3) |
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193 | (2) |
11 k-Sample Studies and Trend Tests |
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195 | (20) |
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195 | (1) |
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11.2 Unordered Groups: k-Sample Tests |
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196 | (7) |
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11.3 Ordered Groups: Trend Tests |
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203 | (1) |
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11.4 Follow-Up Tests after Independence Test and Familywise Error Rates |
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204 | (1) |
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11.5 All Pairwise Comparisons |
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205 | (3) |
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11.6 Many-to-One Comparisons |
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208 | (1) |
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11.7 Max-t-Type Procedures |
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209 | (1) |
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210 | (1) |
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11.9 Extensions and Bibliographic Notes |
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211 | (1) |
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11.10 R Functions and Packages |
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212 | (1) |
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212 | (2) |
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214 | (1) |
12 Clustering and Stratification |
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215 | (20) |
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215 | (1) |
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215 | (6) |
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221 | (9) |
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230 | (2) |
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12.5 Extensions and Bibliographic Notes |
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232 | (1) |
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12.6 R Functions and Packages |
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232 | (1) |
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232 | (1) |
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233 | (2) |
13 Multiplicity in Testing |
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235 | (18) |
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235 | (1) |
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13.2 Defining the Family of Hypothesis Tests |
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236 | (3) |
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13.3 Properties of Multiple Testing Procedures |
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239 | (1) |
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13.4 Procedures Using p-Values Only |
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240 | (1) |
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13.5 Max-t-Type (Generalized Studentized Range) Inferences |
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241 | (3) |
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13.6 Permutation- or Bootstrap-Based Methods |
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244 | (2) |
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13.7 Sequential Testing of Different Hypotheses |
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246 | (1) |
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247 | (1) |
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248 | (1) |
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248 | (2) |
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13.11 Extensions and Bibliographic Notes |
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250 | (1) |
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13.12 R Functions and Packages |
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250 | (1) |
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250 | (1) |
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251 | (2) |
14 Testing from models |
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253 | (24) |
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253 | (1) |
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253 | (2) |
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14.3 Generalized Linear Models |
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255 | (4) |
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14.4 Ordinal Responses or Ranked Responses |
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259 | (2) |
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261 | (5) |
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266 | (2) |
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14.7 Some Problems When Testing from Models |
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268 | (3) |
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14.8 Inference after Model Building |
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271 | (1) |
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271 | (2) |
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14.10 Extensions and Bibliographic Notes |
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273 | (1) |
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14.11 R Functions and Packages |
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273 | (1) |
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274 | (1) |
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275 | (2) |
15 Causality |
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277 | (25) |
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277 | (1) |
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278 | (3) |
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15.3 Why Causal Inference Is Difficult for Observational Studies |
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281 | (2) |
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15.4 Causality and Experimental Studies |
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283 | (6) |
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15.5 Causality and Interference |
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289 | (1) |
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15.6 Causality and Observational Studies: Overview |
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290 | (1) |
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15.7 Observational Studies: Adjustments When Confounders Are Measured |
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290 | (7) |
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15.8 Observational Studies: Analysis with Unmeasured Confounders Using Instrumental Variables |
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297 | (1) |
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298 | (2) |
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15.10 Extensions and Bibliographic Notes |
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300 | (1) |
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300 | (1) |
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301 | (1) |
16 Censoring |
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302 | (25) |
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16.1 Overview: Types of Censoring |
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302 | (1) |
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16.2 One Sample with Right Censoring |
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303 | (5) |
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308 | (1) |
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16.4 Two Samples with Right Censoring |
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309 | (9) |
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318 | (3) |
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321 | (1) |
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322 | (1) |
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16.8 Extensions and Bibliographic Notes |
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323 | (1) |
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16.9 R Functions and Packages |
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324 | (1) |
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324 | (1) |
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325 | (2) |
17 Missing Data |
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327 | (15) |
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327 | (1) |
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17.2 Missing Data Terminology |
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328 | (1) |
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17.3 Sensitivity Analyses for Data Missing Not at Random |
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329 | (4) |
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17.4 Methods for Missing at Random Data |
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333 | (5) |
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338 | (1) |
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339 | (1) |
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17.7 Extensions and Bibliographic Notes |
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340 | (1) |
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17.8 R Functions and Packages |
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340 | (1) |
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340 | (2) |
18 Group Sequential and Related Adaptive Methods |
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342 | (17) |
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342 | (1) |
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18.2 k Preplanned Interim Analyses |
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343 | (3) |
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18.3 Arbitrary Number of Interim Analyses |
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346 | (2) |
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18.4 When the Brownian Motion Approximation Does Not Hold |
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348 | (1) |
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18.5 Estimates and Confidence Intervals after Interim Analyses |
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349 | (3) |
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18.6 Two-Stage Adaptive Designs |
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352 | (2) |
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354 | (2) |
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18.8 Extensions and Bibliographic Notes |
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356 | (1) |
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18.9 R Functions and Packages |
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356 | (1) |
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356 | (1) |
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357 | (2) |
19 Testing Fit, Equivalence, and Noninferiority |
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359 | (18) |
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359 | (2) |
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19.2 Testing Distributions and Lack of Fit |
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361 | (4) |
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365 | (1) |
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19.4 Noninferiority Tests |
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366 | (6) |
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372 | (1) |
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19.6 Extensions and Bibliographic Notes |
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373 | (1) |
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19.7 R Functions and Packages |
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373 | (1) |
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373 | (2) |
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375 | (2) |
20 Power and Sample Size |
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377 | (12) |
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377 | (1) |
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20.2 Power Calculations by Simulation |
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378 | (2) |
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20.3 Power Calculations by Normal Approximations |
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380 | (2) |
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20.4 Simulating the Sample Size |
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382 | (1) |
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20.5 Nonadherence and Other Issues |
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383 | (2) |
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385 | (1) |
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20.7 Extensions and Bibliographic Notes |
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386 | (1) |
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20.8 R Functions and Packages |
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386 | (1) |
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386 | (2) |
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388 | (1) |
21 Bayesian Hypothesis Testing |
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389 | (15) |
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389 | (1) |
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21.2 Brief Overview of Bayesian Statistics |
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389 | (4) |
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21.3 Bayesian Hypothesis Testing Using Bayes Factors |
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393 | (1) |
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21.4 Bayesian Hypothesis Testing Using Decision Theory |
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394 | (2) |
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21.5 When Can p-Values Be Interpreted in a Bayesian Manner? |
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396 | (5) |
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401 | (1) |
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402 | (2) |
References |
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404 | (16) |
Notation Index |
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420 | |
Concept Index |
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42 | |