Preface |
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xi | |
Acknowledgments |
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xiii | |
About the Authors |
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xv | |
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1 Statistical Foundations |
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1 | (16) |
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Some Probability Concepts |
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2 | (4) |
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Some Statistical Concepts |
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6 | (9) |
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15 | (2) |
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2 Binary Results: Single Samples and 2 × 2 Tables |
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17 | (8) |
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17 | (2) |
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17 | (1) |
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18 | (1) |
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19 | (2) |
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19 | (1) |
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20 | (1) |
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21 | (3) |
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21 | (2) |
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23 | (1) |
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24 | (1) |
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25 | (16) |
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25 | (1) |
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26 | (7) |
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33 | (6) |
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39 | (2) |
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4 The Linear Model: Continuous Variables |
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41 | (20) |
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41 | (1) |
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42 | (10) |
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52 | (6) |
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58 | (3) |
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5 The Linear Model: Discrete Regressor Variables |
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61 | (20) |
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61 | (1) |
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62 | (14) |
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More Than One Treatment: Multiple Factors |
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67 | (3) |
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70 | (3) |
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ANOVA and Permutation Tests |
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73 | (2) |
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75 | (1) |
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Analysis of Covariance: Models with Both Discrete and Continuous Regressors |
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76 | (2) |
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78 | (1) |
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Multiple Groupings: One-Way ANOVA |
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78 | (2) |
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80 | (1) |
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6 The Linear Model: Random Effects and Mixed Models |
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81 | (12) |
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81 | (1) |
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Simple Case: One Fixed and One Random Effect |
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82 | (1) |
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82 | (3) |
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More Complex Case: Multiple Fixed and Random Effects |
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85 | (5) |
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90 | (1) |
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91 | (2) |
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7 Polytomous Discrete Variables: R x C Contingency Tables |
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93 | (12) |
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93 | (5) |
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Independence of Two Discrete Variables |
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93 | (1) |
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93 | (5) |
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98 | (4) |
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A Special Goodness-of-Fit Test: Test for Random Allocation |
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100 | (2) |
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102 | (1) |
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103 | (2) |
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8 The Generalized Linear Model: Logistic and Poisson Regression |
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105 | (24) |
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105 | (2) |
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Binary Logistic Regression |
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105 | (2) |
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107 | (17) |
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107 | (6) |
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113 | (3) |
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116 | (4) |
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Zero-Inflated Data and Poisson Regression |
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120 | (4) |
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124 | (4) |
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124 | (2) |
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126 | (1) |
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126 | (1) |
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127 | (1) |
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128 | (1) |
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9 Multivariate Analyses: Dimension Reduction, Clustering, and Discrimination |
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129 | (22) |
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129 | (1) |
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Dimension Reduction: Principal Components |
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130 | (2) |
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131 | (1) |
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131 | (1) |
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132 | (1) |
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132 | (12) |
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Dimension Reduction: Principal Components |
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132 | (3) |
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135 | (7) |
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142 | (1) |
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143 | (1) |
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144 | (5) |
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145 | (1) |
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145 | (3) |
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148 | (1) |
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149 | (2) |
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10 Bayesian and Frequentist Philosophies |
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151 | (18) |
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151 | (6) |
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Bayes' Theorem: Not Controversial |
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151 | (2) |
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153 | (1) |
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153 | (1) |
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154 | (1) |
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155 | (1) |
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Monte Carlo Markov Chain (MCMC) Method |
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156 | (1) |
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157 | (5) |
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157 | (1) |
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Bayesian Regression Analysis |
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158 | (1) |
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159 | (3) |
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162 | (5) |
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Bayesian Regression Analysis |
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162 | (3) |
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A Slightly More Complicated Model |
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165 | (2) |
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An Afterword about Bayesian Methods |
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167 | (1) |
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168 | (1) |
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11 Decision and Game Theory |
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169 | (20) |
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169 | (1) |
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170 | (15) |
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Discrete Choices, Discrete States |
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170 | (3) |
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Discrete Choices, Continuous States: Reward and Cost as a Function of Choice |
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173 | (3) |
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Discrete Choices, Continuous States: An Inverted Problem |
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176 | (5) |
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Game Theory: Types of Games and Evolutionarily Stable Strategies |
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181 | (4) |
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185 | (2) |
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Verifying Models: Frequentist and Bayesian Approaches |
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185 | (2) |
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187 | (2) |
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12 Modern Prediction Methods and Machine Learning Models |
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189 | (22) |
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189 | (1) |
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189 | (1) |
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190 | (13) |
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192 | (5) |
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Artificial Neural Networks |
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197 | (3) |
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Classification and Regression Trees (CART) |
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200 | (3) |
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203 | (4) |
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207 | (2) |
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209 | (2) |
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211 | (18) |
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211 | (1) |
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212 | (3) |
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Comparison of Survival Curves |
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212 | (3) |
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215 | (9) |
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Obtaining an Empirical Survival Model |
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222 | (1) |
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223 | (1) |
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Comparison of Survival Distributions |
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224 | (3) |
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Mantel--Cox LogRank and Peto and Peto Procedures |
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224 | (1) |
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Cox Proportional Hazard Model |
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225 | (2) |
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227 | (2) |
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14 Time Series Analysis and Stochastic Processes |
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229 | (24) |
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229 | (1) |
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229 | (9) |
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Identifying Time Series Model Types and Orders |
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231 | (2) |
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The Box--Jenkins Approach |
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233 | (5) |
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Nonstationarity and Differencing |
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238 | (1) |
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Examples with R Code: Time Series |
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238 | (10) |
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238 | (3) |
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241 | (2) |
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Extensions of Markov Chains |
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243 | (1) |
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Examples with R Code: Markov Chains |
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244 | (4) |
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248 | (2) |
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248 | (1) |
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249 | (1) |
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250 | (3) |
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15 Study Design and Sample Size Considerations |
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253 | (12) |
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Degrees of Freedom: The Accounting of Experimental Design |
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253 | (1) |
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Latin Squares and Partial Latin Squares: Useful Design Tools |
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254 | (4) |
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255 | (3) |
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Sample Size and Confidence Intervals |
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258 | (1) |
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Confidence Intervals for Proportions |
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259 | (1) |
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260 | (2) |
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Too Many p-Values: False Discovery Rate |
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262 | (2) |
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264 | (1) |
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265 | (8) |
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Inadequate Measurement System |
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265 | (1) |
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Incorrect Assignment of Individuals to Groups |
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265 | (1) |
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An Undiscovered Covariate |
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266 | (1) |
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266 | (1) |
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267 | (2) |
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269 | (2) |
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271 | (1) |
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271 | (2) |
Appendix A Matrices and Vectors |
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273 | (14) |
Appendix B Solving Your Problem |
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287 | (2) |
References |
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289 | (4) |
Index |
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293 | |