| Preface |
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xv | |
| Acknowledgments |
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xx | |
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Introduction to Probability |
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1 | (82) |
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2 | (2) |
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Interpretations of Probability |
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4 | (4) |
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5 | (1) |
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5 | (1) |
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Empirical or Relative Frequency (a posteriori) |
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5 | (2) |
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Mathematical or Axiomatic |
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7 | (1) |
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8 | (2) |
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8 | (2) |
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10 | (3) |
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13 | (1) |
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Conditional Probability and Independence |
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14 | (5) |
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19 | (4) |
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23 | (34) |
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Two Fundamental Principles of Counting (FPC) and the Pigeonhole Principle |
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23 | (4) |
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27 | (1) |
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28 | (4) |
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32 | (14) |
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46 | (11) |
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57 | (26) |
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60 | (4) |
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64 | (6) |
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70 | (11) |
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Self Quiz 1A: Conditional Probability |
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81 | (1) |
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Self Quiz 1B: Poker Probability |
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82 | (1) |
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Random Variables, Moments, and Distributions |
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83 | (75) |
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84 | (1) |
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84 | (7) |
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91 | (5) |
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96 | (16) |
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Information Content (Entropy) |
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104 | (4) |
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108 | (4) |
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Standardized Random Variables |
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112 | (2) |
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Jointly Distributed Random Variables |
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114 | (6) |
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Discrete Joint Density Functions |
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117 | (3) |
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Independence of Jointly Distributed Random Variables |
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120 | (1) |
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Covariance and Correlation |
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121 | (5) |
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Conditional Densities Functions |
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126 | (5) |
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Moment Generating Functions |
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131 | (3) |
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Transformation of Variables |
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134 | (4) |
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Transformation of 2 or More Variables |
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136 | (2) |
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138 | (20) |
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140 | (5) |
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145 | (2) |
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147 | (2) |
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149 | (7) |
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156 | (2) |
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Special Discrete Distributions |
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158 | (57) |
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159 | (1) |
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159 | (4) |
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163 | (1) |
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164 | (10) |
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174 | (1) |
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Hypergeometric Distribution |
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175 | (5) |
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180 | (4) |
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Negative Binomial Distribution |
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184 | (3) |
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187 | (7) |
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194 | (21) |
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196 | (9) |
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205 | (1) |
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206 | (8) |
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Self Quiz 3: Discrete Distributions |
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214 | (1) |
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Special Continuous Distributions |
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215 | (54) |
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216 | (1) |
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Continuous Uniform Distribution |
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216 | (4) |
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220 | (1) |
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Gamma Family (Exponential, Chi-Square, Gamma) |
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221 | (3) |
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224 | (4) |
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228 | (3) |
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231 | (12) |
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243 | (2) |
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245 | (2) |
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247 | (3) |
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250 | (2) |
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252 | (17) |
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255 | (5) |
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260 | (1) |
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261 | (1) |
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262 | (6) |
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Self Quiz 4: Continuous Distributions |
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268 | (1) |
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Sampling, Data Displays, Measures of Central Tendencies, Measures of Dispersion, and Simulation |
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269 | (56) |
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270 | (1) |
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271 | (6) |
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273 | (1) |
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Frequency Distributions and Histograms |
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274 | (3) |
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277 | (10) |
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277 | (2) |
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279 | (3) |
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282 | (3) |
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285 | (2) |
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287 | (1) |
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287 | (8) |
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Sample Variance and Standard Deviation |
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287 | (1) |
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Interquartile Range (IQR) |
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288 | (1) |
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Median Absolute Deviation from the Median (MAD) |
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288 | (1) |
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289 | (2) |
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291 | (1) |
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292 | (1) |
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293 | (2) |
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Joint Distribution of X and S2 |
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295 | (3) |
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Simulation of Random Variables |
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298 | (8) |
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303 | (3) |
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Using Monte Carlo for Integration |
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306 | (1) |
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307 | (3) |
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310 | (15) |
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313 | (3) |
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316 | (8) |
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Self Quiz 5: Sampling and Data Displays |
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324 | (1) |
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Point and Interval Estimation |
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325 | (61) |
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326 | (1) |
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Unbiased Estimators and Point Estimates |
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327 | (6) |
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329 | (4) |
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Methods of Finding Point Estimates |
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333 | (14) |
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Method of Moments Estimators (MME) |
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333 | (4) |
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Maximum Likelihood Estimators (MLE) |
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337 | (10) |
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Interval Estimates (Confidence Intervals) |
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347 | (13) |
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351 | (1) |
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Confidence Interval When σ Is Not Known |
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352 | (1) |
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Confidence Interval for the Difference between Two Means (μ1 -- μ2) |
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353 | (2) |
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Confidence Interval for σ2 of a Normal Distribution |
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355 | (1) |
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Confidence Interval for a Proportion |
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355 | (2) |
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Confidence Interval for the Difference between Two Proportions |
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357 | (1) |
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Confidence Interval for the Paired T-Test |
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358 | (1) |
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Confidence Intervals for Ratio of Variances σ2/2/σ2/1 |
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358 | (2) |
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360 | (1) |
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Central Limit Theorem (Revisited) |
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361 | (2) |
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Parametric Bootstrap Estimation |
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363 | (3) |
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366 | (20) |
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369 | (2) |
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371 | (2) |
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373 | (2) |
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375 | (9) |
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Self Quiz 6: Estimation and Confidence Intervals |
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384 | (2) |
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386 | (69) |
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387 | (1) |
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Terminology in Statistical Tests of Hypotheses |
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387 | (10) |
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397 | (6) |
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400 | (2) |
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402 | (1) |
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Hypothesis Tests: Proportions |
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403 | (4) |
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405 | (2) |
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Hypothesis Tests for Difference between Two Means: Small Samples (n ≤ 30) σ2 Known |
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407 | (4) |
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408 | (3) |
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Hypothesis Test with Paired Samples |
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411 | (3) |
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412 | (2) |
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Statistically Significant vs. Practically Significant |
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414 | (1) |
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Hypothesis Tests: Variances |
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414 | (3) |
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Hypothesis Tests for the Equality of Two Variances |
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416 | (1) |
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Hypothesis Tests for Independence, Homogeneity, and Goodness of Fit |
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417 | (18) |
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R x C Contingency Tables Test for Homogeneity and Independence |
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418 | (6) |
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424 | (4) |
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428 | (7) |
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435 | (20) |
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437 | (8) |
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445 | (3) |
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448 | (5) |
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Self Test 7: Hypothesis Testing |
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453 | (2) |
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455 | (92) |
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456 | (1) |
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Review of Joint and Conditional Densities |
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457 | (2) |
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459 | (7) |
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461 | (4) |
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Other Models of Simple Linear Regression |
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465 | (1) |
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Distribution of Estimators with Inference on Parameters |
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466 | (17) |
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467 | (2) |
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469 | (2) |
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471 | (2) |
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473 | (3) |
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476 | (1) |
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Inference on the Intercept α |
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477 | (1) |
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478 | (5) |
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483 | (3) |
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Coefficient of Determination |
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485 | (1) |
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486 | (7) |
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490 | (3) |
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Convertible Nonlinear Forms for Linear Regression |
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493 | (1) |
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494 | (4) |
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Multiple Linear Regression |
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498 | (8) |
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Multiple Linear Regression with Matrices |
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501 | (5) |
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Multiple Regression Techniques |
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506 | (14) |
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506 | (1) |
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507 | (1) |
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Model Variables Selection Criteria |
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508 | (6) |
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514 | (6) |
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520 | (4) |
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524 | (23) |
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527 | (6) |
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533 | (3) |
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536 | (9) |
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545 | (2) |
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547 | (62) |
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548 | (1) |
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548 | (14) |
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The Bartlett Test for Homogeneity of Variances |
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560 | (2) |
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Two-Way ANOVA without Replication |
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562 | (4) |
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565 | (1) |
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Two-Way ANOVA with Replication |
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566 | (5) |
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Multiple Comparisons of Treatment Means |
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571 | (15) |
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572 | (6) |
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Contrast Confidence Intervals |
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578 | (1) |
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Least Significant Difference (LSD), Fisher LSD, and Scheffe Procedures |
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579 | (2) |
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581 | (2) |
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583 | (2) |
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Tukey Method vs. Bonferroni Method |
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585 | (1) |
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586 | (4) |
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590 | (3) |
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Graphical Analysis of Treatment Means |
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592 | (1) |
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593 | (16) |
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596 | (6) |
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602 | (1) |
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603 | (4) |
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Self Quiz 9: Analysis of Variance |
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607 | (2) |
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609 | (50) |
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610 | (1) |
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610 | (3) |
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Nonparametric Bootstrap Estimation |
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613 | (1) |
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The Sign Test for Paired Data |
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614 | (1) |
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Type II Beta Error for the Sign-Test |
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615 | (1) |
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The Wilcoxon Signed-Rank Test |
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615 | (3) |
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Wilcoxon-Mann-Whitney (WMW) Rank Test for Two Samples |
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618 | (5) |
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Spearman Rank Order Correlation Coefficient |
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623 | (2) |
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Kendall's Rank Correlation Coefficient (t) |
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625 | (1) |
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Nonparametric Tests for Regression |
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626 | (4) |
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Nonparametric Tests for ANOVA |
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630 | (7) |
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630 | (4) |
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634 | (3) |
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637 | (4) |
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641 | (4) |
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645 | (14) |
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647 | (6) |
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653 | (6) |
| Appendix A |
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659 | (3) |
| Appendix B |
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662 | (17) |
| References |
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679 | (2) |
| Index |
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681 | |
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