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1 | (8) |
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1.1 Installation: R, LATEX, and Emacs |
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1 | (1) |
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1.2 How to read this book |
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2 | (1) |
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1.3 Some Simple Commands in R |
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2 | (4) |
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6 | (3) |
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2 Randomness and Probability |
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9 | (34) |
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2.1 Elementary Probability Theory |
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9 | (10) |
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2.1.1 The Sum and Product Rules |
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9 | (2) |
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2.1.2 Stones and Rain: A Variant on the Coin-toss Problem |
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11 | (8) |
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2.2 The Binomial Distribution |
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19 | (3) |
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22 | (11) |
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2.4 Standard Deviation and Sample Size |
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33 | (6) |
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2.4.1 Another Insight: Mean Minimizes Variance |
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36 | (3) |
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2.5 The Binomial versus the Normal Distribution |
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39 | (2) |
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41 | (2) |
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3 The Sampling Distribution of the Sample Mean |
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43 | (38) |
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3.1 The Central Limit Theorem |
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47 | (2) |
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49 | (1) |
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3.3 The 95% Confidence Interval for the Sample Mean |
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50 | (2) |
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3.4 Realistic Statistical Inference |
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52 | (1) |
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3.5 s is an Unbiassed Estimator of Σ |
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52 | (3) |
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55 | (1) |
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3.7 The One-sample t-test |
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56 | (1) |
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3.8 Some Observations on Confidence Intervals |
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57 | (4) |
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3.9 Sample SD, Degrees of Freedom, Unbiased Estimators |
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61 | (2) |
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3.10 Summary of the Sampling Process |
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63 | (1) |
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64 | (1) |
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65 | (1) |
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66 | (1) |
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67 | (4) |
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3.15 Hypothesis Testing: A More Realistic Scenario |
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71 | (4) |
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3.16 Comparing Two Samples |
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75 | (4) |
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3.16.1 H0 in Two-sample Problems |
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76 | (3) |
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79 | (2) |
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81 | (16) |
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4.1 Hypothesis Testing Revisited |
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81 | (1) |
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4.2 Type I and Type II Errors |
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82 | (9) |
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91 | (3) |
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4.3.1 Equivalence Testing Example |
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91 | (1) |
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4.3.2 TOST Approach to the Stegner et al. Example |
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92 | (2) |
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4.3.3 Equivalence Testing Example: CIs Approach |
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94 | (1) |
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4.4 Observed Power and Null Results |
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94 | (2) |
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96 | (1) |
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5 Analysis of Variance (ANOVA) |
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97 | (30) |
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5.1 Comparing Three Populations |
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97 | (2) |
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99 | (12) |
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100 | (3) |
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5.2.2 Variance of Sample Means as a Possible Statistic |
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103 | (2) |
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5.2.3 Analyzing the Variance |
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105 | (6) |
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111 | (10) |
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5.3.1 MS-within, MS-between as Statistics |
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112 | (1) |
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113 | (5) |
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118 | (1) |
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5.3.4 MS-within, Three Non-identical Populations |
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118 | (2) |
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5.3.5 The F-distribution with Unequal Variances |
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120 | (1) |
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5.4 ANOVA as a Linear Model |
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121 | (4) |
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125 | (2) |
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6 Bivariate Statistics and Linear Models |
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127 | (18) |
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6.1 Variance and Hypothesis Testing for Regression |
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137 | (5) |
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6.1.1 Sum of Squares and Correlation |
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142 | (1) |
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142 | (3) |
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7 An Introduction to Linear Mixed Models |
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145 | (16) |
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145 | (1) |
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146 | (9) |
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7.3 The Levels of the Complex Linear Model |
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155 | (4) |
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159 | (2) |
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161 | (10) |
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A.1 The Probability Distribution in Statistical Inference |
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162 | (1) |
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162 | (2) |
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A.3 Properties of Expectation |
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164 | (1) |
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165 | (1) |
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A.5 Important Properties of Variance |
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165 | (1) |
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A.6 Mean and SD of the Binomial Distribution |
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166 | (1) |
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A.7 Sample versus Population Means and Variances |
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167 | (1) |
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168 | (1) |
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169 | (2) |
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B Basic R Commands and Data Structures |
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171 | (4) |
References |
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175 | (2) |
Index |
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177 | |