Illuminating Statistical Analysis Using Scenarios and Simulations

<p>Preface ix</p>
<p>Acknowledgements xi</p>
<p>Part I Sample Proportions and the Normal Distribution 1</p>
<p>1 Evidence and Verdicts 3</p>
<p>2 Judging Coins I 5</p>
<p>3 Brief on Bell Shapes 9</p>
<p>4 Judging Coins II 11</p>
<p>5 Amount of Evidence I 19</p>
<p>6 Variance of Evidence I 23</p>
<p>7 Judging Opinion Splits I 27</p>
<p>8 Amount of Evidence II 31</p>
<p>9 Variance of Evidence II 35</p>
<p>10 Judging Opinion Splits II 39</p>
<p>11 It Has Been the Normal Distribution All Along 45</p>
<p>12 Judging Opinion Split Differences 49</p>
<p>13 Rescaling to Standard Errors 53</p>
<p>14 The Standardized Normal Distribution Histogram 55</p>
<p>15 The z–Distribution 59</p>
<p>16 Brief on Two–Tail Versus One–Tail 65</p>
<p>17 Brief on Type I Versus Type II Errors 69</p>
<p>Part II Sample Means and the Normal Distribution 75</p>
<p>18 Scaled Data and Sample Means 77</p>
<p>19 Distribution of Random Sample Means 79</p>
<p>20 Amount of Evidence 81</p>
<p>21 Variance of Evidence 83</p>
<p>22 Homing in on the Population Mean I 87</p>
<p>23 Homing in on the Population Mean II 91</p>
<p>24 Homing in on the Population Mean III 93</p>
<p>25 Judging Mean Differences 95</p>
<p>26 Sample Size, Variance, and Uncertainty 99</p>
<p>27 The t–Distribution 105</p>
<p>Part III Multiple Proportions and Means: The X2– and F–Distributions 111</p>
<p>28 Multiple Proportions and the X2–Distribution 113</p>
<p>29 Facing Degrees of Freedom 119</p>
<p>30 Multiple Proportions: Goodness of Fit 121</p>
<p>31 Two–Way Proportions: Homogeneity 125</p>
<p>32 Two–Way Proportions: Independence 127</p>
<p>33 Variance Ratios and the F–Distribution 131</p>
<p>34 Multiple Means and Variance Ratios: ANOVA 137</p>
<p>35 Two–Way Means and Variance Ratios: ANOVA 143</p>
<p>Part IV Linear Associations: Covariance, Correlation, and Regression 147</p>
<p>36 Covariance 149</p>
<p>37 Correlation 153</p>
<p>38 What Correlations Happen Just by Chance? 155</p>
<p>39 Judging Correlation Differences 161</p>
<p>40 Correlation with Mixed Data Types 165</p>
<p>41 A Simple Regression Prediction Model 167</p>
<p>42 Using Binomials Too 171</p>
<p>43 A Multiple Regression Prediction Model 175</p>
<p>44 Loose End I (Collinearity) 179</p>
<p>45 Loose End II (Squaring R) 183</p>
<p>46 Loose End III (Adjusting R–Squared) 185</p>
<p>47 Reality Strikes 187</p>
<p>Part V Dealing with Unruly Scaled Data 193</p>
<p>48 Obstacles and Maneuvers 195</p>
<p>49 Ordered Ranking Maneuver 199</p>
<p>50 What Rank Sums Happen Just by Chance? 201</p>
<p>51 Judging Rank Sum Differences 203</p>
<p>52 Other Methods Using Ranks 205</p>
<p>53 Transforming the Scale of Scaled Data 207</p>
<p>54 Brief on Robust Regression 209</p>
<p>55 Brief on Simulation and Resampling 211</p>
<p>Part VI Review and Additional Concepts 213</p>
<p>56 For Part I 215</p>
<p>57 For Part II 221</p>
<p>58 For Part III 227</p>
<p>59 For Part IV 233</p>
<p>60 For Part V 243</p>
<p>Appendices 247</p>
<p>A Data Types and Some Basic Statistics 249</p>
<p>B Simulating Statistical Scenarios 253</p>
<p>C Standard Error as Standard Deviation 271</p>
<p>D Data Excerpt 273</p>
<p>E Repeated Measures 277</p>
<p>F Bayesian Statistics 281</p>
<p>G Data Mining 287</p>
<p>Index 295</p>