Preface |
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xiii | |
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An Introduction, an Overview, and Some Reminders |
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1 | (11) |
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An Introduction and Overview |
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1 | (1) |
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The Structure of This Book |
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2 | (4) |
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2 | (4) |
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A Brief Review and Reminder |
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6 | (6) |
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6 | (1) |
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7 | (1) |
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7 | (5) |
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A Review of the Correlation Coefficient and Its Properties |
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12 | (31) |
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12 | (2) |
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14 | (4) |
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Taking a Break: A Numerical Example |
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17 | (1) |
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Properties of (and Comments on) the Correlation Coefficient |
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18 | (12) |
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18 | (1) |
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Scale Transformations and r |
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19 | (2) |
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Extreme Values on X or Y (Outliers) |
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21 | (2) |
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23 | (1) |
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24 | (1) |
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25 | (2) |
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Interpreting the Size of r |
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27 | (3) |
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Other Correlation Coefficients (``Yes, Virginia, there are Many Others'') |
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30 | (9) |
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31 | (2) |
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33 | (3) |
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Point-Biserial and Biserial Correlations |
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36 | (3) |
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39 | (2) |
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41 | (2) |
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Testing Correlations for Statistical Significance |
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43 | (24) |
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43 | (1) |
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Testing a Single Correlation Against Zero |
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44 | (3) |
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A Look at the Test for H0: ρ = 0 |
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45 | (2) |
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Testing a Single Correlation vs. any specified value (the use of Fisher's z) |
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47 | (6) |
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The Problem, the Solution, and the Test |
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48 | (4) |
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An Important Related Result: Averaging Correlations |
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52 | (1) |
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Testing the Equality of Two Independent Correlations |
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53 | (3) |
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An Important Statistical Aside about Differential Validity |
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54 | (2) |
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Testing the Equality of Two Dependent Correlations |
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56 | (2) |
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Thoughts and Facts about Equation III.E |
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57 | (1) |
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Tests of Other Correlation Coefficients |
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58 | (2) |
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58 | (1) |
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58 | (2) |
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60 | (1) |
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Some Comments on ``Harvesting'' Correlations |
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60 | (3) |
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60 | (2) |
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62 | (1) |
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63 | (2) |
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65 | (2) |
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Applications of Pearson Correlation to Measurement Theory |
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67 | (30) |
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67 | (1) |
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68 | (6) |
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69 | (1) |
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Alternate Forms Reliability |
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70 | (1) |
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71 | (3) |
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74 | (4) |
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74 | (1) |
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74 | (1) |
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Criterion-related Validity |
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75 | (2) |
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77 | (1) |
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Some Results in the Theory of Measurement |
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78 | (8) |
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Reliability as a Proportion of Variance |
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79 | (1) |
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Standard Error of Measurement |
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79 | (1) |
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Corrections for Unreliability |
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80 | (2) |
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Some Validity Implications |
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82 | (1) |
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83 | (1) |
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What the Field's Been Doing Lately |
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84 | (2) |
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Some Optional, but Easy, Proofs |
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86 | (6) |
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Exploiting the Covariance |
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87 | (2) |
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Some Classical Test Theory Results |
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89 | (3) |
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92 | (1) |
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93 | (4) |
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97 | (21) |
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97 | (1) |
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98 | (17) |
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100 | (4) |
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104 | (2) |
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Statistical Proof and Assumptions |
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106 | (2) |
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An Extended Break: More Examples |
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108 | (2) |
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110 | (2) |
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112 | (1) |
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Reverse Range Restriction |
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113 | (2) |
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115 | (1) |
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116 | (2) |
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``Simple,'' Two-Variable Regression |
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118 | (40) |
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118 | (1) |
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The ``Best''-Fitting Regression Line |
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119 | (5) |
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123 | (1) |
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Some Thoughts About Regression Lines |
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124 | (7) |
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124 | (3) |
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An Alternate Formula for b1 |
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127 | (1) |
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There are Really Two Regression Lines |
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128 | (3) |
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131 | (5) |
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134 | (1) |
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134 | (2) |
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The Underlying Regression Model |
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136 | (3) |
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136 | (1) |
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137 | (2) |
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139 | (4) |
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140 | (1) |
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Some Thoughts on Distribution Theory Results |
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141 | (1) |
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An Application of Bivariate Regression |
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142 | (1) |
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143 | (2) |
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Some Thoughts about Equation VI.N |
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143 | (1) |
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144 | (1) |
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Some Regression Leftovers |
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145 | (10) |
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145 | (1) |
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145 | (1) |
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Fixed-X Versus Random-X Models |
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146 | (1) |
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147 | (1) |
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148 | (6) |
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154 | (1) |
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155 | (2) |
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157 | (1) |
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Three Applications of Bivariate Regression: Utility Analysis, Regression to the Mean, Partial Correlation |
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158 | (19) |
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158 | (1) |
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159 | (3) |
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Completing the Derivation of Equation VII.A |
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161 | (1) |
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162 | (6) |
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Some Equations, Some History |
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163 | (1) |
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164 | (1) |
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165 | (3) |
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168 | (6) |
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168 | (1) |
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168 | (2) |
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Further Examples, Spurious Correlations, and Mediators |
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170 | (2) |
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Important Leftover 1: Semipartial r |
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172 | (2) |
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Important Leftover 2: Multiple Partial r |
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174 | (1) |
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174 | (1) |
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175 | (2) |
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Multiple (Mostly Trivariate) Regression |
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177 | (30) |
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177 | (1) |
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178 | (11) |
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178 | (2) |
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The Underlying Model and the Prediction Equation |
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180 | (2) |
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182 | (2) |
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184 | (1) |
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185 | (1) |
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185 | (1) |
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Interpreting the Magnitude of R2y.12 |
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186 | (1) |
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``Unpacking'' the Value of R2y.12 |
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187 | (2) |
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An Aside: Why Always Square the Multiple Correlation? |
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189 | (1) |
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189 | (7) |
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The Squared Multiple Correlation |
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189 | (3) |
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The Regression Weights, Bi |
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192 | (2) |
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194 | (1) |
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195 | (1) |
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Multiple Regression in General |
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196 | (8) |
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196 | (1) |
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197 | (2) |
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Two Asides About Tests of Bi = 0 |
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199 | (2) |
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An Example of Multiple Regression |
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201 | (3) |
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204 | (2) |
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206 | (1) |
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Expanding the Regression Repertoire: Polynomial and Interaction Terms |
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207 | (32) |
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207 | (2) |
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209 | (9) |
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An Example (and Some Additional Ideas) |
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211 | (4) |
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215 | (1) |
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Two Additional Comments and Examples |
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216 | (2) |
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218 | (11) |
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219 | (1) |
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Interpreting B3: An Extended Example |
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219 | (6) |
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The Applied Literature Is Chock Full of Interactions |
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225 | (1) |
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My Goodness, What Have We Done? |
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226 | (3) |
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Five ``Leftovers'' About Interactions |
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229 | (4) |
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Yes, Interactions Can Contain More Than Two X's |
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229 | (1) |
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230 | (1) |
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231 | (1) |
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231 | (1) |
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232 | (1) |
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233 | (2) |
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235 | (4) |
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More about Regression, and Beyond |
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239 | (30) |
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239 | (1) |
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240 | (7) |
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243 | (2) |
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Some Comments About Shrinkage |
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245 | (2) |
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247 | (1) |
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248 | (2) |
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250 | (2) |
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251 | (1) |
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252 | (1) |
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252 | (3) |
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255 | (4) |
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256 | (3) |
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259 | (3) |
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261 | (1) |
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Cell Size (and Collinearity) |
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261 | (1) |
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262 | (2) |
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264 | (1) |
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265 | (4) |
Appendix Tables of Critical Values |
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269 | (2) |
ANSWERS TO SELECTED PROBLEMS |
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271 | (16) |
INDEXES |
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275 | (6) |
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281 | (6) |
About the Author |
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287 | |