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Preface | |

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Acknowledgments | |

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About the Author | |

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Introduction | |

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Fundamental Questions | |

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Are Two Variables Related? | |

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What Is the Direction of the Relationship Between Two Variables? | |

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How Strong Is the Relationship Between Two Variables? | |

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Statistical Models | |

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Measuring the Error of the Model | |

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Model Comparison | |

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Summary | |

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Foundations of the General Linear Model | |

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Predicting Scores: The Mean and the Error of Prediction | |

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The Data | |

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The Model | |

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Error of the Model | |

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Counting Errors | |

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Sum of the Absolute Errors | |

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Sum of the Squared Errors | |

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Conceptual Versus Computational Formula | |

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Variance and Standard Deviation | |

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Another Example | |

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A Preview of Model Comparison | |

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Summary | |

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Bivariate regression | |

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Bivariate Regression | |

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The Bivariate Regression Coefficient | |

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Calculate the Regression Coefficient | |

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Graph the Relationship Between X and Y | |

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Estimating the Error of the Model | |

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Centering the Predictor Variable: Mean Deviation of X | |

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Summary | |

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Model Comparison: The Simplest Model Versus a Regression Model | |

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Model Comparison | |

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10 Steps to Compare Models | |

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State the compact Model C and an Augmented Model A | |

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Identify the Null Hypothesis (H<sub>0</sub>) | |

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Count the Number of Parameters Estimated for Each Model | |

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Calculate the Regression Equation | |

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Compute the Total Sum of Squares (SSE<sub>C</sub> or SST) | |

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Compute the Sum of Squares for Model A (SSE<sub>A</sub>) | |

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Compute Sum of Squares Reduced (SSR) | |

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Compute the Proportional Reduction in Error (PRE or R<sup>2</sup>) | |

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Complete the Summary Table | |

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Decide About H<sub>0</sub> | |

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Model Comparison Example | |

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Define the Initial, Compact Model C and an Augmented Model A | |

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Identify the Null Hypothesis (H<sub>0</sub>) | |

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Count the Number of Parameters Estimated in Each Model | |

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Calculate the Regression Equation | |

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Compute the Total Sum of Squares (SST or SSE<sub>C</sub>) | |

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Compute the Sum of Squares for Model A (SSE<sub>A</sub>) | |

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Compute Sum of Squares Reduced (SSR) | |

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Compute the Proportional Reduction in Error (PRE or R<sup>2</sup>) | |

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Complete the Summary Table | |

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Decide About H<sub>0</sub> | |

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Summary | |

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Fundamental Statistical Tests | |

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Correlation: Traditional and Regression Approaches | |

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Magnitude | |

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Direction | |

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Picture the Correlation | |

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Calculate the Correlation | |

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Total or Combined Variance | |

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Common or Shared Variance | |

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Pearson Correlation Coefficient | |

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Demonstration | |

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Null Hypothesis and Correlation | |

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Correlation Coefficient and Variance Explained | |

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Summary | |

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The Traditional t Test: Concepts and Demonstration | |

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Comparing Group Means | |

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t-Test Formula | |

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Using t to Decide About H<sub>0</sub> | |

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The t Distribution | |

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Demonstration | |

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Summary | |

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One-Way ANOVA: Traditional Approach | |

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ANOVA Concepts | |

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Begin With SST | |

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Compute Explained SS | |

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Compute Residual SSE | |

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ANOVA Summary Table | |

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Summary | |

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t Test, ANOVA, and the Bivariate Regression Approach | |

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Test Two Groups Using Model Comparison | |

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State the Compact Model C and an Augmented Model A | |

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Identify the Null Hypothesis | |

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Count the Number of Parameters Estimated in Each Model | |

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Calculate the Regression Equation | |

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Compute the Total Sum of Squares | |

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Compute the Sum of Squared Errors for Model A | |

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Compute the Sum of Squares Reduced | |

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Compute the Proportional Reduction in Error | |

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Complete the Summary Table | |

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Decide About H<sub>0</sub> | |

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Compare the Results o t Test, ANOVA, and Bivariate Regression | |

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Summary | |

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Adding Complexity | |

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Model Comparison II: Multiple Regression | |

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Conducting the Omnibus Test | |

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Isolating the Effects of X<sub>1</sub>, and X<sub>2</sub> | |

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Testing the Relationship Between X<sub>2</sub> and Y | |

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Testing the Relationship Between X<sub>1</sub> and Y | |

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Summary | |

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Multiple Regression: When Predictors Interact | |

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Mean Deviation Revisited | |

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The Interaction Term: A Cross Product of the Predictors | |

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Interpreting the Interaction | |

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Interaction Without Mean Deviation | |

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Summary | |

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Two-Way ANOVA: Traditional Approach | |

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Grand and Group Means | |

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Partition the Sum of Squares | |

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Compute SST | |

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SSB for Sex | |

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SSB for Diagnosis | |

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Interaction of Sex and Diagnosis | |

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Begin the Summary Table | |

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Residual Sum of Squares | |

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Complete the Summary Table | |

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Interpret the F Values | |

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Interpret the Interaction | |

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Summary | |

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Two-Way ANOVA: Model Comparison Approach | |

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Contrast Versus Dummy Codes | |

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Conducting the Omnibus Test | |

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Calculate the Error of the Omnibus Model | |

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Testing the Components of the Model | |

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Testing the Maui Effect of Sex | |

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Testing the Main Effect of Diagnosis | |

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Testing the Interaction of Diagnosis and Sax | |

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Interpreting the Coefficients | |

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Summary | |

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One-Way ANOVA With Three Groups: Traditional Approach | |

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Conducting the Analysis of Variance | |

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Total Variance | |

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Variance Explained | |

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Compute the Residual Variance | |

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Complete the Summary Table | |

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Post Hoc analysis: Where's the Difference? | |

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Risk of Multiple Tests | |

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Calculate the LSD | |

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Summary | |

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ANOVA With Three Groups: Model Comparison Approach | |

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Isolating Effects: Conceptualizing Linear Comparisons of Three Groups | |

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Contrast Codes With More Than Two Groups | |

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Comparing Models to Test the One-Way ANOVA | |

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Conducting the Omnibus Test | |

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Isolating the Effects of the Linear Predictor | |

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Isolating the Effects of the Quadratic Predictor | |

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Summary | |

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Two-by-Three ANOVA: Complex Categorical Models | |

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Sum of Squares Between | |

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Sum of Squares Between for Sex | |

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Sum of Squares Between for Drug Abuse | |

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Interaction of Sex and Drug Abuse | |

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Sum of Squares Within | |

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Interpreting the Results | |

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Summary | |

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Two-by-Three ANOVA: Model Comparison Approach | |

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Omnibus Model | |

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Compute Error for Model A | |

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Isolate the Effects of Each Model A Predictor | |

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Main Effect for Sex | |

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linear Main Effect for Drug Abuse (DA<sub>linear</sub>) | |

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Quadratic Main Effect for Drug Abuse (DA<sub>quadratic</sub>) | |

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Interaction between Sex and Linear Contrast for Drug Abuse (DA<sub>linear</sub>) | |

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Interaction Between Sex and Linear Contrast for Drug Abuse (DA<sub>linear</sub>) | |

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Complete the Summary Table | |

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Summary | |

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Analysis of Covariance: Continuous and Categorical Predictors | |

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Concept of Statistical Covariation | |

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Testing the Effects of Sex, Controlling for Age | |

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They Weren't Related, but Now They Are! | |

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Summary | |

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Repeated Measures | |

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Repeated Measures "Matched Pairs" t Test | |

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Repeated Measures ANOVA: Model Comparison Approach | |

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Finding the Difference Between the Two DVs | |

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Summary | |

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Multiple Repeated Measures | |

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Three Repeated Measures: Weighting Each Score | |

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Linear Change in Mean Scores Over Time | |

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Model A and the Average W<sub>linear</sub> Score | |

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Quadratic Change in Mean Scores Over Time | |

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Combine the Two Analyses Into a Single Summary Table | |

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Summary | |

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Mixed Between and Within Designs | |

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Main Effect Between Groups | |

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Main Effect Within Groups | |

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Groups-by-Treatment Interaction | |

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Summary | |

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A Final Comment | |

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Appendices | |

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Research Designs | |

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Experiment | |

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Quasi-Experiment | |

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Associations! Designs | |

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Variables, Distributions, and Statistical Assumptions | |

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Types of Variables | |

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Ordinal Variables | |

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Nominal Variables | |

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Continuous Variable | |

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Distributions of Continuous Variables | |

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Operational Definition | |

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Statistical Assumptions | |

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Normal Distribution | |

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Homogeneity of Variances | |

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Sampling and Sample Sizes | |

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Null Hypothesis, Statistical Decision Making, and Statistical Power | |

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Null Hypothesis | |

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Statistical Decision | |

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Statistical Power | |

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References | |

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Index | |