Regression, ANOVA, and the General Linear Model A Statistics Primer

ISBN-10: 1412997356

ISBN-13: 9781412997355

Edition: 2014

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Description: The goal of this book is to demonstrate basic statistical concepts from two different perspectives, giving the reader a conceptual understanding of how to interpret statistics and their use. Those two perspectives are a focus on the traditional tests that are used such as t-test, correlation and ANOVA, and a model-comparison approach using General Linear Methods. This text is intended for upper-level undergraduate courses, or first year graduate students. It is not for courses where students have no basic understanding of statistics.

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Book details

List price: $86.00
Copyright year: 2014
Publisher: SAGE Publications, Incorporated
Publication date: 1/14/2013
Binding: Paperback
Pages: 344
Size: 7.25" wide x 8.75" long x 0.50" tall
Weight: 1.496
Language: English

Peter Vik was born and raised in San Diego, California. He left the beaches to attend college at the University of California, Davis, and subsequently moved to Boulder, Colorado, where he earned his PhD in clinical psychology. He completed a clinical internship and postdoctoral fellowship with the Department of Psychiatry at the University of California, San Diego. Peter now lives in Pocatello, Idaho, where he is Professor of Psychology and Director of the University Honors Program at Idaho State University. When he is not writing statistics books (which he hopes is most of the time, for a while at least), Peter plays guitar, skis, mountain bikes, and he and his wife take turns holding and staring at their two brand new grandchildren.

Preface
Acknowledgments
About the Author
Introduction
Fundamental Questions
Are Two Variables Related?
What Is the Direction of the Relationship Between Two Variables?
How Strong Is the Relationship Between Two Variables?
Statistical Models
Measuring the Error of the Model
Model Comparison
Summary
Foundations of the General Linear Model
Predicting Scores: The Mean and the Error of Prediction
The Data
The Model
Error of the Model
Counting Errors
Sum of the Absolute Errors
Sum of the Squared Errors
Conceptual Versus Computational Formula
Variance and Standard Deviation
Another Example
A Preview of Model Comparison
Summary
Bivariate regression
Bivariate Regression
The Bivariate Regression Coefficient
Calculate the Regression Coefficient
Graph the Relationship Between X and Y
Estimating the Error of the Model
Centering the Predictor Variable: Mean Deviation of X
Summary
Model Comparison: The Simplest Model Versus a Regression Model
Model Comparison
10 Steps to Compare Models
State the compact Model C and an Augmented Model A
Identify the Null Hypothesis (H<sub>0</sub>)
Count the Number of Parameters Estimated for Each Model
Calculate the Regression Equation
Compute the Total Sum of Squares (SSE<sub>C</sub> or SST)
Compute the Sum of Squares for Model A (SSE<sub>A</sub>)
Compute Sum of Squares Reduced (SSR)
Compute the Proportional Reduction in Error (PRE or R<sup>2</sup>)
Complete the Summary Table
Decide About H<sub>0</sub>
Model Comparison Example
Define the Initial, Compact Model C and an Augmented Model A
Identify the Null Hypothesis (H<sub>0</sub>)
Count the Number of Parameters Estimated in Each Model
Calculate the Regression Equation
Compute the Total Sum of Squares (SST or SSE<sub>C</sub>)
Compute the Sum of Squares for Model A (SSE<sub>A</sub>)
Compute Sum of Squares Reduced (SSR)
Compute the Proportional Reduction in Error (PRE or R<sup>2</sup>)
Complete the Summary Table
Decide About H<sub>0</sub>
Summary
Fundamental Statistical Tests
Correlation: Traditional and Regression Approaches
Magnitude
Direction
Picture the Correlation
Calculate the Correlation
Total or Combined Variance
Common or Shared Variance
Pearson Correlation Coefficient
Demonstration
Null Hypothesis and Correlation
Correlation Coefficient and Variance Explained
Summary
The Traditional t Test: Concepts and Demonstration
Comparing Group Means
t-Test Formula
Using t to Decide About H<sub>0</sub>
The t Distribution
Demonstration
Summary
One-Way ANOVA: Traditional Approach
ANOVA Concepts
Begin With SST
Compute Explained SS
Compute Residual SSE
ANOVA Summary Table
Summary
t Test, ANOVA, and the Bivariate Regression Approach
Test Two Groups Using Model Comparison
State the Compact Model C and an Augmented Model A
Identify the Null Hypothesis
Count the Number of Parameters Estimated in Each Model
Calculate the Regression Equation
Compute the Total Sum of Squares
Compute the Sum of Squared Errors for Model A
Compute the Sum of Squares Reduced
Compute the Proportional Reduction in Error
Complete the Summary Table
Decide About H<sub>0</sub>
Compare the Results o t Test, ANOVA, and Bivariate Regression
Summary
Adding Complexity
Model Comparison II: Multiple Regression
Conducting the Omnibus Test
Isolating the Effects of X<sub>1</sub>, and X<sub>2</sub>
Testing the Relationship Between X<sub>2</sub> and Y
Testing the Relationship Between X<sub>1</sub> and Y
Summary
Multiple Regression: When Predictors Interact
Mean Deviation Revisited
The Interaction Term: A Cross Product of the Predictors
Interpreting the Interaction
Interaction Without Mean Deviation
Summary
Two-Way ANOVA: Traditional Approach
Grand and Group Means
Partition the Sum of Squares
Compute SST
SSB for Sex
SSB for Diagnosis
Interaction of Sex and Diagnosis
Begin the Summary Table
Residual Sum of Squares
Complete the Summary Table
Interpret the F Values
Interpret the Interaction
Summary
Two-Way ANOVA: Model Comparison Approach
Contrast Versus Dummy Codes
Conducting the Omnibus Test
Calculate the Error of the Omnibus Model
Testing the Components of the Model
Testing the Maui Effect of Sex
Testing the Main Effect of Diagnosis
Testing the Interaction of Diagnosis and Sax
Interpreting the Coefficients
Summary
One-Way ANOVA With Three Groups: Traditional Approach
Conducting the Analysis of Variance
Total Variance
Variance Explained
Compute the Residual Variance
Complete the Summary Table
Post Hoc analysis: Where's the Difference?
Risk of Multiple Tests
Calculate the LSD
Summary
ANOVA With Three Groups: Model Comparison Approach
Isolating Effects: Conceptualizing Linear Comparisons of Three Groups
Contrast Codes With More Than Two Groups
Comparing Models to Test the One-Way ANOVA
Conducting the Omnibus Test
Isolating the Effects of the Linear Predictor
Isolating the Effects of the Quadratic Predictor
Summary
Two-by-Three ANOVA: Complex Categorical Models
Sum of Squares Between
Sum of Squares Between for Sex
Sum of Squares Between for Drug Abuse
Interaction of Sex and Drug Abuse
Sum of Squares Within
Interpreting the Results
Summary
Two-by-Three ANOVA: Model Comparison Approach
Omnibus Model
Compute Error for Model A
Isolate the Effects of Each Model A Predictor
Main Effect for Sex
linear Main Effect for Drug Abuse (DA<sub>linear</sub>)
Quadratic Main Effect for Drug Abuse (DA<sub>quadratic</sub>)
Interaction between Sex and Linear Contrast for Drug Abuse (DA<sub>linear</sub>)
Interaction Between Sex and Linear Contrast for Drug Abuse (DA<sub>linear</sub>)
Complete the Summary Table
Summary
Analysis of Covariance: Continuous and Categorical Predictors
Concept of Statistical Covariation
Testing the Effects of Sex, Controlling for Age
They Weren't Related, but Now They Are!
Summary
Repeated Measures
Repeated Measures "Matched Pairs" t Test
Repeated Measures ANOVA: Model Comparison Approach
Finding the Difference Between the Two DVs
Summary
Multiple Repeated Measures
Three Repeated Measures: Weighting Each Score
Linear Change in Mean Scores Over Time
Model A and the Average W<sub>linear</sub> Score
Quadratic Change in Mean Scores Over Time
Combine the Two Analyses Into a Single Summary Table
Summary
Mixed Between and Within Designs
Main Effect Between Groups
Main Effect Within Groups
Groups-by-Treatment Interaction
Summary
A Final Comment
Appendices
Research Designs
Experiment
Quasi-Experiment
Associations! Designs
Variables, Distributions, and Statistical Assumptions
Types of Variables
Ordinal Variables
Nominal Variables
Continuous Variable
Distributions of Continuous Variables
Operational Definition
Statistical Assumptions
Normal Distribution
Homogeneity of Variances
Sampling and Sample Sizes
Null Hypothesis, Statistical Decision Making, and Statistical Power
Null Hypothesis
Statistical Decision
Statistical Power
References
Index
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