Correlation matrices (along with their unstandardized counterparts, covariance matrices) underlie the majority the statistical methods that researchers use today. A correlation matrix is more than a matrix filled with correlation coefficients. The value of one correlation in the matrix puts constraints on the values of the others, and the multivariate implications of this statement is a major theme of the volume. Alexandria Hadd and Joseph Lee Rodgers cover many features of correlations matrices including statistical hypothesis tests, their role in factor analysis and structural equation…mehr
Correlation matrices (along with their unstandardized counterparts, covariance matrices) underlie the majority the statistical methods that researchers use today. A correlation matrix is more than a matrix filled with correlation coefficients. The value of one correlation in the matrix puts constraints on the values of the others, and the multivariate implications of this statement is a major theme of the volume. Alexandria Hadd and Joseph Lee Rodgers cover many features of correlations matrices including statistical hypothesis tests, their role in factor analysis and structural equation modeling, and graphical approaches. They illustrate the discussion with a wide range of lively examples.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
Alexandria Ree Hadd is an Assistant Professor of Psychology at Spelman College in Atlanta, where she teaches courses on statistics and research methods to undergraduate students. She earned her Masters and Ph.D. in Quantitative Psychology at Vanderbilt University and her B.S. in Psychology and Mathematics from Oglethorpe University. Her Masters thesis - titled "Correlation Matrices in Cosine Space" -- was specifically on the properties of correlation matrices. She also researched correlations in her dissertation, which was titled "A Comparison of Confidence Interval Techniques for Dependent Correlations." At Vanderbilt, she taught introductory statistics and was a teaching assistant for a number of graduate statistics/methods courses. In addition to correlation matrices, her research interests include applying modeling techniques to developmental, educational, and environmental psychology questions. In her spare time, her hobbies include hiking, analog collaging, attending art and music shows, and raising worms (who are both pets and dedicated composting team members).
Inhaltsangabe
Series Editors Introduction Preface Acknowledgments About the Authors Chapter 1: Introduction The Correlation Coefficient: A Conceptual Introduction The Covariance The Correlation Coefficient and Linear Algebra: Brief Histories Examples of Correlation Matrices Summary Chapter 2: The Mathematics of Correlation Matrices Requirements of Correlation Matrices Eigenvalues of a Correlation Matrix Pseudo-Correlation Matrices and Positive Definite Matrices Smoothing Techniques Restriction of Correlation Ranges in the Matrix The Inverse of a Correlation Matrix The Determinant of a Correlation Matrix Examples Summary Chapter 3: Statistical Hypothesis Testing on Correlation Matrices Hypotheses About Correlations in a Single Correlation Matrix Hypotheses About Two or More Correlation Matrices Testing for Linear Trend of Eigenvalues Summary Chapter 4: Methods for Correlation/Covariance Matrices as the Input Data Factor Analysis Structural Equation Modeling Meta-Analysis of Correlation Matrices Summary Chapter 5: Graphing Correlation Matrices Graphing Correlations Graphing Correlation Matrices Summary Chapter 6: The Geometry of Correlation Matrices What Is Correlation Space? The 3 × 3 Correlation Space Properties of Correlation Space: The Shape and Size Uses of Correlation Space Example Using 3 × 3 and 4 × 4 Correlation Space Summary Chapter 7: Conclusion References Index
Series Editors Introduction Preface Acknowledgments About the Authors Chapter 1: Introduction The Correlation Coefficient: A Conceptual Introduction The Covariance The Correlation Coefficient and Linear Algebra: Brief Histories Examples of Correlation Matrices Summary Chapter 2: The Mathematics of Correlation Matrices Requirements of Correlation Matrices Eigenvalues of a Correlation Matrix Pseudo-Correlation Matrices and Positive Definite Matrices Smoothing Techniques Restriction of Correlation Ranges in the Matrix The Inverse of a Correlation Matrix The Determinant of a Correlation Matrix Examples Summary Chapter 3: Statistical Hypothesis Testing on Correlation Matrices Hypotheses About Correlations in a Single Correlation Matrix Hypotheses About Two or More Correlation Matrices Testing for Linear Trend of Eigenvalues Summary Chapter 4: Methods for Correlation/Covariance Matrices as the Input Data Factor Analysis Structural Equation Modeling Meta-Analysis of Correlation Matrices Summary Chapter 5: Graphing Correlation Matrices Graphing Correlations Graphing Correlation Matrices Summary Chapter 6: The Geometry of Correlation Matrices What Is Correlation Space? The 3 × 3 Correlation Space Properties of Correlation Space: The Shape and Size Uses of Correlation Space Example Using 3 × 3 and 4 × 4 Correlation Space Summary Chapter 7: Conclusion References Index
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