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Understanding Correlation Matrices

Understanding Correlation Matrices

December 2020 | 120 pages | SAGE Publications, Inc
Correlation matrices (along with their unstandardized counterparts, covariance matrices) underlie much of the statistical machinery in common use today. A correlation matrix is more than a matrix filled with correlation coefficients. The value of one coefficient in the matrix puts constraints on the values of the others, and this is a major theme of the volume. In Understanding Correlation Matrices authors Alexandria Hadd and Joseph Lee Rodgers illustrate their key points with a wide range of lively examples, including correlations between intelligence measured at different ages through adolescence; correlations between public health expenditures, health life expectancy, adult mortality, and other country characteristics; correlations between wellbeing and state-level vital statistics; correlations between the racial composition of cities and professional sports teams; and correlations between childbearing intentions and childbearing outcomes over the reproductive life course. 
Chapter 1: Introduction
Chapter 2: The Mathematics of Correlation Matrices
Chapter 3: Statistical Hypothesis Testing on Correlation Matrices
Chapter 4: Methods for Correlation/Covariance Matrices as the Input Data
Chapter 5: Graphing Correlation Matrices
Chapter 6: The Geometry of Correlation Matrices
Chapter 7: Conclusion

This volume provides a useful and interesting discussion about the importance and utility of the correlation matrix as a unified entity, beyond the pairwise correlations themselves. As such it provides readers with useful information about the foundations of several important statistical procedures and models.

William G. Jacoby
Michigan State University

This is an exceptional book that brings together information on a technique that has been around for over a century, the correlation. The authors challenge the reader to see correlations not as individuals but as a community that can be interpreted and acted on as such.

Rick Tivis
Idaho State University

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Alexandria R. Hadd

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... More About Author

Joseph L. Rodgers

Joseph Lee Rodgers is Lois Autrey Betts Chair of Psychology and Human Development at Vanderbilt University in Nashville.  He moved to Vanderbilt in 2012 from the University of Oklahoma, where he worked from 1981 until 2012, and where he holds the title George Lynn Cross Emeritus Professor of Psychology.  Joe earned his Ph.D. in Quantitative Psychology from the L. L. Thurstone Psychometric Laboratory at the University of North Carolina, Chapel Hill, in 1981 (and also minored in Biostatistics at UNC).  He has held short-term teaching/research positions at Ohio State, University of Hawaii, UNC, Duke, University of Southern... More About Author

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ISBN: 9781544341095