Understanding Correlation Matrices
- Alexandria Hadd - Spelman College, USA
- Joseph Lee Rodgers - Vanderbilt University
Quantitative Methods | Regression & Correlation | Research Methods in Psychology
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 including correlations between intelligence measured at different ages through adolescence; correlations between country characteristics such as public health expenditures, health life expectancy, and adult mortality; correlations between well-being 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. This volume may be used effectively across a number of disciplines in both undergraduate and graduate statistics classrooms, and also in the research laboratory.
R files for chapters 1 and 3, plus an online appendix which demonstrates the use of the functions, are available on a website for the book at: study.sagepub.com/researchmethods/qass/hadd-understanding-correlation.
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.
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.
Sample Materials & Chapters
Chapter 2: The Mathematics of Correlation Matrices