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.

Graphing Correlation Matrices

Graphing Correlation Matrices

In this chapter, we describe and illustrate a number of graphical methods that have been developed to visually portray the information contained in a correlation matrix. The use of graphical methods has increased systematically since Tukey (1977) defined graphical analysis as one of the four hallmarks of exploratory data analysis (along with robustness and resistance, transformations, and residual analysis). Tukey (1977, pp. 1–3) drew a strong analogy between a research project and a courtroom setting, both of which are devoted to using empirical evidence to understand processes that are unclear or deceiving. He drew an even tighter analogy between the kind of evidence that is collected during a crime investigation—fingerprints, shoeprints, video evidence, document evaluation, and so on—and the kind of ...

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