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.
John B. Carroll (1961), in his Psychometric Society presidential address, stated that the “correlation coefficient is one of the most frequently used tools of psychometricians … and perhaps also one of the most frequently misused” (p. 347). In the almost 60 years since that statement, statistical analysis has been trending in the direction of becoming evermore multivariate (for support, see, among many others, Harlow, 2005). In 2020, when this concluding chapter is being written, it is safe to rephrase Carroll’s statement: The correlation matrix is one of the most frequently used tools of both methodologists and researchers across many different disciplines. To support understanding the correlation matrix, and to avoid misuse of this important statistical tool, has been the goal of this book.