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.

# Introduction

### Introduction

The correlation matrix is a row-by-column arrangement of a set of correlation coefficients. The rows and columns refer to specific variables, which are measured features of the people, animals, or entities that behavioral science researchers study. For example, four variables assessed on people may be height, intelligence, birthweight, and shyness; three variables assessed on animals may be cortisol levels, reaction time, and counts of observed behaviors; and three variables assessed on an entity (e.g., a school) may be the percent low income, teacher turnover rate, and average student performance. A correlation matrix indicates the linear association between each pair of variables, such that the same variables in the same order label both the columns and the rows of the correlation matrix.

However, a correlation ...

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