Question: A study by Nolan and colleagues (2003) examined the relation between externalizing behaviors (acting out) and anxiety in adolescents. Depression has been shown to relate to both of these variables. What role might depression play in the observed positive relation between these variables? The correlation matrix below displays the Pearson correlation coefficients, as calculated by computer software, for each pair of the variables of interest: depression, externalizing, and anxiety. The Pearson correlation coefficients for each pair of variables are at the intersection in the chart of the two variables. For example, the correlation coefficient for the association between depression (top row) and externalizing (second column of correlations) is 0.635, a very strong positive correlation
a. What is the correlation coefficient for the association between depression and anxiety? Explain what this correlation coefficient tells us about the relation between these variables.
b. What is the correlation coefficient for the association between anxiety and externalizing? Explain what this correlation coefficient tells us about the relation between these variables.
c. The partial correlation of anxiety and externalizing is 0.17, controlling for the variable of depression. How is this different from the original Pearson correlation coefficient between these two variables?
d. Why is the partial correlation coefficient different from the original Pearson correlation coefficient between these two variables? What did we learn by calculating a partial correlation?