Chapter 3 Correlation

 Association between scores on two variables –e.g., age and coordination skills in children, price and quality

Graphing Correlations The Scatter Diagram  Steps for making a scatter diagram 1. Draw axes and assign variables to them 2. Determine range of values for each variable and mark on axes 3. Mark a dot for each person’s pair of scores

Graphing Correlations The Scatter Diagram  For example:

Graphing Correlations The Scatter Diagram

Patterns of Correlation  Linear correlation  Curvilinear correlation  No correlation  Positive correlation  Negative correlation

Degree of Linear Correlation The Correlation Coefficient  Figure correlation using Z scores  Cross-product of Z scores –Multiply score on one variable by score on the other variable  Correlation coefficient –Average of the cross-products of Z scores

Degree of Linear Correlation The Correlation Coefficient  Formula for the correlation coefficient:  Positive perfect correlation: r = +1  No correlation: r = 0  Negative perfect correlation: r = –1

Correlation and Causality  Three possible directions of causality: 1.X Y 2. X Y 3. Z X Y

Correlation and Causality  Correlational research design –Correlation as a statistical procedure –Correlation as a kind of research design

Issues in Interpreting the Correlation Coefficient  Statistical significance  Proportionate reduction in error –r 2 –Used to compare correlations  Restriction in range  Unreliability of measurement

Correlation in Research Articles  Scatter diagrams occasionally shown  Correlation matrix