Product Moment Correlation
Part 2. Marketing Research
Published Online: 15 DEC 2010
Copyright © 2011 John Wiley & Sons, Ltd. All rights reserved.
Wiley International Encyclopedia of Marketing
How to Cite
Franke, G. R. 2010. Product Moment Correlation. Wiley International Encyclopedia of Marketing. 2.
- Published Online: 15 DEC 2010
The Pearson product moment correlation coefficient is an index of the degree of linear relationship between two variables. For two variables X and Y the correlation r is computed where r can be interpreted as the predicted standard deviation difference in Y for two observations that are different by one standard deviation in X. Rules of thumb for interpreting r are that population values of r = 0.1, 0.3, and 0.5 (positive or negative) can be viewed as small, medium, and large effects, respectively. The significance of r in a sample of n observations can be tested using values from Student's t distribution with n–2 degrees of freedom.
In general, r can range from −1 to +1. However, many factors can influence the magnitude of r, including nonlinear relationships, restrictions on the range of variables, dichotomization or unequal distributions of variables, outlying observations, and measurement error. Thus, while r is a useful summary of linear relationships between two variables, it may sometimes conceal more than it reveals. Creating a scatter plot of X and Y values is a useful tool to avoid misleading inferences from estimated correlation coefficients.
- effect size;
- difference scores;
- coefficient of determination