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Product Moment Correlation

Part 2. Marketing Research

  1. George R. Franke

Published Online: 15 DEC 2010

DOI: 10.1002/9781444316568.wiem02068

Wiley International Encyclopedia of Marketing

Wiley International Encyclopedia of Marketing

How to Cite

Franke, G. R. 2010. Product Moment Correlation. Wiley International Encyclopedia of Marketing. 2.

Author Information

  1. University of Alabama, Tuscaloosa, AL, USA

Publication History

  1. Published Online: 15 DEC 2010

Abstract

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.

Keywords:

  • correlation;
  • effect size;
  • dichotomization;
  • difference scores;
  • coefficient of determination