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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

#### 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

## SEARCH

### 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