Story, Dale
Department of Political Science
University of Texas at Arlington
CORRELATION COEFFICIENT
The Correlation Coefficient may also be referred to as or symbolized by Pearson product-moment
correlation coefficient, Pearson correlation coefficient, r, R, or Pearson's r.
It is a measure of the strength of an association between two continuous variables. The range is from -1
to +1. A Correlation Coefficient of -1 is a perfect inverse relationship. A Correlation Coefficient of +1 is a
perfect direct (positive) relationship. A Correlation Coefficient of 0 is a perfect “non-relationship.” The
sign (- or +) simply describes the slope or direction of the relationship (inverse or positive). For example,
a Correlation Coefficient of -0.5 is just as “strong” as one of +0.5. The greater the absolute value of a
Correlation Coefficient , the stronger the relationship. Negative and positive coefficients simply have
different slopes.
Since Correlation Coefficients are measures of association, they need to be interpreted in comparison to
other Correlation Coefficients. For example, if the Correlation Coefficient between GDP and a Press
Freedom scale from 1-100 is +0.3; and if the Correlation Coefficient between GDP per capita and the
same Press Freedom scale is +0.5—the latter relationship is stronger—or GDP per capita is a better
predictor of Press Freedom than GDP.
Here is an example of output of a Correlation Coefficient between Population (1989) and Percent
Urbanization (1989). SPSS will always produce a matrix, though only one value is the Correlation
Coefficient between the two variables. Actually, you will find this same value in two cells—but they are
both the correlation between the two variables. The other two cells are the correlation between the
variable and itself, which will always be? The Correlation Coefficient between Population and Percent
Urbanization from the table below is 0.359.
Correlations
Percent
Urbanization,
Population, 1989
Population, 1989
Pearson Correlation
1
Sig. (2-tailed)
N
Percent Urbanization, 1989
Pearson Correlation
Sig. (2-tailed)
N
1989
.359
.131
19
19
.359
1
.131
19
19