Partial Correlation

Partial Correlation Defined

A partial correlation is used to measure the relationship or association that exists between the scores of two variables while controlling for a third, fourth, or even fifth variable. A partial correlation can range from −1 to +1, similar to a conventional Pearson correlation. However, a partial correlation can be larger or smaller than the Pearson correlation between the two variables. The value of a partial correlation explains the influence a third variable (or in some instances, additional variables) has on the relationship of the already calculated Pearson correlation. Partial correlations are accessible and can be used widely but are also easily misunderstood. Conceptual and statistical issues must be kept in mind when working with partial correlations.

As an example, a researcher might be interested in finding out whether the significant correlation between years married and individual’s romantic relationship satisfaction is influenced by their biological sex, but wants to make sure that the relationship between biological sex and romantic relationship satisfaction is not due to the effects of gender role expectations. Partial correlation is valuable in this scenario because gender roles may be confounded with biological sex and as a reasonable explanatory variable in the study. Biological sex may potentially influence the way individuals view gender role expectations. Partial correlation may be used to measure the relationship between biological sex and a variable assessing romantic relationship satisfaction, after accounting for the variability from each of these variables predicted by gender role expectations. The following discussion offers an example using the formula for a partial correlation.

Partial Correlation Formula

Consider a situation in which an interpersonal communication researcher wants to measure each of the 20 subjects on each of the following three variables: X (gender role expectations), Y (romantic relationship satisfaction), and Z (biological sex).[Page 1185] The research question may take the following form: “What is the nature of the relationship between married individual’s gender role expectation, and relationship satisfaction, while controlling for biological sex?” As such, the following correlations are calculated:

First, the values for r2 should be noted: .70 for XY, .80 for XZ, and .75 for YZ. One can now take these scores from each pair of variables (XY, XZ, and YZ) and understand the covariance (or how two variables change together) in terms of percentage. In more detail, X and Y overlap with a 70% variability, X and Z overlap with 80% variability, and Y and Z overlap with 75% variability.

...