Statistics Definitions > Partial Correlation

## What is Partial Correlation?

Partial correlation is a **measure of the strength of a relationship between two variables while controlling for the effect of one or more other variables.** For example, you might want to see if there is a correlation between caloric intake and blood pressure, while controlling for weight or amount of exercise. While it’s possible to control for multiple variables (called control variables or covariates), more than one or two is usually not recommended because the more control variables you have, the less reliable your test.

Like with regular correlation, there will be one independent variable (the x-value) and one dependent variable (the y-value). Both of these are continuous. In the blood pressure example above, the independent variable is caloric intake and the dependent variable is blood pressure. The control variables — weight and amount of exercise should also be continuous.

The correlation coefficient, r, is also used to show the results from partial correlation. Like the regular correlation coefficient, r

_{partial}will have a value from -1 to 1. Subscripts show which variables are used for the correlation and which are controlled for. For example, let’s say you are correlating caloric intake (X

_{1}) against blood pressure (X

_{2}), while controlling for weight (X

_{3}). The correlation coefficient would be written like this:

r

_{12.3}

You might also see it written as r(1,2|3)

Partial correlation is usually carried out by performing multiple regression analysis. Some statistical software programs offer partial correlation. For example, in SPSS choose Analyze > Correlations > Partial. If the partial correlation, r_{12.3}, is smaller than the simple (two-variable) correlation r_{12}, but greater than 0, then variable 3 partly explains the correlation between X and Y.

## Semipartial Correlation

Semipartial correlation is almost the same as partial. With semipartial correlation, the third variable is held constant for *either *X or Y but not both; with partial, the third variable is held constant for both X and Y.