Enter the correlations between x and y, x and z, and y and z into the calculator to determine the partial correlation between x and y, controlling for z.

Partial Correlation Formula

The following formula is used to calculate the partial correlation between two variables, controlling for a third variable. 

r_xy.z = (r_xy - r_xz * r_yz) / sqrt((1 - r_xz^2) * (1 - r_yz^2))

Variables:

  • r_xy.z is the partial correlation between x and y, controlling for z
  • r_xy is the correlation between x and y
  • r_xz is the correlation between x and z
  • r_yz is the correlation between y and z

To calculate the partial correlation, subtract the product of the correlation between x and z and the correlation between y and z from the correlation between x and y. Then, subtract the square of the correlation between x and z from 1, and do the same for the correlation between y and z. Multiply these two results together and take the square root. Finally, divide the first result by the second result.

What is a Partial Correlation?

Partial correlation is a statistical measure that describes the association between two variables while controlling for the effects of one or more additional variables. It is used when researchers want to determine the relationship between two variables without the influence of other variables. This is particularly useful in multivariate analysis where multiple variables may be interrelated. The partial correlation coefficient ranges from -1 to +1, with -1 indicating a perfect negative correlation, +1 indicating a perfect positive correlation, and 0 indicating no correlation.