In an earlier entry, I discussed types of correlation coefficients for variables with different scales of measurement. In this entry, I want to discuss correlation coefficients that are used with three or more variables. These coefficients are known as partial and semi-partial correlation coefficients.
A zero-order correlation coefficient describes how much variance overlaps between two variables ignoring the third variable. This zero-order correlation is the same as a Pearson correlation coefficient as we discussed earlier. The figure below shows a) three variables and their overlaps and b) the overlap of variance described by the zero order correlation coefficient between X1 and Y.
A partial correlation is when the influence of the third variable is removed from the two variables that we are correlating. The figure below shows a) three variables and their overlaps and b) the overlap of variance described by the partial correlation coefficient. Thus, the partial correlation coefficient has the influence of X2 removed from both X1 and Y.
A semi-partial (also known as part) correlation is when the shared variance between the two predictor variables is removed. That is, the shared influence of the third variable is removed from only one of the other variables. The figure below shows a) three variables and their overlaps and b) the overlap of variance described by the semi-partial correlation coefficient. Thus, the partial correlation coefficient has the influence of X2 removed from X1.