Question

in a partial correlation, what happens to the original value of a correlational coefficient when another variable is partialed out

Answer 1

in a partial correlation,

the original value of a correlation coefficient decreases /increase or no effect when another variable is partial out.

Let us see an example.

in this case original correlation decreased from -0.307 to -0.314 after controlling for age.

here y is V02 max ,x1=age x2=weight

we can carry out partial correlation controlling age.

From the above output before correlation coefficient was -0.307 between V02 max and weight.

After controlling age variable by partial correlation,correlation coefficient now was r=-0.314

The results of the partial correlation highlighted by the red rectangle show that there was a moderate, negative partial correlation between the dependent variable, "VO₂max", and independent variable, "weight", whilst controlling for "age", which was statistically significant (r(97) = -.314, n = 100, p = .002). However, when we refer to the Pearson's product-moment correlation – also known as the zero-order correlation – between "VO₂max" and "weight", without controlling for "age", as highlighted by the blue rectangle, we can see that there was also a statistically significant, moderate, negative correlation between "VO₂max" and "weight" (r(98) = -.307, n = 100, p = .002). This suggests that "age" had very little influence in controlling for the relationship between "VO₂max" and "weight".