Statistical Analysis for Education and Psychology Researchers

support of the alternative hypothesis that the true population correlation is not zero.
Notice that a variable correlated with itself is always 1.

Partial Correlation

A partial correlation between two variables adjusts the linear relationship between both
variables to take account of a third variable. This is called a first order partial
correlation. If the RAVEN variable is correlated with both MATHS and SMATHS then
the correlation between SMATHS and MATHS is likely to be reduced when the effect of
the RAVEN variable is partialled out (adjusted for). The general formula to compute a
first order partial correlation is,

First

Order

partial

correla

tion—

8.14

The partial correlation between SMATHS and MATHS with RAVEN partialled out is
given by

Interpretation

Notice that the correlation between MATHS and SMATHS has been reduced slightly
(from 0.896 to 0.836 when the effect of the RAVEN variable has been partialled out. This
indicates that a small portion of the common variance between MATHS and SMATHS is
explained by the third variable RAVEN.
SAS code for producing a partial correlation between SMATHS and MATHS
partialling out the effect of the RAVEN variable is shown,

proc corr data=a pearson csscp ;

var maths smaths raven;

partial raven;

run;

The relevant section of SAS output resulting from this partial statement is:
Pearson Partial Correlation Coefficients /Prob>|R| under Ho: Partial Rho=0/N=10

(^) MATHS SMATHS RAVEN
MATHS 1.00000 0.83722.
Inferences involving continuous data 291