Explaining Part (also known as semipartial) correlations
Try to assess the importance of phonological awareness on predicting Reading Ability which is independent of dysphraxia. You can do this using General Linear Model:univariate. Suppose putting both phonological awareness and dysphraxia as covariates gives
Suppose we have
Dependent Variable=Reading Ability
Source 
df 
Type III SS 
MS 
F 
p 

Dysphraxia 
1 
13.59 
13.59 
9.44 
.013 

Phonological Awareness 
1 
8.45 
8.45 
5.87 
.038 

Error 
9 
12.96 
1.44 



Corrected Total 
11 
35.00 



Rsquared=0.630
This tells us that phonological Awareness has a statistically significant influence on reading ability after taking dysphraxia into account (F(1,9)=8.45, p<0.05).
Fitting just dysphraxia gives
Dependent Variable=Reading Ability
Source 
df 
Type III SS 
MS 
F 
p 

Dysphraxia 
1 
15.50 
15.50 
7.95 
.018 

Error 
10 
19.50 
1.95 



Corrected Total 
11 
35.00 



Rsquared=0.443
Comparing the two Rsquareds tells us that phonological awareness accounts for 0.6300.443 = 0.187 or 18.7% of total variance in reading ability over and above that predicted by dysphraxia. The signed square root of this Sqrt(0.187)=sgn(0.432) is the Part correlation, also called the semipartial correlation of phonological awareness adjusted for dysphraxia with reading ability.
In other words: The square of the (Part) correlation which relates aspects of phonological awareness, unrelated to dysphraxia, to reading ability is the difference in
 Rsquareds of a model with dysphraxia and phonological awareness and
the Rsquared of a model with dysphraxia only with reading ability as dependent (outcome) variable.
Rsquared (or equivalently its signed square root, the part correlation) is often given as a measure of the strength of an association between one or more predictor variables of interest, adjusted for other confounding predictors, with an outcome. Since this is a regression term Rsquared can also be used to describe analysis of (co)variance.