Explaining Part (also known as semi-partial) 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 |
|
|
|
|||||
R-squared=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 |
|
|
|
|||||
R-squared=0.443
Comparing the two R-squareds tells us that phonological awareness accounts for 0.630-0.443 = 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 semi-partial 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
- R-squareds of a model with dysphraxia and phonological awareness and
the R-squared of a model with dysphraxia only with reading ability as dependent (outcome) variable.
R-squared (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 R-squared can also be used to describe analysis of (co)variance.