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

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

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.