Partial eta-squared in an ANCOVA
An example is given here.
The computation is performed in the second powerpoint slide in the above attachment. You just take SS(covariate)/(SS(covariate)+SS(error)) and you get a R-squared (which is also called partial eta-squared) and a signed square root of this gives the (partial) correlation.
In the eg in the univariate ancova for PRE its R-squared = 842.105/(842.105+1397.895) = 0.376 and sqrt(0.376) = 0.613 as given for the partial r (which only pops up if you use regression to fit the equiavalent model). This represents the average within group correlation between the covariate and outcome assuming the correlations within the groups are the same.
Oh, and you can get UNIVARIATE to output the partial R-squared – just ‘ask’ under options>Estimates of effect size and you get the extra column in the ANCOVA which just needs a signed square root.