It is quite common to see the term "Partial R2" in a text. I am referring here to the use of the term in reference to our ANOVA, and not about a partial correlation. What does it mean and how do we calculate it?.
Partial R2 simply means how much of the Corrected Total Sums of Squares can we attribute to the Sums of Squares for this particular effect.
So, if we have an Effect (line in our ANOVA table), for example, a regression term b3, the its partial R2 would be SSb3/(CTSS).
N.B. CTSS = SSRm + SSE
We can just as easily and validly use this with a classification effect. Using my clover treatments example, we can ask what is the partial R2? We simply use the same, above logic, and take the Sums of Squares for our effect and divide by the Corrected Total Sums of Squares.
partial R2 = SStrt / (CTSS)
The partial R2 gives us an indication of just how much of the variation (Sums of Squares) our model term actually explains. It might be statistically significant, but explain only 1% of the Sums of Squares, and hence, in practical terms not really be of much import, or interest.