It is quite common to see the term "Partial R^{2}" 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 R^{2} 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 b_{3},
the its partial R^{2} would be SSb_{3}/(CTSS).

N.B. CTSS = SSR_{m} + 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 R^{2}? 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 R^{2} = SS_{trt} / (CTSS)

The partial R^{2} 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.

R. I. Cue ©

Department of Animal Science, McGill University

last updated : 2011 October 5