# Calculating effect size (partial eta squared) for a planned comparison effect

I have a between-subjects ANCOVA (factors A and B, and covariate C), for which A*B is significant. I decomposed the interaction with a planned comparison described by the contrast A=(-1,1), B=(0,1), which was significant. I would like to find out the effect size (partial eta squared) for this effect, but unfortunately my stats package (Statistica) does not display this statistic for effects obtained via a contrast (planned comparison).

So I set out to compute it manually. I used the definition np^2=SS_treatment/SS_total. Statistica only displays SS_effect and SS_error, so as SS_treatment I took the SS_effect reported in the planned comparison, and as SS_total I took the SS_effect reported for the A*B interaction.

This, however, gives me a value of about 3.0, whereas I was expecting partial eta squared to be in the order of magnitude below 1, which is what I get for other similar effects.

Is the way I computed the partial eta squared incorrect, or have I otherwise made other mistakes? Thanks for any help!

It's probably easiest to compute $\eta^2_p$ directly from the $t$- or $F$-statistic observed with the contrast. You can do that using the formula $$\eta^2_p = \frac{F}{F+v_d/v_n},$$ where $v_d$ is the denominator degrees of freedom for the $F$-ratio and $v_n$ is the numerator degrees of freedom.
• $v_n$ should be 1 in your case. So if the "df" listed by Statistica is greater than 1, then it refers to $v_d$. As for your second question: no. – Jake Westfall Jul 28 '14 at 19:34