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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!

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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.

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  • $\begingroup$ Thanks! Not sure, though, who the denominator and numerator would be in this case (which fraction)? Statistica only gives me df for "M1" (presumably the effect itself) and for "Error". In either case, shouldn't the result computed via the F-statistic be the same as the one computed with the SS terms? $\endgroup$ – z8080 Jul 28 '14 at 18:34
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    $\begingroup$ $v_n$ 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. $\endgroup$ – Jake Westfall Jul 28 '14 at 19:34
  • $\begingroup$ Yes that gives me something of a more appropriate value, thanks again! $\endgroup$ – z8080 Jul 28 '14 at 20:03

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