# Confidence Interval for $\eta^2$

Following my question here, I am also looking at the difference between males and females and I have conducted linear regression in a general linear model setup for this purpose.

My effect size for this part of the project is $\eta^2$ (which is 0.25).

$\eta^2$ is equivalent to $R^2$ (which is the appeal for me in this case).

I am wondering how do I calculate the confidence interval of $\eta^2$. Does anyone know of any online calculators that can I can use?

• what does it mean, "$\eta^2$ is equivalent to $R^2$" ? – Stéphane Laurent Nov 27 '14 at 9:55

I could well be wrong about this, but...I think I would take the square root, yielding eta, which is akin to multiple R. Then I would use the standard method for finding a confidence interval for a correlation, which involves transforming to a Fisher's Z, obtaining upper and lower confidence limits based on Z and N, and transforming back. Then I'd square these limits to get my upper and lower limits for eta-squared. (One online calculator that could help is Vassar's.)

• This is really quite a clever solution, +1. I went looking for my meta-analysis book this morning, but I couldn't find it... – gung May 11 '12 at 21:16
• And intuitive too! – Amarald May 11 '12 at 21:25