# $\eta^2$ and paired t-tests

When doing a paired t-test, is it appropriate to use the paired t value to calculate $\eta^2$?
I ask because it is not appropriate to calculate Cohen's d based on the paired t value.

Thanks.

$$d_{paired}=\frac{\bar{D}}{s_{\bar{D}}}$$
What you can't do is directly compare the paired version of Cohen's d with the Cohen's d for independent data. As is pointed out here, using Cohen's d is probably better than $\eta^2$. (That's a really good answer, by the way, it may be worth your time to read if you're interested in these issues.)
As soon as you entered the paired test arena the question arises, "what should I do with that pesky within observational unit (subjects etc) variance". Your effect size is bound to reflect some opinion in this regard. $d_{paired}$ as in gung's answer contains an assumption that the effect size should be calculated disregarding the variance in observational units. The equivalent assumption is made in a partial $\eta^2$ calculation. In short, there is no reason not to calculate $\eta^2$ or $d_{paired}$. Remember your paired samples-t is the same as a one-sample t-test (this is why you can use the one-sample t equation for Cohen's d as in gung's answer) or a 1 factor 2 level within subjects ANOVA. So, effect sizes which are appropriate for those statistics can also be appropriate for your paired samples t.