Is there a general definition of the effect size? The effect-size tag has no wiki. The wikipedia page about the effect size does not provide a precise general definition. And I have never seen a general definition of the effect size. However when reading some discussions such as this one I am under the impression that people have in mind a general notion of effect size, in the context of statistical tests. I have already seen that the standardized mean $\theta=\mu/\sigma$ is termed as the effect size for a normal model ${\cal N}(\mu,\sigma^2)$ as well as the standardized mean difference $\theta=(\mu_1-\mu_2)/\sigma$ for a "two Gaussian means" model. But how about a general definition ? The interesting property shared by the two examples above is that, as far as I can see,  the power depends on the parameters only through $\theta$ and is an increasing function of $|\theta|$ when we consider the usual tests for $H_0:\{\mu=0\}$ in the first case and $H_0:\{\mu_1=\mu_2\}$ in the second case.  
Is this property the underlying idea behind the notion of effect size ? That would mean that the effect size is defined up to a monotone one-to-one transformation ? Or is there a more precise general definition ?  
 A: I don't think there can be a general and precise answer. There can be general answers that are loose, and specific answers that are precise.
Most generally (and most loosely) an effect size is a statistical measure of how big some relationship or difference is.
In regression type problems, one type of effect size is a measure of how much of the dependent variable's variance is accounted for by the model. But, this is only precisely answerable (AFAIK) in OLS regression - by $R^2$. There are "pseudo-$R^2$" measures for other regression. There are also effect size measures for individual independent variables - these are the parameter estimates (and transformations of them).
In a t-test, a good effect size is the standardized difference of the means (this also works in ANOVA, and may work in regression if we pick particular values of the independent vairables)
and so on.
There are whole books on the subject; I used to have one, I believe that Ellis is an updated version of it (the title sounds familiar) 
