Is there a poisson variant for cohen's D/ Hedges' G? I've got a problem with some count data of mine.
I am using a cohen's D/ Hedges G to compare the effect size between two different treatment groups in my experiment, and then repeating that process for a different strain of fly with the same treatment, and comparing effect sizes for the two different groups to see if effect of treatment varies by strain.
However the actual data I get out at the end is count data in a poisson distribution, not a normal distribution.
Is there an effect size coefficient that is designed for poisson distribution, or should I just stick to these ones and take it with a pinch of salt?

Effect sizes only compare means (or whatever, like $\eta^2$). They make no assumptions about distributions. So they are applicable regardless of the conditional distribution.
Of course, their interpretation hangs on whether the means are the only thing we are interested in. Some events may have a tiny probability but a huge impact if they do occur, so the mean is very small, but in such a case, we should also be concerned about the variance.
