Theoretical questions about Chi goodness of fit & Fisher's Exact tests

Hello statisticians,

My main questions are;
1) For a Chi goodness of fit test, which effect size do you use?
I am being told Cramer's V, Phi, Omega and W!
(There seem to be a lot more answers for a Chi association test, but not for a Chi goodness of fit)

2) Can you use an Odds Ratio with a Chi goodness of fit test? If yes, what would this tell us? Perhaps the odds of "y" happening rather than "x"/the control?

3) I am also running several Fisher's Exact Test for 2x2 contingency tables with small values.
I would love to use some post-hoc analysis or even a measure of effect size/odds to make my results more interesting than a simple Fisher's significance test-- but I have no idea what I can use.

Thank you kindly
Neither do I but apparently they are used! I think maybe the strength of the significance (that the condition population differs from the general population)
I have only read that they can be use theoretically

e.g. “Cramér's phi may also be applied to 'goodness of fit' chi-square models (i.e. those where c=1). In this case it functions as a measure of tendency towards a single outcome”
"For the chi-square goodness of fit test, Cohen suggests an effect size index called omega hat"
"w is the measure for effect size for a chi-square goodness of fit".


Less is more. Stay pure. Stay poor.
In the area of meta-analysis there are many conversions to translate results between correlations, cohen, etc.