# What is the effect size for the interaction of a 2X2X2 contingency table?

I am computing the interaction in several 2X2X2 tables (i.e. in each case, I have eight frequencies), see for an example this file.

I have two predictors (low vs high 'threat' and low vs high 'efficacy') and one dependent variable (whether people perform the desirable behavior ('good') or not ('bad').

My question is whether threat and efficacy interact in their associations with behavior.

I've found this post about a statistical test for difference between two odds ratios, which seems to solve this problem.

My question now is: can I simply take the $e^x$ of the $\delta$ (where $\delta$ = $ln(OR_1)-ln(OR_2)$) to get an odds ratio that would then represent the effect size for this interaction?