Two way ANOVA for binary dependent variable

I am trying to find the effect of two categorical variables on a dichotomous variable.
I am resampling the values in a cell and each time getting a proportion out of it. So now the new values in my cell will be proportions from different samples and so they will be normally distributed ( I am assuming it for now but I will check it later).
Also I am expecting them to be homoscedastic. Then I will be using two way ANOVA for analysis. Is this the correct way to do it?

I know Chi square test or Logistic Regression will be able to solve this but I want to know whether the above method is correct, also the reason for it in case incorrect.

Thanks in advance.


Ambassador to the humans
I don't fully understand what you're doing but it doesn't really sound correct to me. Plus how can you expect proportions to be homoscedastic? Unless the null is true we *know* the variances will be different.