This is a statistics question rather than a Stata question, but would appreciate any advice.

After running an between-subject experiment, in which I had participants randomly assigned to one of four groups, I am trying to analyse my data.
The outcome was a binary response from the participants. Hence my dependent variable is a dummy variable.

Usually in experiments, with a small number of observations, ANOVA works well as the predictor variable (group to which the participant was assigned) is categorical.

Since the dependent variable is a dummy/binary variable, can ANOVA (or a variation of it) be used? Can it be suitable? Or should I simply run a logit with my eyes closed?