I am analyzing an experimental data set. The data consists of a paired vector of treatment type and a binomial outcome:
Treatment Outcome A 1 B 0 C 0 D 1 A 0 ...
In the outcome column, 1 denotes a success and 0 denotes a failure. I'd like to figure out if the treatment significantly varies the outcome. There are 4 different treatments with each experiment repeated a large number of times (2000 for each treatment).
My question is, can I analyze the binary outcome using ANOVA? Or should I be using a chi-square test to check the binomial data? It seems like chi-square assumes the proportion would be be evenly split, which isn't the case. Another idea would be to summarize the data using the proportion of successes versus failures for each treatment and then to use a proportion test.
I'm curious to hear your recommendations for tests that make sense for these sorts of binomial success/failure experiments.