Analysis of variance for binary data I was wondering if there is a test for binary data similar to two-way ANOVA. Basically, I have 50 images analyzed by 3 persons using 2 different methods and thus I obtained 6 samples of paired/dependent binary measurements. What test I can use to compare the variation between these?
Thanks
 A: Depending on the goal of your research, a generalized linear model may be of interest to you. With this you can uncover variation in main effects and interactions of your design. 
A plain generalized linear model (GLM) can be fit in R via the command glm(). In the first argument you'll want to define your model, which is usually done via forumula for simplicity. An example would be DV ~ IV1*IV2. This would fit your dependent variable, DV as a function of your two independent terms terms. Additionally, the * symbol implies inclusion of an interaction between these two terms, whereas + would only include their main effects. 
You'll also want to define what type, or distribution of GLM you're utilizing via the family argument. In your case since you're using binomial data you'll want to set family = binomial. Now say you want to set the type of binomial regression to probit rather than logit (the default for binomial GLM), you'll need to change the link of the family like so: family = binomial(link = "probit").
Finally, here's an example of a binomial outcome data set with a logit regression fitted.

foo <- data.frame("IV1"=rnorm(100), "IV2"=log(runif(100)), "DV"=rbinom(100, 1, .5))
model <- glm(DV ~ IV1*IV2, data=foo, family=binomial(link = "logit"))
model
summary(model)

