Confused about multifactorial design of proportions


New Member
Dear all,

I was given to evaluate data which consists of proportions, categorized in several groups. Different individuals had to make certain decisions (with yes/no) answers on different dates and in different contexts. Example:

Individual1 Date1 Test1 3/10
(three out of ten correct decisions)
Individual1 Date2 Test1 5/10
Individual1 Date1 Test2 7/10
Individual1 Date2 Test2 8/10
Individual2 Date1 2/10
Individual8 Date3 Test4 7/10

We are looking for all sorts of effects: whether some tests are easier than others, whether there is an effect of the Individual.

My knee-jerk reflex was to just use multifactorial ANOVA hoping that it is robust enough to handle binomial data (even though the data is not normal). My second instinct was to use chi^2, but I don't know how to apply it to this case.

Can I ask you for help? Would you recommend some reading? Or, if I am really lucky, an R package to solve it?

Best regards,


Ambassador to the humans
It sounds like you might be interested in Generalized Linear Models using a binomial response. I don't have the time to get into too much detail but if you want to read into these lecture slides it explains the general ideas behind Generalized Linear Models and gives the R code to do it. It starts up with the binomial responses (as opposed to bernoulli) on slide 40 but you might want to read through the first slides to get a feel for whats going on. All of the code and data should be runnable as is so you might want to run the code in there to see how things work.