# GLM for comparing 2 populations with binomial data?

I've been using R to run GLMs with the logit link to compare clutch sizes (a binomial data set) and proportional data among several years. I now need to compare 2 groups of years (good years and poor years) between 2 sites for the same data.

I am not interested in any interactions between year-type (good or poor) and site, but really am just interested in comparing good vs. good and poor vs. poor between sites. If my data were continuous, I'd use a 2-way ANOVA followed up with t-tests for each comparisons, using the Holm–Bonferroni method for these multiple (2) comparisons. However, I'm not entirely sure how to approach these comparisons with binomial data.

To start, I'm considering clutch sizes (proportional data will come next). I'm thinking that this code (below) is akin to the 2-way ANOVA for binomial data?

model<-glm(clutchsize~Site+Year_type, binomial)


Then, since I got a significant result here, I can go forward and make direct comparisons between the good years and the poor 'independently' of each other (using the Holm–Bonferroni method). But how can I make those comparisons? Can I use the glm model for that as well, like this:

model<-glm(clsz_gd~Site_gd,binomial)


where clsz_gd is binomial and Site_gd is a factor with only 2 levels? I presume I can't use t-tests!

Is this the way to approach these data?

• I've decided to go with this...hopefully it's correct! – Mog May 25 '11 at 19:57