Comparing two binary variables of unequal sizes I measured a binary variable from two different populations, and now I'm trying to find out whether the different populations differ with regards to this variable. I could use a Chi-Square test, but that would necessitate that both populations have the same length. Is there an appropriate test for these circumstances? Thank you.
 A: Chi Square doesn't require equal size groups.  In R you can use either prop.test() or chisq.test().    
I do this often with A/B direct mail tests with unequal size groups.  For example, 100K donors are split 90% and 10%: the 90% are sent an email appeal, and 10% are sent nothing.  The binary outcome is whether they donated to the appeal.
The nice thing about prop.test vs chisq.test is that prop.test will both calculate the p-value of the hypothesis that the groups are equal and calculate the confidence interval for the difference
This page gives an example of prop.test() with two groups:
http://cran.r-project.org/doc/contrib/Lemon-kickstart/kr_prop.html
sexsmoke<-matrix(c(70,120,65,140),ncol=2,byrow=T)
rownames(sexsmoke)<-c("male","female")
colnames(sexsmoke)<-c("smoke","nosmoke")
prop.test(sexsmoke)

A: You can do a two sample t-test, perhaps after transforming the proportions using e.g. the arcsine transformation.
A: You can actually use logistic regression / glm with the outcome as dependent variable and group belonging as explanatory factor variable.
A: Weighting by sample size is built into how the expected vaues are computed. The only thing to worry about are the rules about how small an expected value can be. 
