Analysis of Split (A/B) tests using Poisson and/or Binomial Distribution
OK, so here's your data. 

dd &lt;- data.frame(position=rep(1:3, each=2), 
                 variation=rep(c(1,3), 3), 
                 impressions=rep(c(753, 767), 3), 
                 clicks=c(26,7,16,13,2,7))


which is

  position variation impressions clicks
1        1         1         753     26
2        1         3         767      7
3        2         1         753     16
4        2         3         767     13
5        3         1         753      2
6        3         3         767      7


The two model assumptions you're thinking about are Binomial

mod.bin &lt;- glm(cbind(clicks, impressions-clicks) ~ variation + position,
               family=binomial, data=dd)


where the dependent variable is constructed to have the count of the event of interest in the first column, and the Poisson

md.pois &lt;- glm(clicks ~ variation + position + offset(log(impressions)), 
               family=poisson, data=dd)


where the log(impressions) offset is necessary whenever the number of trials differs across observations.  This means coefficients are interpretable in terms of change in rate not change in count, which is what you want.  

The first model generalises the binom.test to a setting with covariates, which is what you have.  That gets you a more direct answer to your question, and better (if not perfect) measurement of the relevant uncertainty.

Notes

Both models assume no interaction between variation and position ('independent effects').  This may or may not be reasonable.  You'd want more replications to investigate that properly.  Swap the + for a * to do so.

In this data summary confirms that the two models give rather similar results, so concerns about Poisson vs Binomial don't seem to matter much.

In the wild, count data is usually overdispersed, that is: more variable than you'd expect from a Poisson with a constant rate or a Binomial with constant click probability, often due to unmodeled determinants of click rate / probability.  If that's the case then prediction intervals from these models will be too narrow.