Normalizing sample sizes to identify trends Every month I send out an email to prospective customers. The client I use tracks the number of recipients and the percentage of the emails that were opened.
Here's a sample, there's thousands of rows in the original.  

I want to know how to calculate which emails were engaged with (i.e. opened) the most. I don't want to draw conclusions from the data in the table because the percentages are percentages of a different number of recipients each time.  
Is this a situation where I should normalize or standardize the recipient values? I tried generating a z-score for recipients but wasn't really sure how to use it once I had it. Is there something I could be doing instead? 
(Note: I'm not looking for the number of recipients who opened the email, rather a way of measuring which campaign had the best open rate relative to the number of recipients.)
I am especially interested in answers that can point me towards a resource to read up on this topic.   
 A: The open rate is already appropriately normalized. It's the count of recipients who looked at the message (and foolishly haven't disabled images in their email client) divided by the number of recipients, so the number of recipients is already being taken into account.
A: A standard model of your campaigns $i$ would be that each campaign has a certain open rate $p_i$.
What you can now hope to test is wether one campaign had a significantly higher $p_i$ than others to a certain significance threshold $\alpha$ wich you should set beforehand.
The data generating process would be a scaled binomial random variable with $n_i$ trials where $n_i$ is not random (it's your second data column)
Let $o_i$ be the number of recipients that opened the mail. We postulate
$$o_i \sim B(n_i, p_i)$$
This model allows us to use hypothesis testing on the hypothesis $p_i \le p_j$. If the test rejects at confidence level of $\alpha$, we can assume that campaign $i$ is better than campaign $j$.
Beware of multiple testing raising your actual significance level. In this case you test $5\cdot 4 = 20$ times so to make a false discovery with maximum probability $5\%$, you would have to set the individual FDR to $\alpha = \frac{5\%}{20} = 0.25\%$.

Testing multiple campaigns in parallel to see if there is an "effect" (i.e. a difference in performance across the campaigns) can be tested with an F-Test using ANOVA.

As you have thousands of rows in your dataset, you could also look into Bayesian inference. This requires you to formulate an a-priori distribution of the parameters $p_i$ of your campaigns.
A possible choice for this would be the empirical distribution function of your measured open rates, maybe weightet by number of recipients to give more credibility to larger campaigns.
Using this a-priori distribution of $p_i$ you can actually compute, assuming the a-priori distributions, the Probability that a certain campaign is better than all others given the observed open rates (a-posteriori distribution). This however is usually infeasible if the a-priori distribution is not "nice".
The results can also be approximated using Markov-Chain Monte-Carlo. This class of algorithms uses a LOT of computational power to generate samples from a distribution close to the a-posteriori distribution. Using these samples you can then, for example, find intervals for each campaign in wich you are to some degree certain that the true open rate lies within.
