I am trying to optimize our AdWords ads and running some statistical tests. I use a chi-squared test and Fisher's exact test for conversion rate data; for example the click-through-rate (CTR) or the click-to-conversion ratio.
But what if I wanted to run stats for cost per conversion. Is it a statistical abomination to run, for example, a chi-squared test using the number of euros spent instead of the number of clicks?
Example problem
Ad 1 saw 300€ spent for 5 conversions (60€ per conversion). Ad 2 saw 500€ spent for 5 conversions (100€ per conversion). Is the difference between the two ads' cost per conversion statistically significant?
