Triple Your Google AdWords CTR Overnight by Doing Nothing
seobook.com
seobook.com
SEOBook recently opened another site focused primarily on PPC at PPCBlog.com and this was a recent discussion in the forums.
I would expect anyone on HN would be capable of running the numbers and generating the actual stats.
If not, it would be a good learning exercise.
But I think it's a very simple, concrete and credible demonstration to users. And if they observe such an expt over time, over a few trials, they'll quickly develop an intuition for when the sample size is large enough. And this is more valuable than an abstract calculation. (Of course, ideal to have both.)
Unfortunately, the empirical approach doesn't take into account the effect of how near the probability is to 50% vs the extremes 0% or 100%; nor of the variance of the population. However, in practice, these are probably similar enough over all ads and populations for the effect to be negligible - especially if you give yourself a margin of safety.