"I did an A/A test, basically testing the same exact page––expecting the results would be the same."
That's not how A/B testing works. :)
Let's say we want to detect a 1% lift in some metric at 95% confidence and we set up an A/A test. We do the math and it tells us we need to sample 1,000 people to reach 95% confidence on a 1% lift.
If we ran the A/A test 100 times, roughly 5 of them would show a statistically significant difference between the two groups. That's what "95% confidence" means -- it means your false positive rate is 5%. This is called a Type I Error.
You could run a kind of meta-analysis and use the false positive rate as the variable you're measuring to see if there's a statistically significant difference between the %5 false positive rate you expect and the false positive rate the A/B testing software generates in practice.
In this case, your null hypothesis is that the "true alpha" of the A/B testing software is 0.05. You'd sample from among all the 95% confidence tests you run and see whether you can reject the null hypothesis.
The original commenter was using off-the-shelf A/B testing software, so the odds of it doing anything other than a simple t-test are virtually zero. Not sure that the frequentist vs. Bayesean debate is the most relevant thing for him right now.
I felt it best to leave out nuance that didn't help him understand why his software was showing a statistically significant outcome for an A/A test.
You're seeing a difference between Control and Variation in an A/A test is because a very small number of visitors have been tested. To explain, suppose you toss a coin 10 times and 7 out of those it shows heads. Just based on these 10 tosses, would you conclude that the coin is loaded? Probably not. Suppose you tossed the coin a 100 times, it'll probably show heads maybe 43 or 47 or 51 or 52 times.
Point being, as you toss it more and more, the number of times it shows a heads or tails comes closer and closer to 50% but you need to toss it a large number of times to be fairly certain that it isn't loaded. The more you toss it, the more certain you are. However, you'll only be more and more certain, but never completely certain. VWO works on a similar principle. The more number of times you toss up Control and Variation to visitors, the more certain you become of either being better, worse or equal to each other.
If you'll read the post, the graph shows the fluctuations in the beginning, after which things kind of settle down. In an A/A test, they'll settle down to a very similar conversion rate.
Some people actually suggest running A/A/B tests just to gauge how much noise is in their numbers, though that requires even more visitors to achieve statistical confidence since they're spread out among more options.
I've worked at companies that tried to do this before. It makes no sense and shows the people running the A/B tests don't really understand the statistics behind A/B testing.
If I'm running an A/A test at 95% confidence and a sufficient number of visitors for whatever effect size I'm interested in, then 1 in 20 A/A tests will register a false positive. That's what "95% confidence" means. It does not mean there is "too much noise."
Moreover, in a proper A/B test, the A group and B group need to be independent and identically distributed. So, in an A/A/B test, if the A/A disagree it shouldn't tell you anything about B. That's what "independent" means.
If you want to be more confident you just increase your alpha. alpha=0.05 is already too high for most consumer web apps anyhow, IMO, but go wild. 99% confidence! Woo!
As a rule you want higher confidence when the cost of a mistake is high, e.g., this medicine gives people brain tumors! Oops.
Perhaps you could view this "A/A/B" test as a very crude form of http://en.wikipedia.org/wiki/Bootstrapping_(statistics) method? At least if you're resampling A1 and A2 from a pool A and then doing separate A1/B and A2/B tests and looking at how much the resulting statistic varies between the two runs.
Agreed this is a silly way to go about it, but there better-thought-out bootstrapped confidence tests which could be used if you don't fully trust the distributional assumptions behind (say) the t-test.
I do this when I'm not confident I set up the experiment correctly. If the A's differ bit quite a bit, it's more likely I made a mistake than there's is normal statistical variance. I make mistakes daily.
I think that's pretty sensible reason for A/A/B testing. Or A/B/B testing. Whatever you like.
The answer is: it depends. How much data did you collect? How big was the difference you observed?
I can't say what went wrong in your case but there is the potential for lots to go wrong.
8) Have a hypothesis of what you're testing and control for variables. Run a MVT test if you're changing a lot of things. If the test wins and it's implemented, everyone is happy and people don't ask too many questions. If it loses, what have you learned? Test a hypothesis.
If a client looks at a comp for a test and asks to change something, I always ask them, "What hypothesis are we testing with that change?"