I hadn't used one before, so wanted to verify the data would actually be accurate.
I did an A/A test, basically testing the same exact page––expecting the results would be the same.
Not only were the results not the same, but they were off by a wide margin.
Given this, I don't know how I'm supposed to trust any of the data.
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.
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.
Given the original comment, yes, I think it's more likely he just didn't understand why a A/A test might sometimes show a false positive.
Even if the system were misconfigured, there's no reason to think it would manifest as a false positive in an A/A test. There are lots of ways it could manifest.
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.
Here's an article from the VWO Knowledgebase that'll help you with running an A/B test correctly http://visualwebsiteoptimizer.com/knowledge/how-to-ideally-r...
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.
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.
No, usually the rule people use is this: "If A1 and A2 show a statistically significant difference, then do not reject the null hypothesis regardless of A1/B or A2/B."
I think that's pretty sensible reason for A/A/B testing. Or A/B/B testing. Whatever you like.
Well, we don't actually know how many samples the OP has, do we?
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.
Now, you just need to discover why one of the populations had better results than the other, and act acordingly. Don't forget to do actual A/B tests to verify your hypotesis.
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?"