confidence in your own decisions can also be referred to as a Bayesian prior ;)
I've treated the A/B tests I've run pretty much as a case of Bayesian parameter estimation (where the true conversion of A and of B are your parameter). You then get nice beta distributions you can sample from, as well as use the prior to constrain expectations of improvement and also reduce the effects of early flukes in your sampling.
Bayesian approaches are probably out of grasp for most small companies. They have a long way to go before being as approachable and easy as frequentist approaches. Schools and the statistics field as a whole need drastic reformation in introductory course offerings that are taken by everyone.
Until then, it's A/B, p value <.05, ignore bias and sample size for companies who aren't large enough to have a statistician or data scientist.
No they aren't. Here is a Bayesian method that is just as easy as any Frequentist one. At my last job, a completely non-technical user who didn't even understand statistical significance used it just fine [1].
The only cost of the Bayesian method is that the bayesian python script is thousands of times slower than the frequentist one. I didn't do benchmarks, but in terms of order of magnitude, the frequentist method might take 1 microsecond while the Bayesian method might take 1 second.
[1] He used a less advanced version of the method which used a normal approximation - not that he needed to know the difference.
You're right. The one exception though is with Bayesian statistics you can estimate an effect size using your experiment results using a credibility interval.
If the differences are drastic enough you can still get value from split testing. Incremental changes are just probably not going to bring you much luck.
There are several things that help. Firstly you're not just looking for a red light/green light significance. Since you're actually modeling the beta distribution for each conversion rate you not only can ask "what's the probability that this test is an improvement?" you can actually sample from both distributions and see what that improvement looks like.
For example I just simulated some bad data. A has 480 observations and a mean conversion of 33%, B has 410 observations and has a mean conversion of 37%. The p-value here is 0.0323 In the traditional A/B testing model we'd be done and claiming better than a 10% improvement!
However when I sample from these 2 beta distributions I see that my credible region is -2% to 34% meaning this new test could be anywhere from 2% worse to 34% better. No magic value is needed to tell you that you really don't know anything yet.
Another huge help is the use of a prior. Until your data overrides your prior belief you aren't going to see anything. Going with the last example, if I had a good prior that the true conversion rate on that page was actually 33% I wouldn't have even gotten a p-value of less then 0.05. On the other hand if I had a strong prior that the conversion rate was 50% that would imply that both A and B were getting strangely unlucky results, which would actually boost the probability that B was in fact an improvement.
On the philosophical side, Bayesian statistics are simply trying to quantify what you know, not give you 'yes'/'no' answers. Maybe the gamble of -2 to 34 is good for you, or maybe you really want to know tighter bounds on your improvement and aren't comfortable with any possibility of decline. Bayesian statistics gives you a direct way to trade off certainty with time.
I've treated the A/B tests I've run pretty much as a case of Bayesian parameter estimation (where the true conversion of A and of B are your parameter). You then get nice beta distributions you can sample from, as well as use the prior to constrain expectations of improvement and also reduce the effects of early flukes in your sampling.