>> Another extremely important point is that the classical
>> statistics you learned to use to decide that something
>> was <5% likely to arise by chance, only apply if you
>> decided in advance to do exactly that many trials and
>> then stop.
I agree. Not doing that I'd say it's "fudging with the numbers". I can't find on their article where they did this though.
Note that in frequentist statistics, the sentence "Probability this is all luck" doesn't even make sense. Either the universe is so that it was luck, or it is not. In frequentist statistics you do not assign probabilities to models of the universe. You only assign probabilities to observations, given a fixed model of the universe.
Lets say I roll a dice two times and get a six both times. The probability of this happening is 1/36 or about 3%.
Would you say I have established with a 95% confidence interval that the particular die I'm using always rolls six? No, because you have good reason to believe that the the results are in fact random. Or in other words, you have a strong prior belief that the hypothesis you're testing is false.
Yes, that is true for the dice roll; You already know most die aren't rigged.
I don't see how this affects the results of optimizely's product; You do not have a strong prior belief if the hypothesis is true or false.
Also note that the number of observations in the article used were in the thousands.