Quote:
Originally Posted by AlanBostick
Here is what I said about it a decade ago:
So, yeah, even though I played the Central Limit Theorem card to take a trick from @peterchi, I regard it, as I say above, as dubious and questionable.
yeah I figured position and other factors had something to do with it. But then similar arguments can be made for almost every other "true average" that we try to study, whether it be in sports, business, or medicine. The question (unless you denounce all frequentist statistics and really are a legit Bayesian) is how much does it violate assumptions and how much does it matter.
In the case of constructing a confidence interval for your own winrate (e.g. the image I posted earlier) and the extent to which that can tell you anything, I think the impact of any erroneous assumptions is fairly small.
In the case of the applet, I was certainly wrong and CLT is fine if what we're really interested in is the ending point of all of the paths. I got thrown off because I was thinking that the actual paths aren't really that accurate since a normal distribution cannot correctly represent what we see from hand to hand, so the actual ups and downs are going to move quite differently. But the endpoint is the sum of a ton of things, so as long as we have agreed to ignore every other violation (non-independence and the like), then CLT does apply.