4 ms·

You're not wrong. I get the initial thrust. The problem is in the solutions. The measuring of those things at the end could very well fall into the realm of

by Xurinos 16y ago

You're not wrong. I get the initial thrust. The problem is in the solutions. The measuring of those things at the end could very well fall into the realm of "streaks", too, unless we have good consideration of sample size. To use one of your examples: Let's say that I do 10 coin flips to determine bias, and I see those 10 heads in a row. Now I want to test this situation further. Is my coin biased? I run the test 10 more times. What happens if I get a "streak" of 10 heads again? Have I verified my claim of bias? No! I just have not flipped my coin a sufficient number of times. From this I see two things: One, an interesting anomaly arose that suggested I need to look into things a bit more. My theory is that the coin is biased towards heads. Two, to solve the problem, I need to narrow down variables where I can (you mention) and perform the test enough times (you did not mention). We know that 10 is not enough. How do we know this? 1000 is arbitrary. What is the right number? In other words, I agree with the fallacy you pointed out. The solutions are just insufficient. The fallacy can continue with the right probability of occurrences, even if someone tried to narrow down the variables.

metellus 16y ago
What you're talking about is called hypothesis testing. Basically, you can figure out exactly how unlikely a given event is under a certain set of assumptions (in this case, how unlikely it would be for a fair coin to show heads 10 times in a row). If it is sufficiently unlikely, where you and people reading your work decide what "sufficiently unlikely" means, you can claim that your initial assumptions were incorrect. I've been away from statistics for too long to go into specifics, but you can mathematically determine how large a sample size you need to be X percent confident that something weird is happening. I'd suggest reading http://en.wikipedia.org/wiki/Hypothesis_test http://en.wikipedia.org/wiki/Hypothesis_test for more info.

by Xurinos 16y ago

metellus 16y ago

What you're talking about is called hypothesis testing. Basically, you can figure out exactly how unlikely a given event is under a certain set of assumptions (in this case, how unlikely it would be for a fair coin to show heads 10 times in a row). If it is sufficiently unlikely, where you and people reading your work decide what "sufficiently unlikely" means, you can claim that your initial assumptions were incorrect. I've been away from statistics for too long to go into specifics, but you can mathematically determine how large a sample size you need to be X percent confident that something weird is happening. I'd suggest reading http://en.wikipedia.org/wiki/Hypothesis_test http://en.wikipedia.org/wiki/Hypothesis_test for more info.