3 ms·
In my medical example, "the chance that the results occurred by chance" is 31%. "The chance that randomness could produce [the result]" was only 5%. For CERN,
by capnrefsmmat 14y ago
In my medical example, "the chance that the results occurred by chance" is 31%. "The chance that randomness could produce [the result]" was only 5%.
For CERN, the chance that randomness could produce this result is 1 in 1.74 million; the chance that the results occurred by chance is larger, but not computable with the information we have,
The guide I linked to above gives a much better explanation than this. I rushed my first post here, and I think I was unclear.
- raldi 14y agoI swear I'm not trying to give you a hard time, but I don't see how these two things you said could both be true: > "The chance that randomness could produce [the result]" was only 5%. > 31% is exactly the chance that randomness produced the effect in the trial.
- capnrefsmmat 14y agoWhoops, poor wording on my part. Imagine flipping a perfectly fair coin 100 times. You'd expect to see 50 heads, but you don't always -- it's just an average. Suppose you see 75 heads. What is the chance that you'd see 75 heads with a fair coin? Very very small. The chance that randomness could produce such a result is small. Now, imagine you test 100 perfectly fair coins. A few of them give more than 75 heads, just by luck. You conclude they're unfair, since the result is unlikely otherwise. The chance that randomness produced the effects you saw is actually 100%, because all the coins are fair. There's a difference between the question "How likely is this outcome to happen if the coin is fair?" and "Given that this outcome happened, how likely is it that the coin is fair?" Statistical significance addresses the first question, not the second.
- raldi 14y agoThanks; I feel like I learned something. Your infinite patience was appreciated.