statistics question

[Razgovory]

If an event has a 30% of happening and there are 100 attempts what is chance that it will happen at least once?

[The Minsky Moment]

It depends whether each attempt is independent.
If it is, the chance is extremely close to 100%.  1 - (0.7^100)

[Liep]

In what situations wouldn't it be independent?

[Admiral Yi]

In what situations wouldn't it be independent?

Non-replacement.  I.e. you don't put the ball back in the jar after you pull it.

[Razgovory]

It depends whether each attempt is independent.
If it is, the chance is extremely close to 100%.  1 - (0.7^100)

How did you calculate it.

[Iormlund]

You calculate the chance that it never happens instead. 0.7^100 (70% 100 times). Once you know that, your subtract it from 1 (100% probability). So 100% minus the probability of no event will be what you are looking for.

[mongers]

It depends whether each attempt is independent.
If it is, the chance is extremely close to 100%.  1 - (0.7^100)

How did you calculate it.

There's about a one in 3 thousand trillion chance of it not happening.

[The Minsky Moment]

In what situations wouldn't it be independent?

Non-replacement.  I.e. you don't put the ball back in the jar after you pull it.

This actually came up in the 2018 election.  A lot of election modelers gave Trump a very low chance to win because he was down in the polls in a bunch of different states.  They figured to win he'd have to string together a bunch of 20-30% chances, which is very unlikely if winning one doesn't increase your chance of winning another.  But a few modelers - 538 was one - didn't model those outcomes independently - i.e. they figured if Trump's support was actually stronger in Ohio then the polling suggested, he was probably also actually stronger in Pennsylvania and other places.  Of course that was the right way to look at it but immediately pre-election there was sharp debate on that point.

[DGuller]

There was?  It seems incredibly stupid for anyone with professional training to ignore correlation of surprises in voting outcomes, I'm surprised there can be a debate about it.  Then again, some professionals also assumed that mortgages default independently, so I guess I shouldn't be too surprised.

[FunkMonk]

I remember the debate about it back then too.

[alfred russel]

There was?  It seems incredibly stupid for anyone with professional training to ignore correlation of surprises in voting outcomes, I'm surprised there can be a debate about it.  Then again, some professionals also assumed that mortgages default independently, so I guess I shouldn't be too surprised.

On the one hand, you had people making sensible statistical arguments. On the other hand, the people making sensible statistical arguments were asserting that an unqualified idiot racist troll had a real chance to be elected president.

[The Minsky Moment]

Post from the old 2016 election thread

Sam Wang has been giving Hillary 99% for quite a while, with fewer "intangibles" in their analysis than 538.

I took a quick glance at his FAQ.  I may not be understanding his method properly.  But it seems that he assumes away the possibility of correlated errors between states, which IMO will over-state certainty of outcome.  He also seems to assume pollster error is completely uncorrelated, with the same effect.

The eyeball test tells me that 99% vastly understates the degree of uncertainty inherent in the state polling and if I'm understanding the methodology correctly, I don't think its reliable.  Silver's model may be too swingey and fat-tailed but takes into account serial correlation.   

[DGuller]

Whew.

Sam Wang has been giving Hillary 99% for quite a while, with fewer "intangibles" in their analysis than 538.

I took a quick glance at his FAQ.  I may not be understanding his method properly.  But it seems that he assumes away the possibility of correlated errors between states, which IMO will over-state certainty of outcome.  He also seems to assume pollster error is completely uncorrelated, with the same effect.

The eyeball test tells me that 99% vastly understates the degree of uncertainty inherent in the state polling and if I'm understanding the methodology correctly, I don't think its reliable.  Silver's model may be too swingey and fat-tailed but takes into account serial correlation.   

If you're right about his methodology, then I definitely agree with you.  Assuming state-by-state uncertainty is uncorrelated is an extremely severe error of analysis.

[The Brain]

Today my bathtub wasn't draining very quickly so I used a plunger.

[The Minsky Moment]

Overall 538 did a pretty good job with the 16 election, arguably as good as in 2012 when they were feted for getting it "right".  A probability in the 30s is something that has a pretty decent likelihood of happening although it is somewhat more likely not to happen.