This reminds me of a "simple example" I found back when the "frequentist vs bayesian" page was posted.
Imagine that one in a million people have, say, splanch cancer. And some doctor created a splanch cancer test that's 99% reliable (which means p = 0.01, as 1% of positives will get a false negative, and 1% of negatives will get a false positive).
In total, this means that of a 100-million people sample:
- 100 have splanch cancer
- 99 will have it correctly diagnosed
- 1 will have an undiagnosed splanch cancer. Sucks to be him.
- 99 999 900 don't have splanch cancer
- 999 999 may have a scare
- 98 999 901 will be correctly tested negative.
By adding the numbers, you see that 1 000 098 people will test positive, but only 99 of them will actually have splanch cancer, so a positive test now simply means that you have one chance in 10102 instead of one in a million.
On the other hand, 98 999 902 will test negative, and one of them will have... problems.
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Indeed.
edited 26th Jan '15 11:09:06 AM by Medinoc
"And as long as a sack of shit is not a good thing to be, chivalry will never die."
Lost in Space
That assumes that the probability of a false-positive and a false-negative are the same, when that's fairly unlikely. Good for a thought experiment, not necessarily for the real world.
"It's Occam's Shuriken! If the answer is elusive, never rule out ninjas!"
Absolutely no relation to NLK
I got a probability and statistics exam on Wednesday. I should probably know this.
Dopants: He meant what he said and he said what he meant, a Ninety is faithful 100%.
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I've got one in the afternoon, what're the odds? It'd be even odder if you also happened to be doing session 3 STAT170 at Macquarie University...
Generally, if the p-value is less than 0.05, you're supposed to reject a null hypothesis, otherwise the null hypothesis is not rejected. Randall actually gets this wrong, because the latter case is "greater or equal to 0.05" instead of simply greater than 0.05.
edited 27th Jan '15 7:30:44 AM by Cronosonic
Oh joy. Math. The one subject I always left knowing less than I did going in.
Absolutely no relation to NLK
Nah, summer course at PUC.
I'd say that arguing over whether a hypothesis should be rejected under "less than or equal to" versus "strictly less than" conditions is rather pointless, given that significance thresholds are already selected with some degree of arbitrariness in the first place.
(I may be biased by being in physics, where unlike mathematics we rarely bother to distinguish between > and ≥ because in any realistic data the exact equality requirement would be smudged out by experimental error.)
わからない
Remember to right-click, rather than using the keyboard shortcut
.
Our Favorite Cowgirl, er, Mare
I liked this one. He's causing more problems than he's fixing. ![[lol]](https://static.tvtropes.org/pmwiki/pub/images/lol2v12_4863.png "[lol]"){kind=small}
I always tried to teach people the Alt+Space then 'M' maneuver myself. It selects the active window's command box, then M to Move it.
Doesn't work for me
Lost in Space
What-If #127: Tug of War. Trust Randall to find a way to turn an innocuous sport (thought not one without injury, apparently) into a catastrophically destructive event.
Troper formerly known as Nohbody
Wargames ref FTW. 
On a less humorous note, I've not experienced it first-hand, luckily, but when I was in boot camp they showed a safety video of a line used to tie up a ship (destroyer, IIRC) at the pier snapping... and cutting the manikin standing in for a sailor in half with one of the broken ends. Ouch
One Winged Egret
I took a sailing class as a kid and basically learned that ropes are terrifying when they have any weight behind them.
Yep. Don't even think about standing near a high-tension steel cable that snaps suddenly, it's even worse.
I just thought about it.
𐀀𐀩𐀯𐀂𐀰𐀅𐀡𐀄
seen it in a thriller.ship cables are scary.
Secret Signature
わからない
Our Favorite Cowgirl, er, Mare
Handegg.
Troper formerly known as Nohbody
Dark Eye
I feel like people actually complaining about sports has now been replaced by people complaining about people complaining about sports. Sure, I don't like sports and so do many other people but (even discounting this comic) I hear the later way more than the former.
literary masochist
And now you are complaining about people complaining about people complaining about sports. 
So you are complaingin about people complaining about... oh no!
The laconic version from a friend: According to his quick Wikipedia research, the P-value is the probability of a false positive, when you assume the truth is negative.
It's not the total probability of a false positive, because it doesn't take in account the truth's probability of being negative in the first place.
"And as long as a sack of shit is not a good thing to be, chivalry will never die."