If you have a least squares analysis on 14 points, and you believe the 95% confidence intervals, then is it fair to say there is a 51% chance that at least one of your points is outside those confidence limits?
(Note 0.95 ^ 14 = 0.488 = probability of all 14 being inside if considered independent)
Where's Kent when you need him?
Bill93, post: 325253, member: 87 wrote: If you have a least squares analysis on 14 points, and you believe the 95% confidence intervals, then is it fair to say there is a 51% chance that at least one of your points is outside those confidence limits?
(Note 0.95 ^ 14 = 0.488 = probability of all 14 being inside if considered independent)
Where's Kent when you need him?
Hello Bill,
My understanding of the problem is: (probability of something not happening) = 1 - (the probability that it will happen)
not all 14 inside = 1 - (all 14 inside)
not all 14 inside = 1 - 0.95^14
not all 14 inside = 1 - 0.488
not all 14 inside = 0.51 = 51%
Statistics can't alter the basic laws of the universe.
Like Murphy's Law!
48 percent of all statistics are made up on the spot.
"Lies, Damn Lies, and Statistics"
Benjamin Disraeli
Mark Twain
Sorry Bill, I know that your question was serious, I just couldn't help myself (either time).
:angel:
Bill93, post: 325253, member: 87 wrote: if considered independent
Aren't they correlated by definition?
Kevin Samuel, post: 325287, member: 96 wrote: Aren't they correlated
Yes. I think that means that if one is out, it is more likely others are out too. What I don't know is whether the computation above is still valid, a reasonable approximation, or useless.
Bill93, post: 325253, member: 87 wrote: If you have a least squares analysis on 14 points, and you believe the 95% confidence intervals, then is it fair to say there is a 51% chance that at least one of your points is outside those confidence limits?
(Note 0.95 ^ 14 = 0.488 = probability of all 14 being inside if considered independent)
Where's Kent when you need him?
Are you saying that if I flip a coin 1000 times and get heads each time that the odds on 1001 are any different than 50-50?
If we aren't guaranteed a fair 50-50 coin, but are estimating how much it is biased by a heavy side (correlating their outcomes), then yes.
The coin isn't a close analogy to the problem at hand.
It's more like rolling 14 special dice. These have 20 sides, each die all white except 1 black side. So we have 95% confidence each die will come up white. We can calculate as given above that there is a 51% chance of getting at least one black side to come up in one roll of the 14 dice. That's true if the dice are all independent. But if the dice are all somehow influenced by a common force (correlation), that calculation may not be true.
The errors in the points after LS analysis are correlated. I don't know if (or how badly) that invalidates the calculation.
If we aren't guaranteed a fair 50-50 coin, but are estimating how much it is biased by a heavy side (correlating their outcomes), then yes.
The coin isn't a close analogy to the problem at hand.
It's more like rolling 14 special dice. These have 20 sides, each die all white except 1 black side. So we have 95% confidence each die will come up white. We can calculate as given above that there is a 51% chance of getting at least one black side to come up in one roll of the 14 dice. That's true if the dice are all independent. But if the dice are all somehow influenced by a common force (correlation), that calculation may not be true.
The errors in the points after LS analysis are correlated. I don't know if (or how badly) that invalidates the calculation.
