- #1
Sleeker
- 9
- 0
I'm a bit of a polling junkie, and in general, I'm pretty good at math, but I can't figure this one out (at least, not yet).
As a concrete example, I'm going to use the latest Gallup survey:
Obama: 49%.
Romney: 44%.
Margin of error (95% confidence) = 2%.
As I've found out, the margin of error applies to each person individually, so Obama's share will be between 47% and 51% in 95 out of 100 cases, and Romney's share will be between 42% and 46% in 95 out of 100 cases.
I'm trying to find a formula that will give me the probability that one candidate (say Obama) is ahead of the other candidate. Each candidate's share of the vote is the peak of a normal distribution.
Now, I believe the following represents the probability that each candidate, individually, has at least x% of the vote:
[itex]P = \frac{1}{2} (1-erf (\frac{x-\mu}{\frac{MOE}{2} \sqrt{2}}))[/itex]
With
[itex]\mu = [/itex] The percentage in the poll for the candidate.
MOE = Stated margin of error.
I don't know if that helps, but that's what I have so far.
Basically, I'm trying to find a function that describes the probability that one candidate is ahead of the other by any amount as a function of (the difference between the two candidates) and (the margin of error).
As a concrete example, I'm going to use the latest Gallup survey:
Obama: 49%.
Romney: 44%.
Margin of error (95% confidence) = 2%.
As I've found out, the margin of error applies to each person individually, so Obama's share will be between 47% and 51% in 95 out of 100 cases, and Romney's share will be between 42% and 46% in 95 out of 100 cases.
I'm trying to find a formula that will give me the probability that one candidate (say Obama) is ahead of the other candidate. Each candidate's share of the vote is the peak of a normal distribution.
Now, I believe the following represents the probability that each candidate, individually, has at least x% of the vote:
[itex]P = \frac{1}{2} (1-erf (\frac{x-\mu}{\frac{MOE}{2} \sqrt{2}}))[/itex]
With
[itex]\mu = [/itex] The percentage in the poll for the candidate.
MOE = Stated margin of error.
I don't know if that helps, but that's what I have so far.
Basically, I'm trying to find a function that describes the probability that one candidate is ahead of the other by any amount as a function of (the difference between the two candidates) and (the margin of error).