There is statistically NO DIFFERENCE between 0bama's percentages and Romney's percentages in this poll.
The sampling error at 95% confidence says that we can say with 95% confidence that the true vote for Romney lies between 40 and 48.6, and between 40.9 and 49.5 for 0bama. That is not the same as your analysis, because these are NOT the true mean values of this statistic, they are sample means.
For example: If the true mean really is Romney 48.6, 0bama 40.9, not only would we rarely see a sampling that gave us 0bama 49.5 - Romney 40, we can make a much stronger statement: with 95% confidence, we can say that we would NEVER see 0bama with 49.5 if his real statistic is 40.9. In that case, you could sample (random) populations a million times and find that with 95% confidence, 0bama doesn't get 49.5.
Sampling over and over again will NOT yield the same distribution centered at 44.3-45.2 -- which is what your example implies -- UNLESS AND ONLY UNLESS -- the TRUE poll result really is 44.3-45.2.
The rest of your statement is correct, and it is the heart of the much more serious problem. The sampling error assumes the errors from the sample mean are RANDOM and we know they are not, because this is not a sample of absolutely truthful people telling us how they have already voted, picked completely at random. This is an imperfect sample which is a) not random, because it includes no refusals b) not composed of 100% truthful respondents, and c) does not consist of people whose votes are already cast.
The real guesswork comes in with trying to get a pure random sample of people who absolutely WILL vote.
Actually not Fred. The poll is statistically significant in that statistically speaking the race is a draw. There is no interpretation involved.
There is statistically NO DIFFERENCE between 0bama's percentages and Romney's percentages in this poll.
Right, which makes the poll statistically significant if one is happy with the methodology.
The sampling error at 95% confidence says that we can say with 95% confidence that the true vote for Romney lies between 40 and 48.6, and between 40.9 and 49.5 for 0bama.
Right, which is exactly what I said. CI means that 95 out of 100 random samples will fall between the error bars. That's it, it's statistics not rocket science.
That is not the same as your analysis, because these are NOT the true mean values of this statistic, they are sample means.
There are no mean values, sample means or otherwise. There is a sample with data. Sample means require values to find the mean. A poll is a single solitary sample with the associated data. There are no means, there are error bars at confidence intervals, in this case 95% because of the sample size.
For example: If the true mean really is Romney 48.6, 0bama 40.9, not only would we rarely see a sampling that gave us 0bama 49.5 - Romney 40, we can make a much stronger statement: with 95% confidence, we can say that we would NEVER see 0bama with 49.5 if his real statistic is 40.9. In that case, you could sample (random) populations a million times and find that with 95% confidence, 0bama doesn't get 49.5.
Outliers have a normal distribution above and below the error bars.
Sampling over and over again will NOT yield the same distribution centered at 44.3-45.2 -- which is what your example implies -- UNLESS AND ONLY UNLESS -- the TRUE poll result really is 44.3-45.2.
My "example" implies no such thing nor did I state it. Your inference is out of left field.