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jobyts
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If each individual poll has a margin of error, when you combine all the polls, why do they say poll of polls has no margin of error? Shouldn't the margin of error get multiplied when you combine many polls?
jobyts said:why do they say
Because "they" refers in this case to people who don't know what they are talking about.jobyts said:If each individual poll has a margin of error, when you combine all the polls, why do they say poll of polls has no margin of error? Shouldn't the margin of error get multiplied when you combine many polls?
The CNN Poll of Polls, which does not have a margin of error, includes the USA Today/Suffolk poll; the ABC News Poll conducted October 21-24; the CNN/ORC poll conducted October 20-23; the Quinnipiac University poll conducted October 17-18; and the Fox News poll conducted October 22-25.
That doesn't make it right.jobyts said:Pretty much all US media says that.
jobyts said:Pretty much all US media says that. As an example,
http://edition.cnn.com/2016/10/26/politics/cnn-poll-of-polls-october/
EDIT: Not sure if it is all media or just cnn.
phinds said:That doesn't make it right.
phinds said:I interpreted the OP's original statement "why do they say poll of polls has no margin of error" as meaning there was no error.
jim mcnamara said:You cannot lump data from many disparate methodologies into one amorphous blob and make sense of it.
How does Chebyshev help at all??Borek said:I wonder if that's true. Chebyshev's inequality gives some upper limit to the variance (with very weak assumptions). Perhaps some analogous model could be used for a case where you mix data from different sources.
Could be the upper limit would be so huge it is not worth calculating though.
Yes, and I would expect the result to have a narrower error margin, even if it is tough to quantify.Bystander said:"Poll of polls?" Isn't that on a par with combining the forecast tracks for hurricanes?
micromass said:How does Chebyshev help at all??
IIRC, only in the case that the polls are i) statistically independent, ii) the errors Gaussian. A big IF.collinsmark said:It is possible to combine the results of individual polls to obtain a meta-poll. It's also possible to calculate a margin of error for that meta-poll, and that margin of error will have a expected, general trend to be 1√N1N \frac{1}{\sqrt{N}} of that of an individual poll,
The errors do not have to be Gaussian. They can be of any probability distribution that you can think up (assuming the standard deviations are finite). The sum will approach being Gaussian, but that is not a requirement of the individual trials. That's part of the beauty of the Central Limit Theorem.mheslep said:IIRC, only in the case that the polls are i) statistically independent, ii) the errors Gaussian. A big IF.
Is it not? Assuming that we're careful on how percentage and percentage points are used here, I think your method of combining is correct.Vanadium 50 said:Also, what do you do if you get one poll that measures 40 +/- 1% and the other that measures 60 +/- 1%? I don't think 50 +/- 0.7% is the right answer.
A "Poll of Polls" is a method used to combine the results of multiple polls in order to create a more accurate estimate of public opinion. This is done by taking the average of the results from each individual poll and accounting for the margin of error in each poll.
Margin of error is a measure of the accuracy of a poll. It represents the amount of sampling error in the results, meaning the potential difference between the poll results and the true opinion of the entire population. It is typically expressed as a percentage and is affected by the sample size and the level of confidence chosen for the poll.
Margin of error is important because it helps to gauge the reliability and accuracy of the poll results. A larger margin of error means there is a greater chance that the results are not an accurate representation of the entire population's opinion. It also helps to account for any potential biases or limitations in the sampling method used for the poll.
In a "Poll of Polls," multiple polls are combined by taking the average of the results from each individual poll. This helps to reduce the impact of any outliers or biases in a single poll and produces a more accurate estimate of public opinion. Additionally, the margin of error for each poll is taken into account to create a more precise result.
While "Poll of Polls" can provide a more accurate estimate of public opinion, it also has its limitations. It assumes that all of the individual polls are unbiased and equally reliable, which may not always be the case. Additionally, it does not take into account any changes in public opinion over time, as it is based on a collection of polls at a specific point in time.