Need some statistics refresher…
Caveat: I don’t want to bring in discussion of the merits of specific polls or lack thereof, methodologies, flawed sampling, or any discussion about the 2008 election, etc.
With the various polls, you usually have a given sample size, the percentages of who gave what answer, and a margin of error usually represented as a 95% confidence interval. Of course, there is weighting and adjusting involved, but I ignore those for the purposes of this question.
My questions are:
http://en.wikipedia.org/wiki/Margin_of_error suggests that a margin of error is normally distributed; e.g., it is not a flat probability line where the “actual data” is just as likely to be on the edge of the MOE as it is in the middle. Is it a safe assumption to make that a poll that is representative of the population has a MOE that looks like a Gaussian curve, and does a cite for the answer exist?
Does any formalized way exist to analyze the movements in polls, whether one poll or multiple? E.g., let’s say 4 polls taken over the same period of time show movement of 1 point over their respective previous poll. Is there a way to determine the probability that the movement is significant in one poll, and can we show that probability that the movement is significant increases when combining multiple polls?