I have seen this several times on CNN recently. Every so often they put up a poll which they say is a “poll of polls”. I guess they compile a bunch of polls from different sources and mush them together. Wouldn’t this increase the margin of error considerably? How can you be certain each of the polls used was given properly? Is the poll of polls just another meaningless graphic to fill airtime? Feel free to be technical but be gentle with me, I know nothing of the science of polling and little about statistics. Please keep this about the process of polls and not the election.
Strictly speaking if you have a set of polls that were all done properly then the sum of all of them has a lower margin of error than the sum of any given poll. Think of it this way, if you have one poll that says 50% Kerry, 50% Bush with a margin of error of + or - 3, then there is a certain small probability p that the actually number supporting Kerry is 47%. But if you have two identical polls that both say 50% Kerry, then the probability of the actual number for Kerry is pp*, which is smaller than p.
As long as the polls were all done more or less the same, you’re basically just increasing the sample size, which decreases the margin of error.
I seem to remember seeing that the CNN “poll of polls” is a compilation of polls of likely voters. I’m no staticitian, but I think that makes it a load of junk. Each poll – whether Zogby or Time or whatever – has a different method of calculating what a likely voter is, so I am at a loss how to find any scientific merit in simply throwing all that data together would bring any clarification to the matter.
Ok I understand that. In a perfect world where all the polls are done the same I can see how that would make it more accurate. What if the sample size of each one is different? Lets say poll 1 asked 6000 and got 1300 responses, poll 2 5,000 and 1,000 reponses and poll 3 7,000 and 1,500. Each one has a slightly different result and the margin of error is +/- 3%. Does the differing sample size effect the accuracy? I have not seen two different polls that were done exactly the same so I’m not too sure about the accuracy of lumping them together.
If you polled 3000 people in one poll and 3000 people in another poll, and you asked the EXACT same question, and you knew there was NO overlap between the polls, then that is exactly the same as polling 6000 separate people which would have a margin of error smaller than that of either poll.
If you polled the exact same 3000 people twice, then your new poll would have the same margin of error as the original ones.
I suspect the poll of polls would fall somewhere in between.
I don’t think the margin of error could ever go UP when taking a poll of polls.