Monmouth NH: Trump way up

[Zanas]

Two polls of NH Pubs put up on the same day, and Jeb has twice as high a percentage in the other poll as this one. Assuming both polls are accurate, can that be within the margin of error? Muon2? For an individual candidate, with a poll have a 4.8% margin of error, can an individual candidate polling at 4%, really have a 5% chance of really being as high as 8.8%? Inquiring minds want to know. 4.8% of 4% of course, would be next to nothing.

That's not how margins of error work. The figure of a MoE is not in %, it's in percentage points, and it's given for scores of 50%. When the score decreases or increases, the margin of error decreases.

In this instance, the poll has a 4.8 pt MoE for scores of 50%.
For scores of 20% or 80%, the MoE would be around 3.8 pt.
And for scores of 5% or 95%, the MoE would be around 2.1 pt.
So for a score of 4%, the MoE should be about 2 pt.

So in this poll, a candidate polling at 4% would have a 95% chance of really being inside the 2-6% bracket.

If he's polling 8% in the other poll, with 600 LV polled and a 4.1 pt MoE for a 50% score, the MoE for his 8% would be around 2.2 pt, so he would have a 95% chance of really being inside the 5.8-10.2 bracket.

Safe to assume he's around 6 in reality.

Go to page 5 of this pdf file, everything's there.

[Zanas]

Margin of error is not very helpful for small percentages. The quoted value is the limit that a 50% measurement is 95% likely to be in that range. That is if Trump polled at 50% with a 4.8% MoE, then it would be 95% likely that Trump would get somewhere between 45.2% and 54.8% if every likely Pub were asked.

The actual range scales with the percentage. At 32% in the polls with 414 responses the 95% confidence level is 4.5%. So if every likely voter responded Trump would be 95% likely to get between 27.5% and  36.5%.

Now let's look at Jeb in this poll. He comes in at 4% and the simple calculation is that the MoE on that is 1.9%. Naively it means that it's 95% likely Jeb is between 2.1% and 5.9%. If I make the same calculation for 8% the MoE is 2.6% (using the same sample size) so the 95% confidence interval is from 5.4% to 10.6%. Note that if the actual value among likely Pubs is 5.7% it would be within the MoE of both polls.

It's actually more complicated, since the range becomes less symmetric as the poll number gets close to either extreme. It has to be asymmetric since the real value for the entire population can't be less than 0 or more than 100%. The effect would be to make fluctuations upward typically range greater than fluctuations downward for values near 0. I'd like to know the raw counts from the poll to make the calculation.

footnote: I'm using MoE = 1.96 sqrt[(p(1-p)/n], where p is the percentage listed in the poll and n is the sample size. It presumes a random unweighted sample.
 

Thank you. Are you the only poster here who properly understands margins of error and thus, well, polling, or are there any other ?