On Thu, 02 Nov 2000 14:02:48 GMT, Gene Gallagher
<[EMAIL PROTECTED]> wrote:
> A URL for the 1 Nov Gallup poll:
>
> http://www.gallup.com/Poll/releases/pr001101c.asp
>
> This poll has Bush over Gore 48% to 43% with margin of error of 2%.
> Wolfgang's post and the thread below indicates that this +/- 2% is the
> 95% CI, which makes sense given the sample size. With the 2% 95% CI, we
> can conclude that these estimates are significantly different at the
> 0.05 level, can we not?
Basically, yep, that difference would be "reliable." Thanks for the
URL. That article was more informative than the usual -- it gives
results for three different totals per survey, and reports consistency
of results over time.
Yesterday's NY Times had an interesting article which explicitly
converted its own "3%" size of the +/- error, to the same confidence
in a 6 point difference.
The article went on to describe various differences, where the state
by state polls are (it seems) guiding the candidates in spending their
last-minute millions in TV advertising. Both candidates will ignore
the states with an 8-point margin. Too big, and too late to matter.
The results in the NY Times article showed a lead for Bush of about
3%, nationally, "among likely voters," at the same time that Bush
could lose in the ultimate Elector College tabulation. Based on those
chances, I guess, TV reporting has started trying to re-teach us all
this distinction -- each state is winner-take-all for its lump of
votes (ranging from 3 to about 50: however many California has), so
winning a national, popular majority does not ensure victory.
Do I mis-remember, or did Zogby have results, this week, that showed a
Gore lead nationally? I can believe that the two polls would differ,
because the "error" claimed by each does not include "differences in
method." The claimed error describes how their own sampling should
reproduce itself, and not whether it under-represents, say, Latinos
among the people who will vote this year;
> What is the correct formula for the confidence interval for the
> difference in proportions from the same poll? Is the 5% difference
> different at the 0.05 level?
Assuming multinomial, the "difference" in proportions has to take into
account the strong covariance between large counts. When there are
only two cells, then the total adds to 100%, the covariance is 100%,
and it takes twice as many points as the claimed accuracy to describe
the accuracy of the "difference." Question: Does the Nader vote
"covary" especially with the Gore vote? Does the Nader run
especially hurt Gore?
Differences between two polls? - Yes, you do need to account for
"sampling" in each, and the size of the CI would increase by that
fraction:
> < snip, some > For similar sample sizes and proportions not
> too different, tt would be roughly equivalent to multiplying the 95% CI
> for one poll times sqrt(2) to get the 95% CI for the difference.
< snip, some more >
> I may not be the only one confused on what these confidence intervals
> mean. In the above press release, the Gallup organization provides this
> description of what their +/- 2% means:
>
> "For results based on the total sample of likely voters, one can say
> with 95% confidence that the margin of sampling error is +/- 2
> percentage points."
Those guys are supposed to be professionals, and they should have
been polishing their syntax for 50 years, but my first reaction to
that statement was "UGH."
Is that what you are pointing to?
I think that I want to say, with 100% confidence, that I have computed
certain results. Beyond that, I am not sure how to describe them to
the public.
"The 95% CI is +/- 2 points" -- seems too technical.
"The 95% margin of sampling error... "?
The public has to have trouble with the "95%," but I haven't yet
accepted the solution quoted above. In addition, that phrase, "margin
of sampling error," annoys me. (But, I am closer to accepting it
today, than I was yesterday.)
Is this just me? Or, what should they be saying?
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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