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?
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? If Bush's proportion had increased from
48% from 43% in different polls, we could use the formula for the
standard error for differences in proportions to state that this 5%
increase is significant. 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. This
is not appropriate because the 48% and 43% in one poll are certainly not
independent.
What is the correct approach for judging the significance of a
difference in one poll?
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."
> [EMAIL PROTECTED] (Wolfgang Rolke) wrote:
> Hallo again,
>
> A couple of days ago I wrote a message concerning the polls for the
> presidential campaign that are currently being published on a daily
basis, and
> especially the usual +-4% error and how it is computed. I received
three replies
> pointing out some of the difficulties such as the fact that these
estimates are
> based on stratified samples rather than simple random sampling. A very
nice
> discussion of the issues involved can be found at
> http://slate.msn.com/framegame/entries/00-10-26_92147.asp . An
explanation of the
> methodology of the Gallup tracking poll is at
> http://www.gallup.com/poll/faq/faq000101.asp , where they say that the
+-4% is
> for a 95% confidence interval. I would like to pose another question,
though,
> namely what a reader should make of all these polls. There is of
course the
> additional problem of the horse race question: if Bush's percentage is
estimated
> at 46%+-4% and Gore gets 44%+-4%, than in fact Bush is 2% ahead of
Gore, but this
> difference has an error of +-8% and so is clearly not significant. Now
if a poll
> would put one of them at 49% and the other at 41%, then the difference
would be
> 8% and that would be borderline statistically significant at the 5%
level. But
> then there are all these other differences between polls (I guess we
might call
> them systematic errors) which probably mean the +-8% error on the
difference in
> percentages is in fact too small. So here is my question: how large a
lead of one
> candidate over the other should really be taken seriously? I am sure
there is no
> definitive answer to this question, but I would like to know your "gut
feeling".
<Snip>
Eugene D. Gallagher
ECOS, UMASS/Boston
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