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".
Wolfgang
> Wolfgang Rolke wrote:
>
> > Today the following polling results were given on cnn.com for the
> > Presidential race:
> >
> > CNN/USA TODAY/GALLUP POLL
> > October 20-22
> > Likely Voters' Choice for President
> > Bush 46%
> > Gore 44%
> > Nader 4%
> > Buchanan 1%
> > Sampling error: +/-4% pts
> > Sample size: 769
> >
> > For details go to
> > http://www.cnn.com/2000/ALLPOLITICS/stories/10/23/tracking.poll/index.html
> >
> > I am wondering how they find the Sampling error of +/-4% pts. The usual
> > estimate for the standard error of a binomial would be (for Bush)
> >
> > SQRT(0.46*(1-0.46)/769) = 0.01797
> >
> > The error in a 95% CI would then be 1.96*0.01797 = 3.5%
> >
> > and in a 99% CI it would be 2.576*0.01797 = 4.6%
> >
> > Am I doing something wrong here?
> >
> > Thanks
> >
> > Wolfgang
>
>
"Drake R. Bradley" wrote:
> Wolfgang,
>
> They are probably using stratified sampling methods, and that reduces the
> margin or error somewhat by eliminating sampling error associated with over-
> or under-sampling certain groups (which occurs with simple random samples). I
> don't recall the formula used for computer the SE in this case, but I have
> seen one in a methods textbook used by sociologists.
>
> Regards,
>
> Drake Bradley
> Dept. of Psychology
> Bates College
Donald Burrill wrote
> Not for a simple random sample (SRS); but the Gallup sample is not a
>SRS, and the sampling error is slightly larger than it would be for a
>SRS. (And it's reported only to the nearest integral number of
>percentage points, so the correct value could be anywhere between 3.5%
>and 4.5%, presumably.) Also, I wouldn't be surprised to find
>(although I don't _know_ this) that it was calculated on the basis of a
>population proportion of 0.5, and is therefore slightly conservative for
>most results and _highly_ conservative for results like 4% and 1%.
Bob Hayden wrote
>I don't have a complete answer, but it does look like they are
>rounding to the nearest whole percentage, in which case their $% might
>agree with your 3.5%. In addition, the formula you quote is for
>simple random sampling, which is rarely used by polling agencies.
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