MW wrote:
> In article <[EMAIL PROTECTED]>,
> Jake <[EMAIL PROTECTED]> wrote:
> >
> > This year, circumstances dictated that the US Presidential race boiled
> > down to the results in Florida. That's where the decisive Electoral
> > Votes were and that's where the outcome was most uncertain. Since
> then,
> > Bush supporters have been insisting that all the votes have been
> counted
> > and Gore supporters have insisted that all the votes were not counted.
> > The problem is that they are both right, given the ambiguity of the
> verb
> > "to count". For the purpose of clarity, I will discuss whether the
> votes
> > were *properly categorized* rather than whether they were "counted".
> >
> > On Election day, there were four categories of votes in Florida as far
> > we are concerned: "Bush", "Gore", "Third Party" and "Rejected by
> > machine". The very fact that the difference between "Bush" and "Gore"
> > (1,725) was less than one percent of the "Rejected by machine" votes
> > (180,299) alone justified a recount, even if one wasn't automatically
> > required by Florida law. Florida law also allows for requested
> > handcounts and determination of voter intent by human beings, not
> > counting machines. Never mind that Bush and his supporters tried to
> > dismiss all handcounts as worse than machine counts (unless they take
> > place in New Mexico) and that Gore and his supporters failed to call
> for
> > a state-wide handcount before the deadline, thereby laying themselves
> > open to charges of "data mining".
> >
> > We've all heard about the ongoing vote recount in Florida now being
> done
> > by various media groups rather than any political parties, and some
> have
> > dismissed it as a waste of time, or worse. To be fair, some of these
> > critics may feel they are being entirely objective in their assessment
> > and to call them partisan is unwarranted until proven. Critics like
> > Stephen Gould feel that the result is basically an ineradicable
> > "statistical tie", thanks to an ineradicable "margin of error". This
> is
> > a fallacy.
> >
> > Most of us feel that we know what "margin of error" means but to make
> > sure we're all on the same page, let's review.
> >
> > "Margin of error" is a term out of survey polling that refers to the
> > confidence we have in the results of a given survey. In general, the
> > margin of error corresponds to the 95% confidence interval. For
> example,
> > if a pre-election survey indicates that 49% of "likely voters" want
> > Bush, 47% want Gore and 4% want neither, but the margin of error is
> > +/-3%, this is a "statistical tie" because the difference between Bush
> > and Gore falls within the margin of error.
>
> Wrrong. As you suggest below, the "margin of error" you describe above
> is not the real margin of error. The error could be far higher than
> 3%; the +/-3% refers to an estimate that it is, say, 96% probable that
> that error is three percentage points or less.
OK, you're confused. Above was an example in which the margin of error was
+/-3%. When you look at a small sample of a large population, the binomial
analysis works just fine because the difference between the fpc and one is
negligible.
The margin of error (aka sampling error) is determined entirely by the
sample size in pre-election and similar samples. The sample size is an
entirely controllable parameter.
> > If the difference between
> > Bush and Gore was 6 or more percentage points, we could say (given a
> > 95% confidence interval) that in only one such survey out of twenty
> > would such a difference occur purely by chance. Only by taking a
> larger
> > sample (more expensive, more time-consuming) can we reduce the margin
> of
> > error further.
>
> Not the margin of error. You're talking about an estimate of a likely
> error.
No, I'm talking about the margin of error aka the sampling error.
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