Marking papers well is a difficult but educative process.
"Margin of error" is frequently used in North America to refer to half
of the width of the 95% confidence interval around an estimate from a
survey or audit. Although it is not technical language, it is an
improvement over simply presenting a point estimate. The statistical
community considered it a major advance when leading newspapers
formulated a practice of presenting a margin of error with reported
percentages.
Also relevant to presentation is the question of whether the level of
confidence should be reported in non-technical contexts. My view is
that it need not be, but that the level of confidence should be held at
95%. Mathematically there is no reason for any particular confidence
level. Psychologically the most communicative approach is to keep the
confidence level at 95% in most circumstances, and to live with the
wider interval (effect size) it relates to. This is analogous to the
practice that chemistry studies are done at STP - standard temperature
and pressure.
When a margin of error is presented, most people grasp that there is
uncertainty around the result, but do not deal with it quantitatively.
I have been doing statistical consulting since 1972. For several years,
I informally asked asked internationally recognized sampling experts and
other PhD level statisticians about the relative precision of two
reports of surveys with 500 cases and a finding of 50 percentage points.
One survey had
a 5 percentage point margin of error at the 90% confidence level, and
the other had
a 6 percentage point margin of error at the 95% confidence level.
None were able to do the mental comparison. They are the same for all
practical purposes, the 5% gives the illusion of greater precision
because people don't do the arithmetic. (1.96/1.645 is close to 6/5).
Also, I might not take off points if percentages in point and interval
estimates were reported to an unreasonable number of places after the
decimal point, but I would comment on it. In most circumstances, I
advocate percentages being presented as integers from zero to 100%,
with the exceptions being for very close comparisons or single digit
whole percentages.
Hope this helps.
Art
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Social Research Consultants
University Park, MD USA
(301) 864-5570
R. Allan Reese wrote:
> A student has submitted work using the phrase "margin of error". From
> checking a few web pages, this appears widely used as a synonym for
> confidence interval. Am I alone in finding this a sloppy misuse?
>
> I would associate "margin of error" with engineering, not as a
> probabilistic measure but as the envelope of acceptable range. As such,
> the margin of error is something you specify rather than measure -
> inverting the use implies abdicating control.
>
> Comments please, to me. Should I correct the student, or update my own
> thinking?
>
> R. Allan Reese Email: [log in to unmask]
>
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