How to express certain statistics

If I remember right from college, there's a particular, formal way of
expressing certain statistics, and I'd like to learn more about that
way.

As an example (and I know I'll mangle this), one might aver, "According
to our survey, X% of Americans believe the moon is made of green cheese,
plus or minus Y somethings, with a confidence level of Z%."

Does any of this ring a bell? If so, can you teach me more, either by
explaining it or by citing some authoritative URLs, or both.

Thanks.

--Johnny
johnnyg aattssiiggnn kc.rr.com
[Only registered users see links. ]

"Johnny" <[Only registered users see links. ].com> wrote in message
news:dji3d.25857$[Only registered users see links. ]-kc.rr.com...

You are close.

The quantity being statistically estimated (in your example, the X% of ...)
is usually expressed first.

The error bounds (aka margin of error, uncertainty, and similar names) are
usually expressed as a "plus or minus," in absolute terms, using the same
units as the quantity estimated.

Then the quantity being estimated is a percentage itself, the error bounds
are (by most reputable statisticians) taken as absolute percentages, as the
"plus or minus Y somethings" in your example. Relative percentages are also
sometimes used, but only when the quantity being estimated is *not* a
percentage.

The confidence level is usually taken at certain convenient value, usually
90%, 95%, or 99% because this allows use of existing statistical tables for
more sophisticated analyses.

For example, a colleague of mine once determined the helium-4 content of the
air is 5.2204 +/- 0.0010 parts-per-million (ppm) at the 95% level.

Remembering that statistics provides *estimates* and not exact measurements,
the number of significant figures in the uncertainty is never greater than 2
(and then only if the first digit is 1), and rounding of uncertainties is
always done to the larger number. The relative percentage error in my
friends determination is thus:

0.0010 ppm / 5.2204 ppm = 0.0001916 => 0.02%

Few things betray ignorance faster than reporting *insignificant* figures.

HTH


Tom Davidson
Richmond, VA