My short answer:

20 % +/- 5 % does not equal 20 +/- 5 % does not necessarily equal 20% +/- 5

Thus, if you mean 15%-25% an unmistakeable way to say that is 20% +/- 5%.
Alternative 1 (20 +/- 5%) is actually 19-21, which is very different from
15%-25%. Alternative 2 (20% +/- 5) could be anything, depending upon what
the point estimate is 20% of. Hence Alternative 2 can easily lead to
confusion.

The same goes for meters. The term 20 m +/- 5m does not equal 20 +/- 5m,
because 20 in the second expression is unitless. This would allow the
reader to become confused. Is it 20 cm +/- 5m? 20km +/- 5m? Something
else? Similarly, 20m +/- 5 is unitless. In a technical document that may
use many different units, a reader may become confused. Better, I
believe, to be clear in the text, rather than ride on conventions readers
of the future (or in different nations) may not share or even know.

Anyway, that's my 2 cents +/- 1 cent.

Take care.
Sam



On Wed, 1 May 2002, David Smith wrote:

> Ah, Yes! Amiong the all-time burning questions!
>
> More seriously, this is a matter of style or usage. For example, in
> America, numbers up through nine, when in text, are spelled out rather than
> shown in numerals, e.g., nine rather than 9. This is a convention, followed
> by many, but which can differ among authorities. Who are the authorities?
> Well, large newspapers have their own style manuals. Small newspapers buy
> one of those and tell all their editors and reporters to use it. The
> University of Chicago Press has a famous one. It's so long that the editor
> wrote a much shorter one for use in American dissertations and theses. The
> big one, apparently, is only for books that get published by real
> publishers, such as the University of Chicago Press.
>
> The answer may be idiomatic. That is, it follows a convention of usage that
> may not make sense in all cases, and isn't written down, but nonetheless
> there it is and everybody does it. This one will brook no appeal.
>
> One principle that could be applied is that mathematical symbols are just
> shorthand notation for ordinary English, even numbers. How would these
> expressions sound if you read them and then spelled out the results without
> using numbers or symbols? This is a little hard because of the +/- that
> also occurs.
>
> If people can agree on this, you may have an answer about how most people do
> it. Note that this may not be right or wrong. After all, it's just a
> convention or custom that allows life to slide along effortlessly and
> reduces trouble, like driving on the right side of the road. (Oops, bad
> example! On the other hand, maybe it's a good example, if the word "right"
> means the socially accepted side in the society you happen to be in.)
>
> So, how about this: "Twenty percent plus or minus one-half percent."
> or this: "Twenty plus or minus one-half percent."
>
> The first sounds more like the following looks: 20.0% +/- 0.5%.
> The second sounds more like: 20.0 +/- 0.5%
>
> What we really mean by this is still shorthand for something like: A
> ninety-five percent confidence interval for the mean is twenty percent plus
> or minus one-half percent.
>
> Observe that all these expressions are much more complicated if we want to
> say something like 21.2% +/- 0.53%. Now wouldn't that be a mouthful.
> Written out in words, this could increase the length of some reports or
> journal articles by something like twenty-one and two-tenths percent plus or
> minus fifty-three hundredths percent with a confidence level ninety-five
> percent. Or maybe even more, if editors don't put their collective feet
> down and stop all such nonsense cold.
> Manuals of style should address this sort of trivia. Several of them might
> even differ, then the right one is the one the editor of a journal or book
> designates as the correct one. If manuals of style have utterly failed in
> their responsibility to prescribe the smallest detail then they should be
> punished severely, maybe by copying out their entire manual in longhand ten
> times.
>
>
> This brings us to the answer. (Since it's mine, it must be the right one.)
> What should be in the manuals of style? Obviously, 20.0% +/- 0.5%. Why?
> Because it's closer to what we say when we speak.
>
> Could an editor choose qanother answer and enforce it? Yes. They could
> argue that so many % symbols are unnecessary and if we can substitute
> something like +/- for the language above we can certainly eliminate a
> mostly redundant and unnecessary % that is going to get reused frequently.
>
> If so, I think a better choice would be 20.0% +/- 0.5. This puts the %
> symbol up next to the primary number of interest in the expression. (Here
> comes the rain of kneejerk comments about the obvious and natural
> superiority of a confidence interval over a point estimate. Oh dear me!
> Everyone's a critic.) Nonetheless, it seems more natural to say "Twenty
> percent plus or minus one-half" than "Twenty plus or minus one-half
> percent."
>
> Just my two percent worth.
>
> Stylishly yours (or is it stylistically yours?),
>
> David Smith
>
>
> David W. Smith, Ph.D., M.P.H.
>
> (518) 439-6421
>
> 45 The Crosway
> Delmar, NY 12054
>
> [log in to unmask]
> ----- Original Message -----
> From: "Steve Bousquin" <[log in to unmask]>
> To: <[log in to unmask]>
> Sent: Wednesday, May 01, 2002 1:21 PM
> Subject: Units in confidence intervals
>
>
> > Settle (or join) a debate: should a confidence interval with units be
> > written as, for example:
> >
> > 20.0 +/- 0.5% *OR* 20.0% +/- 0.5%
> >
> >
> > 20.0 +/- 0.5 m *OR* 20.0 m +/- 0.5 m
> >
> >
> > Thanks!
> >
> >
> > Steve
> >
>