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From: gwyn@brl-smoke.ARPA (Doug Gwyn )
Newsgroups: net.sci
Subject: Re: Adding Standard Deviations
Message-ID: <1951@brl-smoke.ARPA>
Date: Thu, 20-Mar-86 02:27:00 EST
Article-I.D.: brl-smok.1951
Posted: Thu Mar 20 02:27:00 1986
Date-Received: Mon, 31-Mar-86 06:28:40 EST
References: <1794@sphinx.UChicago.UUCP> <12410@ucbvax.BERKELEY.EDU>
Reply-To: gwyn@brl.ARPA
Distribution: net
Organization: Ballistic Research Lab (BRL)
Lines: 25

In article <12410@ucbvax.BERKELEY.EDU> desj@brahms.UUCP (David desJardins) writes:
>>From: ihnp4!gargoyle!sphinx!fdot (Tom Lippincott)
>>How about error handling?  I've never seen *any* program where you could,
>>for example, add 1.23+/-.02 to 4.56+/-.04 and get 5.79+/-.06, let alone
>>perform more complicated math, graph them with error bars automatically, etc.
>
>   Maybe that's because (1.23 +- .02) + (4.56 +- .04) = (5.79 +- .045)?
>(Or do you want the program to figure out the correlation coefficient? :-))

If one adds two Gaussian distributions, does he get a Gaussian?
How about other arithmetic operations (e.g. sqrt)?

Tom seems to have had what is known as "range arithmetic" in mind;
there have been several such packages, some in Fortran.  The trouble
with range arithmetic is that the range of uncertainty grows really
fast as more and more operations are performed.

It is true that "n +- s" conventionally means: best estimate for a
quantity is "n" and the standard error of that estimate is "s".  I
have seen simplified rules for combining such (n,s) entities under
arithmetic operation, on the assumption that the relative errors
are sufficiently small; unfortunately, many such rules have been
simply wrong.  The best discussion of error analysis I know of is
in a book by Bevington, entitled something like "Data Reduction and
Error Analysis for the Physical Sciences".