Date: Wed, 8 Dec 1999 09:08:15 -0700
Reply-To: Mark S Dehaan/MSD/LMITCO/INEEL/US <MSD@INEL.GOV>
Sender: "SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>
From: Mark S Dehaan/MSD/LMITCO/INEEL/US <MSD@INEL.GOV>
Subject: Re: When large number of significant digits may be required
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Lary,
it is quite surprising to me that the additional insignificant digits would
make the effect MORE statistically significant. I would think of these
digits as random noise and therefore they would make the results slightly
LESS significant if anything. From what you say, I guess the extra digits
were not truly random but incorporated some other unknown factor. But I
suspect you are talking about very small differences in the p-values (you
said >this could easily have been detected by reviewing the results).
Following your thread, how would you propose treating values that are known
to be "less that detectable" (i.e. values below what the instrument can
reasonably detect accurately)? This is a big headache in the environmental
chemistry field I sometimes work in. The techs want to just flag the obs.
and report a zero value. This greatly complicates most any stat. analysis,
even though one could argue that they have rounded to the correct
significant digit. I prefer they give me the actual measurement (which has
very useful info for variance estimates) and let me know what the
instrument is capable of. Your point of carrying too many signif digits is
well taken, but even this can be tricky.
My 2cents worth,
Mark DeHaan
Lary Jones <ljones@BINGHAMTON.EDU>@LISTSERV.VT.EDU> on 12/08/99 07:24:35 AM
Please respond to Lary Jones <ljones@BINGHAMTON.EDU>
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Subject: Re: When large number of significant digits may be required
At 12:37 AM 12/8/99 +0000, John Whittington wrote:
...
>Indeed - but they also need to be sensible about how they 'manage'
whatever
>degree of precision they deem appropriate. I am, in particular, reminded
>that rounding to an appropriate (and realistic) number of significant
>figures generally should only be done *once*, at the end of all the
>calculations - which themselves should utilise data to the full extent of
>whatever precision is available.
>
>I have seen some very serious errors resulting from 'repeated stages of
>rounding' ...
Again, Dr. John is right on the button. I would make one minor alteration.
The values input to the analysis should not exceed the precision of the
measurements from which they are derived.
I had one case where a researcher had done a preliminary analysis which
indicated a significant effect. Being unsure of the specification for some
additional statistics, he asked me to take a crack at the data. I noticed
that the data (in an Excel spreadsheet ;-) had about 7 decimal places, and
asked about the precision of the measurements. I forget whether we decided
that the (reaction time) measurements were really only accurate to 2 or 3
places. In any case, after rounding to one extra digit (3 or 4 places) the
significant effect almost disappeared.
Now, this could easily have been detected by reviewing the results even if
we kept all 7 digits. Nevertheless, keeping or displaying the original
data with precision beyond the measurements can affect the way we think and
talk about our research--even occasionally leading us to believe that
insubtantial differences are significant.
-lary
_______________________________________________________
Lary Jones % Statistical Computing Analyst
Computing Services % ..........................
Binghamton University % LJones@Binghamton.EDU
Binghamton, NY 13902-6000 % (607) 777-2614
