|Date: ||Thu, 9 Dec 1999 14:31:18 -0500|
|Reply-To: ||Lary Jones <ljones@BINGHAMTON.EDU>|
|Sender: ||"SAS(r) Discussion" <SAS-L@LISTSERV.UGA.EDU>|
|From: ||Lary Jones <ljones@BINGHAMTON.EDU>|
|Subject: ||Re: When large number of significant digits may be requir|
|Content-Type: ||text/plain; charset="us-ascii"|
At 05:14 PM 12/9/99 +0000, John Whittington wrote:
>However, I think we need to examine what is meant by using 'all the
>precision that is available' during those earlier steps. If an instrument
>or measurement produces a ludicrous degrees of significant figure (maybe
>just because it happens to have 'a 12-digit display'!) ...
>are probably therefore best 'dropped' at the very start.
>If all one is 'dropping' at the start is a pile of essentially 'random
>numbers', then that should not have any impact on what follows.
Dr. John and I must have studied from the same books ;-) Yes, the excess
digits normally will be random.
The case I mentioned earlier included a situation where there was an
induced constant error in what should have been random digits. In reality,
the displayed values turned out to be composed to treatment effects +
constant error + random error. Knowledge from previous studies indicated
that while treatment effects likely occurred in units of .01, or at best
.001, seconds, there was constant error, unfortuanately correlated with
treatment conditions, in the range of .001 to .0001. This produced a false
amplification of an expected difference.
The timing of international and olympic events is sometimes in hundredths
(and thousandths?) of seconds. I have often wondered whether the
chronometers and procedures used at different venues justifies recording
records to this precision. Does the image from a "photo finish" show the
winner exactly as the "touch" the finish line, or somewhat later? I saw
one case where the image showed two individuals across the line, one
slghtly further than the other. A slow motion of the video of the event
indicated that the moment they "touched" the projected finish line was
indistiguishable--after which one person continued to bend forward at the
waist while the other was in the process of strightening up. 1/100 of a
second later, there was a discriminable difference. On the other hand,
such events demand that there be a winner. A tie is unacceptable. We need
to determine if political factors and expectations are driving the
precision of our measurments, or whether higher precision leads to a more
accurate description of the phenomena being observed. Unexpected factors
can result in small constant errors which may can expand over the train of
I think John Wittington's advice is right on. Are the digits extended to
"...ludicrous degrees?" I never would advocate that we only enter two
decimal places because that is the previous limit of a detectable
difference. Rather, if we know that differences are usually detectable to
two decimal places, round to 3, 4, or 5 decimal places based on the error
in previous estimates; using more decimal places the less confident we are
in previous research.
I wonder if this thread has been redigested ad nauseum ;-) Now what was
the original question?
Lary Jones % Statistical Computing Analyst
Computing Services % ..........................
Binghamton University % LJones@Binghamton.EDU
Binghamton, NY 13902-6000 % (607) 777-2614