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 calculations.

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

_______________________________________________________ Lary Jones % Statistical Computing Analyst Computing Services % .......................... Binghamton University % LJones@Binghamton.EDU Binghamton, NY 13902-6000 % (607) 777-2614