Usage: Keeping the number of digits consistent?

[neilson at windstream.net]

Geoff wrote:
> One standard stylistic approach in the sciences is to ensure that  
> numbers have the same number of decimal places so that comparisons  
> between numbers are facilitated. For example, in the series 0.02,  
> 0.031, and 0.025, the first number should be changed to 0.020.

[more story omitted]

Indeed. One possible interpretation is that the entire paper is in
error, and all the research will need to be done over, perhaps with
better equipment.

I observed a failed PhD thesis where the candidate had been supplied
(by his advisor, I believe) data that turned out to be sampled at
less than the Nyquist frequency. That is, he was looking for
results that were more frequent than the sampling interval could
properly detect. All his evidence consisted of artifacts from the
instrumentation, rather than true data, and he had to do everything
over again. Took another year.

Whether that number 0.02 is really 0.020 or perhaps something else
deserves careful scrutiny, and is not merely a matter of editorial
judgment. How can one know that a 0 belongs there, and not a 4, for
instance? The number itself, and actually ALL the numbers in the
particular group, are suspect, and should be marked for review by
the original author. Where there is one error there are likely
others.

My wife the quality engineer has a similar attitude towards
numbers. When told she must test a failing part "until the results
come out good" she asks why she shouldn't also test a passing part
until the results come out bad. It's not "just numbers." There's
a depth of meaning in every one of them, even integers. All
numbers are suspect until proven right. And even then there's
a lurking doubt. (To test the possible difficulties with integers,
try counting a few dozen sheep and goats. Try to get the same number
in three successive counts.)

On the one hand, scientists do not like to hear opinions that go
against their written material that is nearly finished, but on
the other, they usually prefer to find out the bad news *before*
publication. One does not want to join the company of Trofim
Lysenko or Hwang Woo-Suk.

--Peter Neilson