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# Re: st: rounding the minimum of a negative number

 From Nick Cox To statalist@hsphsun2.harvard.edu Subject Re: st: rounding the minimum of a negative number Date Thu, 10 Jan 2013 15:51:05 +0000

```Agreed, and this is a problem for display and reporting of _results_,
when (as in your example) P-values can range over several orders of
magnitude.

As far as data are concerned, several things are tied up together
here. When we have very big or very small numbers with associated
units, then the choice of units is a matter of convention. So, GDP is
not usually expressed in currency such as US dollars, but in millions,
billions or trillions of dollars.

Yesterday I was looking at some geochemical text in which
concentrations were expressed as pg/g, i.e. parts per trillion by
mass. Here the users don't want to see numerous decimal places, as
they use sensible units and the inherent precision of the data does
not justify more than a few decimal places.

Nick

On Thu, Jan 10, 2013 at 3:36 PM, Richard Williams
<richardwilliams.ndu@gmail.com> wrote:
> At 09:53 AM 1/10/2013, Maarten Buis wrote:
>>
>> On Thu, Jan 10, 2013 at 3:19 PM, annoporci wrote:
>> > Yes. I guess another way of expressing my puzzlement is that Stata does
>> > not display, by default, to a greater number of decimal places.
>>
>> Stata is a program for statistical analysis. In any real statistical
>> analysis involving real data, any number beyond the first (maybe, if
>> you are lucky the second) is in essence random noice. So from that
>> perspective Stata is reporting way too many digits.
>
>
> I don't remember the exact details, but somebody did post a while back about
> why they needed a seemingly ridiculous number of decimal places. Maybe it
> had something to do with genetics, where one chance in a trillion was
> important and meaningful. Given what I do, it would be silly for me to ask
> for accuracy to 12 decimal places, but in other work it may be necessary and
> reasonable.
>
>
>> This is not to say that precision is not a problem. During
>> computations numerical precision is a major issue. However, my
>> impression, based on the couple of contacts I have had with the people
>> from StataCorp (mainly at Stata Users' Group meetings and just reading
>> what they have written), is that StataCorp tends to take this
>> extremely seriously.
>>
>> > to the documentation: "On a typical machine running Python, there are 53
>> > bits of precision available for a Python float." And, to quote more:
>> >
>> > If Python were to print the true decimal value of the binary
>> > approximation
>> > stored for 0.1, it would have to display:
>> >
>> > 0.1000000000000000055511151231257827021181583404541015625
>> >
>> > So that's still quite a few zeros after the first 1.
>>
>> Compare that with Stata:
>> . di %30.25f 0.1
>> 0.1000000000000000100000000
>>
>> Does not look too different to me.
>>
>>  > Would I get a more accurate approximation of "-1.981" with Stata if I
>> > input "-1.981000000001" than if I input "-1.981" ? in the sense that it
>> > would "force" Stata to store the zeros after 981? (or am I
>> > misunderstanding the whole issue?)
>>
>> If you want to store a number equivalent to -1.981 exactly than you
>> need think in terms of integers, as computers can store integers up to
>> a given size(*) exactly. In this case you would store the number 1981.
>>
>> Hope this helps,
>> Maarten
>>
>> (*) To see the limits see the the reference Nick gave you:
>> <http://blog.stata.com/2012/04/02/the-penultimate-guide-to-precision/>
>> and the references therein.
>>
>> --
>> ---------------------------------
>> Maarten L. Buis
>> WZB
>> Reichpietschufer 50
>> 10785 Berlin
>> Germany
>>
>> http://www.maartenbuis.nl
>> ---------------------------------
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>
>
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
> OFFICE: (574)631-6668, (574)631-6463
> HOME:   (574)289-5227
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>
>
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```