Re: st: RE: Re: STATA mistakes divisions!

["Roger B. Newson" <r.newson@imperial.ac.uk>]

The phrase 1-1e-8 (which I think Tiago really meant) seems to imply 
RELATIVE rather than ABSOLUTE precision to me, ie numbers VERY close to 
1, which are routinely encountered in genome scan calculations. Given an 
uncorrected P-value of 1e-8, the expression 1-1e-8 will appear in the 
formula for the q-values generated by the Sidak and Holland-Copenhaver 
methods. See Newson (2010) for these formulas.

Roger

References

Newson RB. Frequentist q-values for multiple-test procedures. The Stata 
Journal 2010; 10(4): 568-584.

Roger B Newson BSc MSc DPhil
Lecturer in Medical Statistics
Respiratory Epidemiology and Public Health Group
National Heart and Lung Institute
Imperial College London
Royal Brompton Campus
Room 33, Emmanuel Kaye Building
1B Manresa Road
London SW3 6LR
UNITED KINGDOM
Tel: +44 (0)20 7352 8121 ext 3381
Fax: +44 (0)20 7351 8322
Email: r.newson@imperial.ac.uk
Web page: http://www.imperial.ac.uk/nhli/r.newson/
Departmental Web page:
http://www1.imperial.ac.uk/medicine/about/divisions/nhli/respiration/popgenetics/reph/

Opinions expressed are those of the author, not of the institution.

On 16/03/2012 18:36, Nick Cox wrote:
> I said precision of 1 part in 10^7, meaning relative precision.
>
> I didn't mean absolute values of that order (or finer).
>
> Nick
>
> On Fri, Mar 16, 2012 at 5:40 PM, Tiago V. Pereira
> <tiago.pereira@mbe.bio.br>  wrote:
>
> > Some general comments/questions:
> >
> > (1) Nick has asked "What science are you in that needs precision to 1 part
> > in 10^7? Particle physics?"
> >
> > I can comment on my area: genetics. We routinely need calculations with
> > very high precision (1-10^8 often)
> >
> > That's EXACTLY why I am using Stata.
> >
> > (2) Maarten wrote: "Some computations are even done in quad precision
> > (approximately 34 decimal digits)."
> >
> >
> > Question: Can one perform every calculation in quad precision? I would
> > very interested in that.
>
>   Thu, Mar 15, 2012 at 3:48 PM, Francesco Vidoli  wrote:
>
> > > But therefore by default, without writing in every division "float",
> > > STATA mistake divisions?
> > > It's not only a visualization problem, we are trying to compare a SAS
> > > OLS regression and  results simply do not add up if you calculate the
> > > variables of SAS or STATA ...
> >
> > No, there is no mistake. This is a phenomenon known as precision, and
> > it is a result of the fact that computers cannot store most numbers
> > with infinite precision. Stata (note: not STATA) has some smart
> > defaults on how much precision to use for variables, computations,
> > scalars, etc. In short data is by default stored with less precision
> > (about 7-8 decimal digits) than computations (about 17-18 decimal
> > digits). This is smart as even the 7-8 digits is complete overkill for
> > real world data. Some nice examples of this can be found here:
> > <http://blog.stata.com/2011/06/17/precision-yet-again-part-i/>.
> >
> > However if you want to do computations with variables than you want to
> > overwrite this default, as many tiny rounding errors can start to add
> > up to a large or at least noticeable error. You do so as follows:
> >
> > gen double varname = expression
> >
> > The key part is -double-, that tells you that the variable is supposed
> > to be stored in double precision, i.e. about 18 decimal digits, which
> > corresponds to the precision used by SAS and others. This is also what
> > Stata programs do internally when they are using variables to do
> > computations. Some computations are even done in quad precision
> > (approximately 34 decimal digits).
>
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