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Re: st: z statistics in bootstrap output

From   Maarten buis <[email protected]>
To   [email protected]
Subject   Re: st: z statistics in bootstrap output
Date   Sat, 6 Sep 2008 18:12:00 +0100 (BST)

--- Carlo Lazzaro <[email protected]> wrote:
> I would kindly ask you for a clarification and the related formula
> concerning the meaning of z in bootstrap output.

By default the output of -bootstrap- estimates the standard error using
the bootstrap, but than for testing and confidence intervals assumes
that the sampling distribution is normal. This is a sensible default as
the default number of replications is small as well, which means that
the estimate of the standard error is likely to be ok, but percentile,
bias corrected confidence intervals would need much more replications.
Having a small number of replications as a default seems sensible to me
as well, as convenience matters most in an exploratory stage of the
analysis, and in the exploratory stage you don't want to wait long for
a result, while in the final stage you can afford to type a bit more to
set the replications to a larger number. In those cases you should look
at -help bootstrap postestimation- to see how you can get the other
types of confidence intervals. 

Anyhow, the z is just the estimate divided by the standard error, and
it is compared to the standard normal distribution to give you a test
of the hypothesis that the coefficient equals zero.

*------------------ begin example -------------------
sysuse auto, clear
replace mpg = mpg-21
bootstrap mean=r(mean), reps(100): sum mpg, meanonly
di _b[mean]/_se[mean]
di 2*normal(-abs(_b[mean]/_se[mean]))
*-------------------- end example -------------------
(For more on how to use examples I sent to the Statalist, see )

Hope this helps,

Maarten L. Buis
Department of Social Research Methodology
Vrije Universiteit Amsterdam
Boelelaan 1081
1081 HV Amsterdam
The Netherlands

visiting address:
Buitenveldertselaan 3 (Metropolitan), room Z434

+31 20 5986715

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