# st: R: R: bootstrapped p-values

 From "Carlo Lazzaro" To Subject st: R: R: bootstrapped p-values Date Sat, 6 Dec 2008 12:07:12 +0100

```Dear Richard,
I suppose that confusion arose because you are implicitly referring to two
different things:

- the meaning of p-value reported in bootstrap printout (and Nick's

- the bootstrap p-value vs the original one in searching for the
significance of the difference of the mean with skewed data.
As widely reported in literature (please see for instance, Desgagne A,
Castilloux A, Angers J, LeLorier J. The use of the bootstrap statistical
method for the pharmacoeconomic cost analysis of skewed data.
Pharmacoeconomics 1998; 13:487-497.Barber JA and Thompson SG. Analysis of
cost data in randomized trials: an application of the non-parametric
bootstrap. Statistics in Medicine 2000; 19:3219-3236), ttest procedure needs
the fulfilments of some prerequisite before being invoked, which are
systematically violated whenever data are skewed (please, take a look at the
following example sketched via Stata 9.2/SE):
---------------------------begin example---------------------------
sysuse auto
save "C:\Documents and
Settings\carlo\Documenti\Statistiche\Stata\Richard_1.dta", replace
ttest mpg, by(foreign) unequal
scalar tobs=r(t)
sum mpg, mean
scalar omean=r(mean)
sum mpg if foreign==0, mean
replace mpg = mpg-r(mean) + scalar(omean)  if foreign==0
sum mpg if foreign==1, mean
replace mpg = mpg-r(mean) + scalar(omean)  if foreign==1
sort foreign
by foreign: sum mpg
keep mpg foreign
set seed 1
bootstrap r(t), reps(1000) nodots strata(foreign) saving(C:\Documents and
Settings\carlo\Documenti\Statistiche\Stata\Richard_2.dta, every(1)
replace)verbose : ttest mpg, by(foreign) unequal
save "C:\Documents and
Settings\carlo\Documenti\Statistiche\Stata\Richard_1.dta", replace
use "C:\Documents and
Settings\carlo\Documenti\Statistiche\Stata\Richard_2.dta", clear
generate indicator =abs(r(t))>=abs(scalar(tobs))
sum indicator, mean
display "ASLboot="r(mean)
------------------------------end example----------------------------

HTH, Kind Regards and enjoy your W-E,

Carlo
-----Messaggio originale-----
Inviato: venerdì 5 dicembre 2008 23.37
A: Carlo Lazzaro
Oggetto: Re: R: bootstrapped p-values

hi,

thanks nick and carlo..

I understand your point about the p value in the statout now. I am a

for example  the following

http://compdiag.molgen.mpg.de/ngfn/docs/2003/nov/Exercises_Bootstrap.pdf

discusses non parametric bootstrap on page 4 and on page 5 it talks about

"The two-sided p-values are now calculated by determining the
percentage of situation where the
absolute value of the test statistics calculated from the groups with
permutated values is at least
as large as the absolute value of the test statistics calculated from
the original groups."..

and the following page

westfall.ba.ttu.edu/Finance%20Pres.ppt

talks about something similar on page 11 and page 12

I am not what that means and how that is related to the stata p-value?
and the following page

westfall.ba.ttu.edu/Finance%20Pres.ppt

talks about something similar on page 11 and page 12

I am not what that means and how that is related to the stata p-value?

thanks
rich

2008/12/5 Carlo Lazzaro <carlo.lazzaro@tiscalinet.it>:
> Dear Richard,
> I would refer you to Stata Archives and recommend to take a look at
Maarten
> Buis' and Martin Weiss' kind replies to one thread I have posted on 2008
Sep
> 6 (which was not so different from yours, as it would seem):
>
> st: z statistics in bootstrap output
>
> Kind Regards and enjoy your W-E,
> Carlo
> -----Messaggio originale-----
> Da: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] Per conto di Richard Harvey
> Inviato: venerdì 5 dicembre 2008 18.40
> A: statalist@hsphsun2.harvard.edu
> Oggetto: st: bootstrapped p-values
>
> Hi,
>
> Could someone please explain how stata computes the bootstrap p-values?
>
> suppose i issue the following commands
>
> sysuse auto
> bootstrap t=r(t), rep(1000)  saving(bsauto, replace): ttest mpg==0
>
> i get
>
>
> Bootstrap results                                               Number
> of obs=        74
> Replications       =      1000
>
>
> Observed   Bootstrap            Normal-based
> Coef.   Std. Err.       z       P>z     [95% Conf. Interval]
>
> t    31.66644   2.900212        10.92   0.000     25.98213    37.35075
>
>
> how does stata compute the P>z?
>
> does it...
>
> look at the proportion of bootstrapped t-values which are less than or
> equal to the original t-value ( from
> ttest mpg==0) say x and the proportion of bootstrapped t-values which
> are greater than or equal to the original t-value ( from ttest mpg==0)
> say y then computes p as 2 min(x,y) ?
>
> --
> rich
> *
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>
>
>

--
rich

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```