# st: RE: RE: -sampsi- command and exact tests

 From "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" To "'statalist@hsphsun2.harvard.edu'" Subject st: RE: RE: -sampsi- command and exact tests Date Thu, 3 Feb 2005 13:04:32 -0600

```For whatever it's worth, Russ Lenth's applet gives N = 598 ("exact").
http://www.stat.uiowa.edu/~rlenth/Power/

AL Feiveson

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of Yulia
Marchenko
Sent: Wednesday, February 02, 2005 12:31 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: RE: -sampsi- command and exact tests

On Tuesday, David wrote:

>I understand from several previous posts that the command  -sampsi- uses
>an approximate large sample test on proportion. power, and sample size
>calculations.  Specifically, it uses the normal approximation (with
>correction) as opposed to an exact test.  The advice in a previous post
>was that the following equalities must hold in order for sampsi to work

>n1p1>=10
>n1(1-p1)>=10
>n2p2>=10
>n2(1-p2)>=10

>(see post from ymarchenko@stata.com entitled st:RE: calculation of
>sample size,  dated 8 Oct 2004)

>I am trying to use sampsi to estimate the required number of  samples as
>follows:

>sampsi 0.4 0.46, alpha(0.05) power(0.90) onesample

>Stata indicates that 711 samples are required as indicated in the Stata
>output
>This seems to meet the n1p1>=10 etc. requirements listed above to use
>the -sampsi- command.  However,  I am told that the right answer using
>NQuery Advisor and its  exact test for single proportions is 610
>observations.  S-Plus gives 613 as an answer.  StatXact also gives a

>Does anyone know if Stata's use of the normal approximation  (with
>continuity correction)  is indeed what is causing the 100+ discrepancy
>here?  Is there is an exact test in Stata that can be used instead of
>-sampsi-?  And are there additional criteria beyond the n1p1>=10 etc.
>criteria listed in the  referenced previous post that should be checked
>before using -sampsi- ?

The command -sampsi- uses continuity correction only for two-sample
proportion test.  However, the discrepancy of 100 may be explained if other
packages by default report sample size for one-sided test. By
default -sampsi- uses two-sided test. For one-sided test Stata gives n=580
as shown below.

. sampsi 0.4 0.46, onesample onesided

Estimated sample size for one-sample comparison of proportion
to hypothesized value

Test Ho: p = 0.4000, where p is the proportion in the population

Assumptions:

alpha =   0.0500  (one-sided)
power =   0.9000
alternative p =   0.4600

Estimated required sample size:

n =      580

This is closer to 610 and 613 obtained from other packages by using the
exact test.

We can simulate the exact power for these three sample sizes (580, 610, 613)
using exact Binomial test ( Stata -bitest- command):

capture program drop exactpow
program exactpow, rclass
args n p0 pa alpha
qui {
rndbin `n' `pa' 1
bitest xb=`p0'
}
return scalar p=(r(p)<`alpha')
end

clear
local numlist="613 610 580"
qui foreach n of local numlist{
clear
simulate "noi exactpow `n' 0.4 0.46 0.1" p=r(p), reps(10000)
summ p
noi di in gr "Sample size = " in yel `n' in gr " Exact power:"
r(mean)
}
exit

Here are my results:

Sample size = 613 Exact power:.9131
Sample size = 610 Exact power:.9159
Sample size = 580 Exact power:.9001

The above results support the guess about other packages reporting sample
size for one-sided test.

--Yulia
ymarchenko@stata.com

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