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st: RE: Comparison of a distribution with a value from the literature


From   "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" <alan.h.feiveson@nasa.gov>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: RE: Comparison of a distribution with a value from the literature
Date   Fri, 18 Apr 2003 13:45:35 -0500

Andrea - 

Here's some thoughts on your question - perhaps they will be of some use.

The only way to make use of the information that sd(A) = 0.2 is assume some
distribution (such as a normal) for A. If you are willing to assume such a
distribution, one easy approach  you could try  is to simulate many values
of A (say 1000)  and use -ranksum- to compare that distribution against your
data. Of course, doing so would not give perfectly  repeatable results
except in the limit as the number of simulated A-values grows large. 

A theoretical  approach to derive a repeatable result would be to do a
binomial test for fixed A (see below), then
average the conditional p-value over the assumed distribution of A. Whether
this could be done analytically in closed form, depends on what distribution
you use for A.

You could approximate this second approach numerically by:  (1) simulate a
single value of A (2) do the fixed test below, then repeat (1) and (2) many
times and look at the average p-value. The p-value from the -bitest- command
is obtainable as the two-sided test p-vlaue, r(p).

FIXED CASE:
For the fixed A, nonparameteric case, suppose A0 is the hypothetical median
from the literature and A is your data. Then just calculate the proportion
of observations of A less than or equal to A0 and do a binomial test for the
mean = 0.5. Or you could use the confidence interval command -ci- on a
binary variable which is 1 if a <= A0, 0 otherwise and see if the confidence
interval contains 0.5; e.g.

scalar A0 = 1.0
gen na0 = A<= A0
bitest na0=0.5  
ci na0

Al Feiveson




-----Original Message-----
From: Andrea Baccarelli [mailto:andreastata5@hotmail.com]
Sent: Friday, April 18, 2003 12:43 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: Comparison of a distribution with a value from the
literature


I have the following question:

I am studying how the continuous variable A varies after a specific 
treatment.
In addition to compare A after the treatment with A before the treatment or 
in controls (no treatment), I need to compare it also with standard 
reference values from the literature.
Let's say that most book assume that A is equal to 1.0 with SD=0.2.

I thought to use the ttest command:

ttest A=1.0

I have two points:
1-This not take into account the variability (SD=0.2) of the measure taken 
from the literature. Does anyone have any suggestion about how to include it

in the analysis?
2-Most variables in the study are not normally distributed. Is there any 
non-parametric test I can use to this end? [Stata's "ranksum" do not allow 
comparisons to a fixed value]

Thanks,
Andrea









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