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st: correct confidence intervals of -mean- ?

From   Dirk Enzmann <>
Subject   st: correct confidence intervals of -mean- ?
Date   Sat, 06 Mar 2010 13:47:41 +0100

Very carefully I want to ask: Are the confidence intervals given by -mean- really correct?

Below I compare the results of -mean- with the results of a different procedure:

* --------------------------------------
sysuse auto, clear
mean price, over(rep78)

local df = e(df_r)
display "degrees of freedom = n-1 = `df'"
* Note that here df is the number of the total sample - 1!

* alternative route:
collapse (mean) mprice=price (sd) sdprice=price (count) nprice=price if (rep78 < .), by(rep78)
* calculate the confidence intervals the -mean- way:
gen ci95la = mprice - invttail(`df',.025)*sdprice/sqrt(nprice)
gen ci95ua = mprice + invttail(`df',.025)*sdprice/sqrt(nprice)
* calculate the confidence intervals a different way:
gen ci95lb = mprice - invttail(nprice-1,.025)*sdprice/sqrt(nprice)
gen ci95ub = mprice + invttail(nprice-1,.025)*sdprice/sqrt(nprice)
* compare both sets of confidence intervals (..a vs ..b):
* --------------------------------------

My question: Which procedure is correct?

Dr. Dirk Enzmann
Institute of Criminal Sciences
Dept. of Criminology
Schlueterstr. 28
D-20146 Hamburg

phone: +49-(0)40-42838.7498 (office)
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