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st: -ttest- does not report the pooled standard deviation


From   "Paul Dickman" <paul.dickman@mep.ki.se>
To   <statalist@hsphsun2.harvard.edu>
Subject   st: -ttest- does not report the pooled standard deviation
Date   Wed, 4 Sep 2002 16:57:50 +0200

Can anyone explain why -ttest- without the unequal option does not report
the pooled standard deviation. In the output below, for example, it is
possible one might erroneously conclude that the pooled standard deviation
was 5.785503.

Paul Dickman (paul.dickman@mep.ki.se)

. use "C:\Program Files\stata7\auto"
(1978 Automobile Data)

. ttest  mpg, by(foreign)

Two-sample t test with equal variances

----------------------------------------------------------------------------
--
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf.
Interval]
---------+------------------------------------------------------------------
--
Domestic |      52    19.82692     .657777    4.743297    18.50638
21.14747
 Foreign |      22    24.77273     1.40951    6.611187    21.84149
27.70396
---------+------------------------------------------------------------------
--
combined |      74     21.2973    .6725511    5.785503     19.9569
22.63769
---------+------------------------------------------------------------------
--
    diff |           -4.945804
 1.362162               -7.661225   -2.230384
----------------------------------------------------------------------------
--
Degrees of freedom: 72

                Ho: mean(Domestic) - mean(Foreign) = diff = 0

     Ha: diff < 0               Ha: diff ~= 0              Ha: diff > 0
       t =  -3.6308                t =  -3.6308              t =  -3.6308
   P < t =   0.0003          P > |t| =   0.0005          P > t =   0.9997

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