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# RE: st: RE: standard deviation for the difference in means

 From "Lachenbruch, Peter" To "'statalist@hsphsun2.harvard.edu'" Subject RE: st: RE: standard deviation for the difference in means Date Mon, 7 Jun 2010 08:43:46 -0700

```Yes it does.  If you want unpooled variances, you can simply use the ttest command with uneq option (or the welsh option) two methods of adjusting the d.f. for the standard error.  Check the ttest help (or ttesti)
Here's an example with auto - sorry for the wraparound. My email won't let me reduce font size.
. sysuse auto
(1978 Automobile Data)

. ttest price, by(foreign)
-Assuming equal variance-
Two-sample t test with equal variances
------------------------------------------------------------------------------
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
Domestic |      52    6072.423    429.4911    3097.104    5210.184    6934.662
Foreign |      22    6384.682    558.9942    2621.915     5222.19    7547.174
---------+--------------------------------------------------------------------
combined |      74    6165.257    342.8719    2949.496    5481.914      6848.6
---------+--------------------------------------------------------------------
diff |           -312.2587    754.4488               -1816.225    1191.708
------------------------------------------------------------------------------
diff = mean(Domestic) - mean(Foreign)                         t =  -0.4139
Ho: diff = 0                                     degrees of freedom =       72

Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
Pr(T < t) = 0.3401         Pr(|T| > |t|) = 0.6802          Pr(T > t) = 0.6599

. ttest price, by(foreign) uneq
-Satterthwaite approximation for d.f.-
Two-sample t test with unequal variances
------------------------------------------------------------------------------
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
Domestic |      52    6072.423    429.4911    3097.104    5210.184    6934.662
Foreign |      22    6384.682    558.9942    2621.915     5222.19    7547.174
---------+--------------------------------------------------------------------
combined |      74    6165.257    342.8719    2949.496    5481.914      6848.6
---------+--------------------------------------------------------------------
diff |           -312.2587    704.9376               -1730.856    1106.339
------------------------------------------------------------------------------
diff = mean(Domestic) - mean(Foreign)                         t =  -0.4430
Ho: diff = 0                     Satterthwaite's degrees of freedom =  46.4471

Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
Pr(T < t) = 0.3299         Pr(|T| > |t|) = 0.6599          Pr(T > t) = 0.6701

. ttest price, by(foreign) w
-Welch approximation for d.f.-
Two-sample t test with unequal variances
------------------------------------------------------------------------------
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
Domestic |      52    6072.423    429.4911    3097.104    5210.184    6934.662
Foreign |      22    6384.682    558.9942    2621.915     5222.19    7547.174
---------+--------------------------------------------------------------------
combined |      74    6165.257    342.8719    2949.496    5481.914      6848.6
---------+--------------------------------------------------------------------
diff |           -312.2587    704.9376               -1729.232    1104.714
------------------------------------------------------------------------------
diff = mean(Domestic) - mean(Foreign)                         t =  -0.4430
Ho: diff = 0                             Welch's degrees of freedom =  48.5288

Ha: diff < 0                 Ha: diff != 0                 Ha: diff > 0
Pr(T < t) = 0.3299         Pr(|T| > |t|) = 0.6598          Pr(T > t) = 0.6701

Tony

Peter A. Lachenbruch
Department of Public Health
Oregon State University
Corvallis, OR 97330
Phone: 541-737-3832
FAX: 541-737-4001

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Michael McCulloch
Sent: Sunday, June 06, 2010 6:08 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: standard deviation for the difference in means

Thanks Peter, I'm not sure. I'm comparing two groups randomly assigned
to treatment, so they are independent, but my understanding was the
pooled variance assumes equal variances in each group.

<snip>

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