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RE: st: RE: standard deviation for the difference in means
From
"Lachenbruch, Peter" <[email protected]>
To
"'[email protected]'" <[email protected]>
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: [email protected] [mailto:[email protected]] On Behalf Of Michael McCulloch
Sent: Sunday, June 06, 2010 6:08 PM
To: [email protected]
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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