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st: Ttest and Welch's degrees of freedom
From
Garry Anderson <[email protected]>
To
<[email protected]>
Subject
st: Ttest and Welch's degrees of freedom
Date
Mon, 18 Apr 2011 18:37:34 +1000
Dear Statalist,
I was reading the -ttest- entry in the manual on page 1998 (example 3)
and noticed that use of Welch's degrees of freedom can increase the
degrees of freedom compared with the usual degrees of freedom obtained
from an unpaired t-test.
Should Welch's degrees of freedom be larger than n1 + n2 - 2 ?
The commands and output are shown below.
. use http://www.stata-press.com/data/r11/fuel3
. ttest mpg, by(treated)
Two-sample t test with equal variances
------------------------------------------------------------------------
------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf.
Interval]
---------+--------------------------------------------------------------
------
0 | 12 21 .7881701 2.730301 19.26525
22.73475
1 | 12 22.75 .9384465 3.250874 20.68449
24.81551
---------+--------------------------------------------------------------
------
combined | 24 21.875 .6264476 3.068954 20.57909
23.17091
---------+--------------------------------------------------------------
------
diff | -1.75 1.225518 -4.291568
.7915684
------------------------------------------------------------------------
------
diff = mean(0) - mean(1) t =
-1.4280
Ho: diff = 0 degrees of freedom =
22
Ha: diff < 0 Ha: diff != 0 Ha: diff
> 0
Pr(T < t) = 0.0837 Pr(|T| > |t|) = 0.1673 Pr(T > t) =
0.9163
. ttest mpg, by(treated) welch
Two-sample t test with unequal variances
------------------------------------------------------------------------
------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf.
Interval]
---------+--------------------------------------------------------------
------
0 | 12 21 .7881701 2.730301 19.26525
22.73475
1 | 12 22.75 .9384465 3.250874 20.68449
24.81551
---------+--------------------------------------------------------------
------
combined | 24 21.875 .6264476 3.068954 20.57909
23.17091
---------+--------------------------------------------------------------
------
diff | -1.75 1.225518 -4.28369
.7836902
------------------------------------------------------------------------
------
diff = mean(0) - mean(1) t =
-1.4280
Ho: diff = 0 Welch's degrees of freedom =
23.2465
Ha: diff < 0 Ha: diff != 0 Ha: diff
> 0
Pr(T < t) = 0.0833 Pr(|T| > |t|) = 0.1666 Pr(T > t) =
0.9167
.
Kind regards, Garry
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