By chance, I found the standard error of mean values obtained from ttest is
different from linear regression. Please look at the following example.
The data is auto.dta in STATA.
. ttest price, by(foreign)
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
----------------------------------------------------------------------------
--
Degrees of freedom: 72
Ho: mean(Domestic) - mean(Foreign) = diff = 0
Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
t = -0.4139 t = -0.4139 t = -0.4139
P < t = 0.3401 P > |t| = 0.6802 P > t = 0.6599
. reg price foreign
Source | SS df MS Number of obs =
74
-------------+------------------------------ F( 1, 72) =
0.17
Model | 1507382.66 1 1507382.66 Prob > F =
0.6802
Residual | 633558013 72 8799416.85 R-squared =
0.0024
-------------+------------------------------ Adj R-squared
= -0.0115
Total | 635065396 73 8699525.97 Root MSE =
2966.4
----------------------------------------------------------------------------
--
price | Coef. Std. Err. t P>|t| [95% Conf.
Interval]
-------------+--------------------------------------------------------------
--
foreign | 312.2587 754.4488 0.41 0.680 -1191.708
1816.225
_cons | 6072.423 411.363 14.76 0.000 5252.386
6892.46
----------------------------------------------------------------------------
--
ttest and linear regression provide exactly the same estimates of mean
difference of price between domestic and foreign autos, which is 312.2587 in
this example. As well as its standard error, which is 754.4488. However,
look at _cons in the linear regression. In this example, the coefficient of
_cons should be the mean price of domestic auto, since varible "foreign" is
coded as 0 if the autos were from domestic, 1 if foreign. The coefficient of
_cons is exactly the same as the mean value in ttest, which is 6072.423. But
its standard error in ttest is 429.4911, whereas 411.363 in linear
regression. Can anybody tell me how this can happen? Thank you very much in
advance.
Aijing Shang
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