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From |
"Aijing Shang" <[email protected]> |

To |
<[email protected]> |

Subject |
st: standard error obtained from ttest and linear regression |

Date |
Thu, 19 Feb 2004 17:02:24 +0100 |

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 * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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