# Re: st: Re: Re: ST: one-tailed test

 From Richard Williams To statalist@hsphsun2.harvard.edu Subject Re: st: Re: Re: ST: one-tailed test Date Mon, 11 Oct 2004 08:38:46 -0500

```At 09:09 PM 10/11/2004 +0800, Levy Lee wrote:
```
```thanks again,

but i do not think this is precise, are there other way to go?
```
No, unless I misunderstand you, it is exactly right. Consider a regression where you have a single dichotomous independent variable:

. reg income race

Source | SS df MS Number of obs = 20
-------------+------------------------------ F( 1, 18) = 8.55
Model | 586.444492 1 586.444492 Prob > F = 0.0090
Residual | 1233.98098 18 68.5544991 R-squared = 0.3221
Total | 1820.42548 19 95.8118671 Root MSE = 8.2798

------------------------------------------------------------------------------
income | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
race | -10.83 3.702823 -2.92 0.009 -18.60934 -3.050657
_cons | 29.83 2.618291 11.39 0.000 24.32917 35.33083
------------------------------------------------------------------------------

The reported 2-tailed significance of race is .009. You can do an equivalent analysis with the t-test command:

. ttest income, by(race)

Two-sample t test with equal variances

------------------------------------------------------------------------------
Group | Obs Mean Std. Err. Std. Dev. [95% Conf. Interval]
---------+--------------------------------------------------------------------
white | 10 29.83 2.639573 8.347062 23.85887 35.80113
black | 10 19 2.596836 8.211915 13.12555 24.87445
---------+--------------------------------------------------------------------
combined | 20 24.415 2.188742 9.788354 19.83391 28.99609
---------+--------------------------------------------------------------------
diff | 10.83 3.702823 3.050657 18.60934
------------------------------------------------------------------------------
Degrees of freedom: 18

Ho: mean(white) - mean(black) = diff = 0

Ha: diff < 0 Ha: diff != 0 Ha: diff > 0
t = 2.9248 t = 2.9248 t = 2.9248
P < t = 0.9955 P > |t| = 0.0090 P > t = 0.0045

The 2-tailed significance is again .0090; the 1-tailed significance is exactly half that, .0045. (The only difference is that the t-test basically reversed the 2 groups from what the regression had done.)

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Richard Williams, Notre Dame Dept of Sociology
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