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

 From "Levy Lee" To Subject Re: st: Re: Re: ST: one-tailed test Date Mon, 11 Oct 2004 21:42:52 +0800

```thanks, i am afraid that i mis-understand it before

thanks again

----- Original Message -----
From: "Richard Williams" <Richard.A.Williams.5@nd.edu>
To: <statalist@hsphsun2.harvard.edu>
Sent: Monday, October 11, 2004 9:38 PM
Subject: Re: st: Re: Re: ST: one-tailed test

> 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
> -------------+------------------------------           Adj R-squared =
0.2845
>         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.)
>
>
> -------------------------------------------
> Richard Williams, Notre Dame Dept of Sociology
> OFFICE: (574)631-6668, (574)631-6463
> FAX:    (574)288-4373
> HOME:   (574)289-5227
> EMAIL:  Richard.A.Williams.5@ND.Edu
> WWW (personal):    http://www.nd.edu/~rwilliam
> WWW (department):    http://www.nd.edu/~soc
>
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```