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

[Richard Williams <Richard.A.Williams.5@nd.edu>]

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
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