/* This is the dummy variable example given in class */
** In this example we show that the two sample t-test
** and the regression based test that regresses a dummy
** variable on average income yields identical results.
**
**  Steps:
**  1.  Create a dummy variable that takes the value 1 if income in
**      the district is above average and zero otherwise.
**      . summarize avginc
**      . generate highinc = 0
**      . replace highinc if avginc > 15.31
**  2.  Do the two sample t-test.  To get identical results we assume
**      that the variances in the two subsamples are the same.
**      . ttest avginc, by(highinc)
**  3.  Run the regression.
**      . regress avginc highinc
**
**  Output from the STATA log file follows.
*/


  log:  C:\Temp\public_html\class\4213\f2004\dummy.smcl
  log type:  smcl
 opened on:  13 Oct 2004, 15:19:27

. use "C:\Gauss\Papers\probit\caschool.dta", clear

. summarize avginc

    Variable |       Obs        Mean    Std. Dev.       Min        Max
-------------+--------------------------------------------------------
      avginc |       420    15.31659     7.22589      5.335     55.328

. gen highinc = 0

. replace highinc = 1 if avginc > 15.31 (152 real changes made)

. ttest avginc, by(highinc)

Two-sample t test with equal variances

------------------------------------------------------------------------------
   Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
---------+--------------------------------------------------------------------
       0 |     268    11.46686    .1433048    2.346001    11.18471    11.74901
       1 |     152    22.10426    .6410858    7.903837    20.83761    23.37092
---------+--------------------------------------------------------------------
combined |     420    15.31659    .3525873     7.22589    14.62353    16.00965
---------+--------------------------------------------------------------------
    diff |            -10.6374     .518575               -11.65674   -9.618062
------------------------------------------------------------------------------
Degrees of freedom: 418

                      Ho: mean(0) - mean(1) = diff = 0

     Ha: diff < 0               Ha: diff != 0              Ha: diff > 0
       t = -20.5128                t = -20.5128              t = -20.5128
   P < t =   0.0000          P > |t| =   0.0000          P > t =   1.0000

. regress avginc highinc

      Source |       SS       df       MS              Number of obs =     420
-------------+------------------------------           F(  1,   418) =  420.77
       Model |  10974.8903     1  10974.8903           Prob > F      =  0.0000
    Residual |   10902.559   418  26.0826771           R-squared     =  0.5017
-------------+------------------------------           Adj R-squared =  0.5005
       Total |  21877.4493   419  52.2134829           Root MSE      =  5.1071

------------------------------------------------------------------------------
      avginc |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
     highinc |    10.6374    .518575    20.51   0.000     9.618062    11.65674
       _cons |   11.46686    .311967    36.76   0.000     10.85364    12.08008
------------------------------------------------------------------------------

. log close
       log:  C:\Temp\public_html\class\4213\f2004\dummy.smcl
  log type:  smcl
 closed on:  13 Oct 2004, 15:19:57
-------------------------------------------------------------------------------