Liz's Stata Guide

ttest

Performs a statistical test as to whether a variable has a specified mean, whether two variables are equal, or whether the mean of one variable is equal across values of another variable.

Typical Use:
ttest varx = 2   - or -
ttest varx == vary, unpaired   - or -
ttest varx, by(groupvar)

Examples

1. Instructions given to surveyors were supposed to ensure that the sample was half male and half female, however, the final sample is actually 51% male. We test the hypothesis that respondent selection was actually carried out correctly such that male and female respondents had an equal chance of being interviewed (we cannot reject this hypothesis).

   . ttest male == 0.5
   
   One-sample t test
   
   ------------------------------------------------------------------------------
   Variable |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
   ---------+--------------------------------------------------------------------
       male |    1100    .5136364    .0150768    .5000414    .4840538     .543219
   ------------------------------------------------------------------------------
   Degrees of freedom: 1099
   
                               Ho: mean(male) = 0.5
   
       Ha: mean < 0.5             Ha: mean != 0.5            Ha: mean > 0.5
          t =   0.9045                t =   0.9045              t =   0.9045
      P < t =   0.8170          P > |t| =   0.3660          P > t =   0.1830
   

2. Next, let's test whether the same fraction of the population own a bicycle as own a TV. Again, we cannot reject this hypothesis.

   . ttest own_TV == own_bicycle, unpaired
   
   Two-sample t test with equal variances
   
   ------------------------------------------------------------------------------
   Variable |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
   ---------+--------------------------------------------------------------------
     own_TV |    1098    .0801457    .0081978    .2716424    .0640606    .0962308
   own_bi~e |    1098     .079235    .0081551    .2702282    .0632336    .0952363
   ---------+--------------------------------------------------------------------
   combined |    2196    .0796903    .0057803    .2708749    .0683549    .0910258
   ---------+--------------------------------------------------------------------
       diff |            .0009107    .0115633               -.0217654    .0235869
   ------------------------------------------------------------------------------
   Degrees of freedom: 2194
   
                  Ho: mean(own_TV) - mean(own_bicycle) = diff = 0
   
        Ha: diff < 0               Ha: diff != 0              Ha: diff > 0
          t =   0.0788                t =   0.0788              t =   0.0788
      P < t =   0.5314          P > |t| =   0.9372          P > t =   0.4686
   

3. Finally, let's test whether the average age of male respondents is equal to average age of female respdondents. We find that we can reject this hypothesis -- male respdondents are significantly older on average.

   . ttest age, by(gender)
   
   Two-sample t test with equal variances
   
   ------------------------------------------------------------------------------
   Variable |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf. Interval]
   ---------+--------------------------------------------------------------------
       male |     563    43.56838    .6611666    15.68791    42.26972    44.86704
     female |     530    38.91698     .642816    14.79873     37.6542    40.17977
   ---------+--------------------------------------------------------------------
   combined |    1093     41.3129     .466795     15.4325    40.39698    42.22882
   ---------+--------------------------------------------------------------------
       diff |            4.651403    .9237718                2.838832    6.463973
   ------------------------------------------------------------------------------
   Degrees of freedom: 1091
   
                     Ho: mean(male) - mean(female) = diff = 0
   
        Ha: diff < 0               Ha: diff != 0              Ha: diff > 0
          t =   5.0352                t =   5.0352              t =   5.0352
      P < t =   1.0000          P > |t| =   0.0000          P > t =   0.0000
   

Options

• Without the option , unpaired, the second syntax does a one-sample test that the mean of the difference of the two variables is 0. Thus ttest varx == vary is equivalent to

  gen diff = varx - vary;
  ttest diff == 0;

• When doing a two-sample test (second or third syntax) Stata tests the hypothesis that not only are the means of the two samples equal, but that their variances are equal as well. Sometimes, we don't care about the variances, and just want to test if the means of the two samples are equal. The option , unequal allows us to test this (slightly weaker) hypothesis. Usually it makes little difference, but if you did have two samples with similar means but very different variances it would.

Notes

• ttest does not know whether or not a variable is binary, and always uses the sample variance to compute the standard error. If the variable is binary, the command bitest uses the standard error implied by the hypothesis, but it is irritating in that it doesn't give you the value of the t-stat, only the p-value. Redoing the first example:

  . bitest male == 0.5
  
      Variable |        N   Observed k   Expected k   Assumed p   Observed p
  -------------+------------------------------------------------------------
          male |     1100        565          550       0.50000      0.51364
  
    Pr(k >= 565)             = 0.190959  (one-sided test)
    Pr(k <= 565)             = 0.825022  (one-sided test)
    Pr(k <= 535 or k >= 565) = 0.381918  (two-sided test)
  

• See the official Stata help for ttest.