### Stata FAQ How can I do a t-test with survey data?

There is no svy: ttest command in Stata; however, svy: mean is a "true" estimation command and allows for the use of both the test and lincom post-estimation commands. It is also easy to do a t-test using the svy: regress command. We will show each of these three ways of conducting a t-test with survey data below.

We will illustrate this using the hsb2 dataset pretending that the variable socst is the sampling weight (pweight) and that the sample is stratified on ses. Let's say that we wish to do a t-test for write by gender. In our dataset, the variable female is coded 1 for females and 0 for males.

use http://www.ats.ucla.edu/stat/stata/notes/hsb2, clear

svyset [pw=socst], strata(ses)

pweight: socst
VCE: linearized
Strata 1: ses
SU 1:
FPC 1: 

#### Method 1: Using the test command

First, we use the svy: mean command with the over option to get the means for each gender.  Next, we use the test command to test the null hypothesis that these two means are equal.

svy: mean write, over(female)
(running mean on estimation sample)

Survey: Mean estimation

Number of strata =       3          Number of obs    =     200
Number of PSUs   =     200          Population size  =   10481
Design df        =     197

male: female = male
female: female = female

--------------------------------------------------------------
|             Linearized
Over |       Mean   Std. Err.     [95% Conf. Interval]
-------------+------------------------------------------------
write        |
male |   51.65351   1.041066      49.60045    53.70658
female |   55.81467    .721354       54.3921    57.23723
--------------------------------------------------------------

test [write]male = [write]female

( 1)  [write]male - [write]female = 0

F(  1,   197) =   10.45
Prob > F =    0.0014

We can see from the output above that the means are not statistically equivalent.

#### Method 2: Using the lincom command

We could also use the lincom command to test the two means.  This command should be run after the svy: means command shown above.  The lincom command gives us the difference between the means (51.65351 - 55.81467 = -4.161156), the standard error of the difference, as well as the t-value and the p-value.  Notice that the p-value is the same as above, and that squaring the t-value yields the F-value shown above ( (-3.23)^2 = 10.45).

lincom [write]male - [write]female

( 1)  [write]male - [write]female = 0

------------------------------------------------------------------------------
|      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
(1) |  -4.161156     1.2871    -3.23   0.001    -6.699419   -1.622892
------------------------------------------------------------------------------

#### Method 3: Using the regress command

The svy: regress command can also be used to compute the t-test.  To do this, simply include the single dichotomous predictor variable.  The coefficient for female is the t-test.  As you can see, you get the same coefficient and p-value that we did when we used the lincom command.  The sign of the coefficient is different because above, the mean of the males was subtracted from the mean of females.  Below, the mean of females was subtracted from the mean of the males.

svy: regress write female

(running regress on estimation sample)

Survey: Linear regression

Number of strata   =         3                  Number of obs      =       200
Number of PSUs     =       200                  Population size    =     10481
Design df          =       197
F(   1,    197)    =     10.45
Prob > F           =    0.0014
R-squared          =    0.0519

------------------------------------------------------------------------------
|             Linearized
write |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
female |   4.161156     1.2871     3.23   0.001     1.622892    6.699419
_cons |   51.65351   1.041066    49.62   0.000     49.60045    53.70658
------------------------------------------------------------------------------

We can use the test command after the svy: regress if we would like to get the F-ratio.

test female

( 1)  female = 0

F(  1,   197) =   10.45
Prob > F =    0.0014

Regardless of the method that we use, we obtain an F-ratio of 10.45 or a t-value of 3.23 with a p-value of 0.0014.

Note: This FAQ was inspired by several responses to a question on the Statalist.

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