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

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:

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]femaleAdjusted Wald test ( 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.

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 ------------------------------------------------------------------------------

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.

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.test femaleAdjusted Wald test ( 1) female = 0 F( 1, 197) = 10.45 Prob > F = 0.0014

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

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