T-test with survey data

[Silvana Builes Gaitan]

Hello. I am using survey data:

gen fs_strata = state + sector + stratum + sub_stratum
svyset fsu_serial_no [pweight=weights], strata(fs_strata) singleunit(centered) || hhid

I am comparing hospitalization expenditures among two types of houhseholds is_hhmem_pmjay ==1 and is_hhmem_pmjay ==0. I have obtained that the first households spend more than the later ones.
I would like to know if that difference is statistically significant.

I have donde the following:

svy: regress hosp_exp i.is_hhmem_pmjay

Output:

. svy: regress hosp_exp i.is_hhmem_pmjay
(running regress on estimation sample)

Survey: Linear regression

Number of strata = 75 Number of obs = 1,382
Number of PSUs = 1,272 Population size = 1,521,963
Design df = 1,197
F( 1, 1197) = 2.56
Prob > F = 0.1100
R-squared = 0.0045

----------------------------------------------------------------------------------
| Linearized
hosp_exp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------+----------------------------------------------------------------
1.is_hhmem_pmjay | 8475.219 5299.549 1.60 0.110 -1922.22 18872.66
_cons | 26223.55 1539.171 17.04 0.000 23203.78 29243.32
----------------------------------------------------------------------------------
Note: Strata with single sampling unit centered at overall mean.


....and as the data is skewed, I have done this:

gen ln_hosp_exp = ln(hosp_exp) if hosp_exp>0

svy: regress ln_hosp_exp i.is_hhmem_pmjay



svy: regress ln_hosp_exp i.is_hhmem_pmjay
(running regress on estimation sample)

Survey: Linear regression

Number of strata = 75 Number of obs = 1,382
Number of PSUs = 1,272 Population size = 1,521,963
Design df = 1,197
F( 1, 1197) = 1.06
Prob > F = 0.3040
R-squared = 0.0011

----------------------------------------------------------------------------------
| Linearized
ln_hosp_exp | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-----------------+----------------------------------------------------------------
1.is_hhmem_pmjay | .108841 .1058323 1.03 0.304 -.0987965 .3164784
_cons | 9.256737 .0591909 156.39 0.000 9.140607 9.372866
----------------------------------------------------------------------------------
Note: Strata with single sampling unit centered at overall mean.


Is this correct ? how can I run a t-test on this survey data?

Thank you,

[Leonardo Guizzetti]

The classic t-test (-ttest-) does not support survey estimation (-svy:- prefix), however a t-test is a special case of a linear regression with a single binary predictor. The regression command you show is correct for the survey-adjusted analogue of a t-test. I make no judgements about whether log-transformation is correct, though it's common enough to do this for expenditure data.

[Carlo Lazzaro]

Silvana:
as an aside to Leonardo's helpful reply, I find weird that a simple OLS (that is, an OLS with one regressor only) (or a -ttest-) is enough.
R-sq is, as expected, really low and you cannot exclude that the difference between the two households is zero (95% CI of the predictor -.0987965 .3164784).

[Silvana Builes Gaitan]

Dear Leonardo and Carlo,
Thank you for your clear replies!