# st: RE: Question on "ttest" command

 From "reardon, sean f." To Subject st: RE: Question on "ttest" command Date Mon, 10 Oct 2005 21:25:52 -0700

```the standard error of a sum (or difference) is the square root of the
sum of the squared standard errors;

so se[(B-A)-(Y-X)] = sqrt[se(B-A)^2+ se(Y-X)^2] = sqrt[.0324503^2 +
.0084813^2]

=.0335

you could make an interaction variable of your 2 dummy variables and use
-regress-  the coefficient and se on the interaction term will be what
you want (if you make the interaction term correctly).

hope this helps.
sean.

_____________________________

sean f. reardon
associate professor of education and (by courtesy) sociology
school of education
485 lasuen mall, #315
stanford university
stanford, ca 94305-3096
650.736.8517 (office phone)
650.725.7412 (office fax)
sean.reardon@stanford.edu
_____________________________

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu
[mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of kannika
damrongplasit
Sent: Monday, October 10, 2005 7:15 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: Question on "ttest" command

To Stata Users,

I am writing to ask about how to compute standard error associated with
the differential change for treatment effect evaluation.

Here is the concept.

Group                 Before the policy            After the policy
Change          Differential Change

Treatment                     A                                    B
B-A               (B-A)-(Y-X)

Control                          X                                    Y
Y-X

where A, B, X, and Y are the average value (i.e. mean) of each group.
My goal is to evaluate the impact of the policy by computing the
differential change (B-A)-(Y-X).  In addition to finding the mean of
each cell, I also need to find the associated standard error for each of
them.

I use the command "ttest" to compute all the numerical value for the
column entitled "Change".  The command ttest and the results are shown
below for both treatment and control groups.

ttest smoke if nt==1, by(before)      --> treatment group

Two-sample t test with equal variances

------------------------------------------------------------------------
------
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf.
Interval]
---------+--------------------------------------------------------------
------
0 |    1332    .2845345    .0123672    .4513619    .2602731
.3087959
1 |     222    .2342342     .028489    .4244764    .1780894
.2903791
---------+--------------------------------------------------------------
------
combined |    1554    .2773488    .0113604    .4478342    .2550655
.299632
---------+--------------------------------------------------------------
------
diff |            .0503003    .0324503               -.0133507
.1139513
------------------------------------------------------------------------
------
Degrees of freedom: 1552

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

Ha: diff < 0               Ha: diff != 0              Ha: diff > 0
t =   1.5501                t =   1.5501              t =
1.5501
P < t =   0.9393          P > |t| =   0.1213          P > t =
0.0607

ttest smoke if decrim==0, by(before)  --> control group

Two-sample t test with equal variances

------------------------------------------------------------------------
------
Group |     Obs        Mean    Std. Err.   Std. Dev.   [95% Conf.
Interval]
---------+--------------------------------------------------------------
------
0 |   16152    .1618995    .0028985      .36837    .1562181
.1675808
1 |    2108     .142315    .0076113    .3494558    .1273886
.1572414
---------+--------------------------------------------------------------
------
combined |   18260    .1596386    .0027106    .3662805    .1543255
.1649516
---------+--------------------------------------------------------------
------
diff |            .0195845    .0084813                .0029602
.0362087
------------------------------------------------------------------------
------
Degrees of freedom: 18258

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

Ha: diff < 0               Ha: diff != 0              Ha: diff > 0
t =   2.3091                t =   2.3091              t =
2.3091
P < t =   0.9895          P > |t| =   0.0209          P > t =
0.0105

What I want to do next is to compute the "Differential Change" and its
associated standard error.  The average differential change is easy to
compute.  I just uses the information provided in the "Diff" rows.

The average differential change is (.0503003 - .0195845) = 0.0307158

MY QUESTION: HOW CAN I CALCULATE THE ASSOCIATED STANDARD ERROR FOR THIS
DIFFERENTIAL CHANGE (i.e. standard error of (B-A)-(Y-X)?  In other
words, I would like to find out whether 0.0307158 is significantly
different from zero.  Please let me know which command in STATA can be
used here.  Can I use the "ttest" command?  If so, how? Is there user
written command for it?

Best regards,

Kannika

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```