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st: difference in means for conditional decile grouping


From   Michael Crain <michaelcrain@ymail.com>
To   statalist@hsphsun2.harvard.edu
Subject   st: difference in means for conditional decile grouping
Date   Fri, 15 Mar 2013 13:34:47 -0700 (PDT)

I am trying to test the difference in means (t-test) with a bit
of a complex design and cannot figure how to do this.

I have split my sample observations into two subsamples based on
two conditions, Condition A and Condition B. These are
independent samples (not paired). For each of the two subsamples,
I assign the observations to decile groups.  My code to create
the deciles is:

-xtile condAdecile = var1 if conditionvar > 0, nq(10)-   // create Condition A deciles
-xtile condBdecile = var1 if conditionvar <= 0, nq(10)-  // create Condition B deciles

After forming deciles, I can determine the mean decile returns in
each condition with -table-. Below is an example of the
conditional mean decile returns.


Decile     Condition A     Condition B
------     -----------     -----------
1             10              12      
2             13              17      
3             18              21      
4             24              30      
5             28              31      
6             30              34      
7             34              38      
8             39              45      
9             44              54      
10            49              60

What I want to do is test whether the difference between Deciles
1 and 10 (10-1) differs between the two conditions. Put
differently, 10-1 in Conditions A and B are 39 and 48,
respectively. I want to test whether these two values are
different.

The closest I could come to accomplishing this is keep only the
observations in deciles 1 and 10 (dropping observations in
deciles 2 through 9) and then creating a dummy variable for these
2 deciles. Then I run a standard t-test (independent samples) on
10-1 in each condition.

-bys conditionABdummy: ttest var1, by(decile10_1dummy)-

The output gives me the confidence interval of 10-1 in each
condition. I can observe the confidence intervals in both
conditions for any overlap. However, I want to do a formal t-test
between 10-1 in both conditions: H0: 48-38 = 0

Any advice? I am using Stata 12.
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