st: Conceptual Question with Permutation Two-Sided vs One-Sided Test

[johnclin <johnclin@umich.edu>]

My question is a conceptual question regarding how to interpret a two- 
sided permutation test under Stata 11.  [My question is framed around  
Example 1 of the permute command in the Stata Reference Manual for  
Stata 11 for those who has the documentation handy (page 1312).]

Under the permute command:
1.  If the test statistic is the sum of the observations of the  
treated group, and
2.  if all the values for both the treated and the untreated group are  
positive,

then there is no difference in the reported p-value between a one- 
sided test versus a two-sided test.

This seems strange!  After thinking about this puzzling result, I  
realized that this result is driven by the fact that the values of the  
sampling distribution are positive because the values for both the  
treated and the untreated groups are all positive.  And given how  
Stata defines the two-sided test for permute, there is no difference  
between the one-sided and the two-sided test in this case.

I can understand the mechanics of how Stata calculated the p-value for  
a one-sided and a two-sided test, but the definition of the two-sided  
test in this context seems counter-intuitive.  For example, a  
parametric equivalent situation is a two-sided Chi-square test because  
the Chi-square distribution only has positive values.  But in  
constructing the two-sided test for the Chi-square distribution, we  
don't ignore the left-tail of the two-sided test by defining the two- 
sided test with absolute values as we do in defining the two-sided  
test under the permutation test.

-- John Lin
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