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


From   johnclin <johnclin@umich.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: Conceptual Question with Permutation Two-Sided vs One-Sided Test
Date   Mon, 14 Sep 2009 21:04:03 -0400

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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