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st: re: one-sided p-value using test x1=x2


From   Kit Baum <baum@bc.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: re: one-sided p-value using test x1=x2
Date   Wed, 30 Sep 2009 15:52:21 -0400

<>
Recognize that any F statistic with one numerator d.f. and K denominator d.f.s is the square of a t-statistic with K d.f., and has exactly the same p-values. So you can always turn an F test that involves one numerator d.f. (which may involve more than two coefficients, by the way) into a t-test.

When doing one-sided tests, the important thing is to recognize that if the point estimate is on the 'wrong' side, you can never reject. So if Ho: \beta_1 >= \beta_2 vs Ha: \beta_1 < \beta2, and your point estimate for \beta_1 is greater than your estimate for \beta_2, you can never reject the null. You need a \beta_1 that is sufficiently less than \beta_2 to do so. That said, if you're on the 'right' side, you can halve the reported p-value, as it is calculated for a two- tailed test.

sysuse auto,clear
reg price i.foreign#c.mpg
test 0b.foreign#c.mpg = 1.foreign#c.mpg

In this example the domestic coefficient (\beta_1) is less than the foreign coefficient (\beta_2), and on a one-tailed test we can reject at better than 99%.

Kit Baum   |   Boston College Economics & DIW Berlin   |   http://ideas.repec.org/e/pba1.html
An Introduction to Stata Programming | http://www.stata-press.com/books/isp.html
   An Introduction to Modern Econometrics Using Stata  |   http://www.stata-press.com/books/imeus.html

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