st: Re: one-tailed tests

[Christopher Baum <kit.baum@bc.edu>]

For a single hypothesis test, the test may be considered either a t with n-k d.f. or an F with (1, n-k) d.f. Mathematically, t^2 = F(1, n-k).

For one-sided hypothesis testing--say, your null is that \alpha <= 0 -- you can never reject if the estimated \alpha is zero or less. You can only reject that null in favor of the alternative that \alpha >-0 if the estimate is sufficiently positive.

The logic in the FAQ (which appears more complicated than it really need be) relates to the fact that you do not want to consider the two-tailed p-value, but rather one-helf the two-tailed p-value if you in the rejection region. I.e. if the computed t-value for large n was +1.96, Stata prints out a p-value of 0.05, but there is 97.5% of the mass of the distribution to the left of +1.96, so the p-value for your one-tailed test is 0.025.

That also follows if you use the Stata -test- command, which always returns an F-stat. For instance in the FAQ example

. test _b[weight]=1

you will note that at the end of the day, she ends up dividing the F-stat's reported p-value in half, as I suggest above.

Kit

On May 29, 2012, at 3:02 PM, Lorena Barberia wrote:

> Dear Kit,
> 
> I am writing with another question. I am reading your book, An Introduction to Modern Econometrics Using Stata.
> 
> I am trying to better understand one-sided hypothesis testing. On page 95, you state how to test a hypothesis Ho: Bj= theta where theta is any value. 
> Based on the analysis of the output, you explain we can read the output from the test to reject or not reject the null hypothesis. 
> 
> I am trying to reconcile this summary, however, with the note "The results from estimation commands display only two-sided tests for the coefficients" as I want to understand more fully how to test different hypotheses depending on whether the parameter estimates are negative or positive.  The note  was written by Kristin MacDonald, StataCorp. The page is available here:http://www.stata.com/support/faqs/stat/oneside.html.  She claims we have to calculate the  the square root of the F statistic (which is the absolute value of the t statistic for the one-sided test). 
> 
> I am not clear why her explanation is different from your explanation. Can you help clarify?
> 
> Thanks so much,
> 
> Lorena
> Prof. Lorena Barberia
> Departamento de Ciência Política
> Universidade de São Paulo
> 
> Tel: +55.11.3091-3754 
> E-mail:lorenabarberia@usp.br
> 
> 
> 
> 
> 



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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