One-tailed test

[Ashani Abayasekara]

Hi all,

I'm interested in testing whether there are statistically significant differences in reactions to unemployment rate changes (in terms of perceived job security) by mental health status. I estimated the regression below and then used 'lincom' to test for significant differences in coefficient magnitudes, where mh8_qn1=1 for those in poor mental health.

xtreg job_sec_sat mh8_qn1##(c.unemp_av6 i.sa4 i.year) if entry3==0, fe i(id) cluster(id)

lincom 0b.mh8_qn1#co.unemp_av6-1.mh8_qn1#c.unemp_av6

 ( 1)  0b.mh8_qn1#co.unemp_av6 - 1.mh8_qn1#c.unemp_av6 = 0

------------------------------------------------------------------------------
 job_sec_sat | Coefficient  Std. err.      t    P>|t|     [95% conf. interval]
-------------+----------------------------------------------------------------
         (1) |  -.0225103    .016949    -1.33   0.184    -.0557338    .0107132
------------------------------------------------------------------------------

I now want to perform a one-tailed test, to specifically test whether the negative effect of unemployment on job security is larger for those in better mental health (mh8_qn1=0). How would I test this?

Many thanks in advance.

[Maarten Buis]

First of, you don't need lincom: Remember that the coefficient of the reference category is by definition 0. You are using a somewhat unusual definition of the difference. Normally you would subtract the reference category from the other category, and you do it the other way around. But if you really want your definition, you just change your reference category with the ib# prefix, see help fvvarlist. After that the coefficient of the interaction term is the number you are looking for. (In your case now, it is negative the coefficient of the interaction term.)

After that you just look if the coefficient has the expected sign. If that is not the case than you don't reject your null hypothesis. If it is, you divide the reported p-value by 2, and compare that with your chosen level of significance.

[Ashani Abayasekara]

Hi Maarten, thank you very much for your explanation. I defined it this way since I wanted to see how much more negative the reaction of the the 1 category is relative to the 0 or reference category, but I get your point about the norm being the other way around.

So in this case, the one-tailed test would simply entail dividing 0.184 by 2, and concluding that the difference is significant only at the 10% level (i.e. p-value of 0.092)?

[Maarten Buis]

I defined it this way since I wanted to see how much more negative the reaction of the the 1 category is relative to the 0 or reference category, but I get your point about the norm being the other way around.

That is fine, just change the reference category so you get the comparison you want

So in this case, the one-tailed test would simply entail dividing 0.184 by 2, and concluding that the difference is significant only at the 10% level (i.e. p-value of 0.092)?

Yes

[Ashani Abayasekara]

Thank you!