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Calculating p-value for 1-tailed test in a linear model

6 messages · Andrew Campomizzi, Rolf Turner, David Winsemius

Original
Rolf Turner
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On 20/08/11 10:20, Andrew Campomizzi wrote:
The r-help mailing list is *not* for giving assistance with homework.

     cheers,

         Rolf Turner
David Winsemius
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On Aug 19, 2011, at 6:20 PM, Andrew Campomizzi wrote:

            

      
      
      
    

        
You need to clearly state your hypothesis. Then using the output from  
the regression function should be straightforward.

(Yes. this is a intentionally vague answer designed to elicit further  
information about your understanding of the statistical issues and how  
they relate to your domain knowledge. Many time peole already have the  
data and because they didn't get the answer they wanted, they search  
for other ways to "game the system" by ad-hoc changes in the  
statistical "rules of the road".)

--

David Winsemius, MD
West Hartford, CT

  
  


  


      

    

    
1 day later

    

      
      

        


  

        

      Andrew Campomizzi
    

    

      
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David,
It's fair to question my intentions.  I'm running power analyses using
simulations (based on Bolker's Ecological Models and Data in R) and need to
provide decision-makers with options.  So, I'm attempting to make it clear
that if the research hypothesis (e.g., response variable declines with an
increase in predictor variable) can be clearly answered with a 1-tailed
test, then one might need a sample size of n to get a particular power,
given variance and alpha.
I think Mark's response answers my question.
Thanks,
Andy

-----Original Message-----
From: David Winsemius [mailto:dwinsemius at comcast.net] 
Sent: Saturday, August 20, 2011 6:02 PM
To: Andrew Campomizzi
Cc: r-help at r-project.org
Subject: Re: [R] Calculating p-value for 1-tailed test in a linear model

        
On Aug 19, 2011, at 6:20 PM, Andrew Campomizzi wrote:

        

            

      
      
      
    

        
You need to clearly state your hypothesis. Then using the output from  
the regression function should be straightforward.

(Yes. this is a intentionally vague answer designed to elicit further  
information about your understanding of the statistical issues and how  
they relate to your domain knowledge. Many time peole already have the  
data and because they didn't get the answer they wanted, they search  
for other ways to "game the system" by ad-hoc changes in the  
statistical "rules of the road".)

--

David Winsemius, MD
West Hartford, CT

  
  


  


      

    

    

      
      

        


  

        

      David Winsemius
    

    

      
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On Aug 22, 2011, at 9:44 AM, Andrew Campomizzi wrote:

        

            

      
      
      
    

        
So the possibility that the response variable will be increased by the  
predictor variable is known to be false? It would be unusual to have  
such prior knowledge but I suppose it is possible if the starting  
point is at the ceiling, but then typical regression methods may not  
be appropriate.

            

      
      
      
    

        
Mark's response was not copied to the list.

  
    

      
      
    

  


  


      

    

    

      
      

        


  

        

      Andrew Campomizzi
    

    

      
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It's not that it's known to be false, rather it's not of interest in this
case.  If animal density (response) decreases with increasing year
(predictor), then a change in land management practices might be needed.
Whereas, if animal density is increasing, then the status quo should
suffice.  Decision makers might decide they only need to know if density is
decreasing so that management actions can be taken to mitigate the problem.

Mark's message:
Hi: jake the value of beta_ j hat ( whatever the coefficient is from the
output ) along with the standard deviation of that coefficient , sigma_ j
hat.

Then, if you want to test the alternative that beta is greater than zero,
then calculate

t* = (beta _j - 0)/sigma_j

and 1-pt(t*, df) will give you the p-value.

the only slightly tricky part tricky part is getting sigma_j hat. If you
take the summary of the lm and call it summlm. then take diag(summlm$cov)
and then the sigma_ j hat that you want is depends on which coefficient you
want to test. if you want the third coefficient, then take the third one
etc.

       mark

p.s: you could also divide the two tailed pvalue that have by 2 and that
will give you the right answer also but it doesn't show the understanding.

-----Original Message-----
From: David Winsemius [mailto:dwinsemius at comcast.net] 
Sent: Monday, August 22, 2011 9:12 AM
To: Andrew Campomizzi
Cc: r-help at r-project.org
Subject: Re: [R] Calculating p-value for 1-tailed test in a linear model

        
On Aug 22, 2011, at 9:44 AM, Andrew Campomizzi wrote:

        

            

      
      
      
    

        
So the possibility that the response variable will be increased by the  
predictor variable is known to be false? It would be unusual to have  
such prior knowledge but I suppose it is possible if the starting  
point is at the ceiling, but then typical regression methods may not  
be appropriate.

            

      
      
      
    

        
Mark's response was not copied to the list.