Yes, the effect size is ultimately more important.  But one needs
to be somewhat sure that the effect is real, and that it is estimated
appropriately.  p-values can contribute to a story that gives some 
smaller or larger confidence that claimed effects are real.  They 
are just one of several routes that contribute to this end. Opinions 
differ on whether, in any particular circumstance,  they are the 
best route.

The discussion that prompted these various comments related to 
a different use of p-values (and p-value 'alternatives'), one that is 
even more controversial.  It related to the use of p-values in 
excluding or including model explanatory terms.  Here, there are 
several related issues:

1) Inference for model parameters should take account of the
process that has generated the model that is under consideration.  
This includes any omission of terms that are judged of no statistical 
consequence.  The standard interpretations of p-values apply, 
strictly, only if there has been no  elimination/selection of variables.

2) In models that have certain types of imbalance, parameter
estimates can change markedly (even to changing sign), depending
on what other terms are in the model.  

3) Point 2 argues for choosing the model that is on scientific grounds 
most reasonable, and sticking with it.  If model parameters are
important to the subsequent discussion, be sure that their estimates
condition on the 'correct' other set of model variables, i.e., that the
other variables that are in the model are the ones that are required
to allow this interpretation.

4) One may however allow fine tuning that simplifies the model, while 
changing nothing of consequence (and it really is necessary to check 
that there are no changes of consequence).  p-values may have a
limited use in such fine tuning, but for that purpose the p=0.05 cutoff is 
not appropriate.

John Maindonald             email: john.maindonald@anu.edu.au
phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
Centre for Mathematics & Its Applications, Room 1194,
John Dedman Mathematical Sciences Building (Building 27)
Australian National University, Canberra ACT 0200.
http://www.maths.anu.edu.au/~johnm

On 29/03/2011, at 10:35 PM, Manuel Spínola wrote:

> I am not a statistician, but what the p-value is telling me?
> 
> Is not more important the effect size?
> 
> Best,
> 
> Manuel
> 
> On 28/03/2011 04:40 p.m., Ben Bolker wrote:
>> 
>> On 03/28/2011 06:15 PM, John Maindonald wrote:
>> 
>>> Elimination of a term with a p-value greater than say 0.15 or 0.2 is
>>> however likely to make little differences to estimates of other terms
>>> in the model.  Thus, it may be a reasonable way to proceed.  For
>>> this purpose, an anti-conservative (smaller than it should be)  
>>> p-value will usually serve the purpose.
>>   Note that naive likelihood ratio tests of random effects are likely to
>> be conservative (in the simplest case, true p-values are twice the
>> nominal value) because of boundary issues and those of fixed effects are
>> probably anticonservative because of finite-size effects (see PB 2000
>> for examples of both cases.)
>> 
>>> John Maindonald             email: john.maindonald@anu.edu.au
>>> phone : +61 2 (6125)3473    fax  : +61 2(6125)5549
>>> Centre for Mathematics & Its Applications, Room 1194,
>>> John Dedman Mathematical Sciences Building (Building 27)
>>> Australian National University, Canberra ACT 0200.
>>> http://www.maths.anu.edu.au/~johnm
>>> 
>>   Ben
>> 
>> _______________________________________________
>> R-sig-mixed-models@r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>> 
>> 
> 
> 
> -- 
> Manuel Spínola, Ph.D. 
> Instituto Internacional en Conservación y Manejo de Vida Silvestre 
> Universidad Nacional 
> Apartado 1350-3000 
> Heredia 
> COSTA RICA 
> mspinola@una.ac.cr 
> mspinola10@gmail.com 
> Teléfono: (506) 2277-3598 
> Fax: (506) 2237-7036 
> Personal website: Lobito de río 
> Institutional website: ICOMVIS


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