R help - Nov 1999 - Nested Designs

Dear R list,

What is the proper way to specify a nested model so that
the F values agree with the expected mean square errors?
Specifically, suppose I have a design where "Heads" are 
nested within "Machines".  I would like to model the 
following Y_ijk = Mu + Machine_i +Head_j(i) +Error_k(ij).  

Using the commands below, 
> summary(aov(Strain~Machine + Head%in%Machine ))
             Df Sum Sq Mean Sq F value  Pr(>F)  
Machine       4  45.07   11.27  1.0532 0.38762  
Machine:Head 15 282.87   18.86  1.7625 0.06252 .
Residuals    60 642.00   10.70    

the F value to test "Machine" uses the MS residual 
instead of MS Head(Machine).

When I use the following no F value is reported
> summary(aov(Strain~Machine + Head%in%Machine + Error(Machine)))
Error: Machine
        Df Sum Sq Mean Sq
Machine  4 45.075  11.269

Error: Within
             Df Sum Sq Mean Sq F value  Pr(>F)  
Machine:Head 15 282.88   18.86  1.7625 0.06252 .
Residuals    60 642.00   10.70  

Is the second approach the best I can do?

Thanks  ALAN 

___________________________________
Alan T. Arnholt
Office phone: (828) 262 - 2863
Office fax  : (828) 265 - 8617

-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !)  To: r-help-request at
stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._

"Alan T. Arnholt" <arnholt at math.appstate.edu> writes:
> > summary(aov(Strain~Machine + Head%in%Machine ))
>              Df Sum Sq Mean Sq F value  Pr(>F)  
> Machine       4  45.07   11.27  1.0532 0.38762  
> Machine:Head 15 282.87   18.86  1.7625 0.06252 .
> Residuals    60 642.00   10.70    
> 
> the F value to test "Machine" uses the MS residual 
> instead of MS Head(Machine).
> 
> When I use the following no F value is reported
> 
> > summary(aov(Strain~Machine + Head%in%Machine + Error(Machine)))
> 
> Error: Machine
>         Df Sum Sq Mean Sq
> Machine  4 45.075  11.269
> 
> Error: Within
>              Df Sum Sq Mean Sq F value  Pr(>F)  
> Machine:Head 15 282.88   18.86  1.7625 0.06252 .
> Residuals    60 642.00   10.70  
> 
> Is the second approach the best I can do?
Hmm. You're not giving us any data to try it on, but I think I'd have

aov(Strain~Machine + Error(Machine:Head))

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907
-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-.-
r-help mailing list -- Read http://www.ci.tuwien.ac.at/~hornik/R/R-FAQ.html
Send "info", "help", or "[un]subscribe"
(in the "body", not the subject !)  To: r-help-request at
stat.math.ethz.ch
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._