[R] question about anova() output

[Peter Dalgaard BSA]

Robert Burrows <rbb at nebiometrics.com> writes:

> Hello,
> 
> I am getting output from anova() and summary(aov()) that depends on the
> order of the factors in the fitted model object, and this has me baffled. I
> see this dependency with the data.frame below but not with an example (table
> 6.4) from Montgomery's DOE book. This is with R 1.3.0 on Debian GNU-Linux.
> 
> Where have I gone wrong?

In assuming that the order should not matter. Anova() gives the
incremental SS, and in an non-orthogonal design the order *does*
matter. You might want to try 

drop1(lm(CH50mg~run+sample))

and also

anova(lm(CH50mg~run))
anova(lm(CH50mg~sample))

Also, if you remove one of the first four observations, you will get a
balanced design and the order-dependence should disappear.

> > centerpts
>     run sample CH50mg
> 1  day1 dev126   0.56
> 2  day1 dev126   0.70
> 3  day1 dev126   0.82
> 4  day1 dev126   0.72
> 5  day2 dev126   0.57
> 6  day2 dev126   0.60
> 7  day3 dev126   0.61
> 8  day3 dev126   0.64
> 9  day3 dev126   0.68
> 10 day3 dev126   0.68
> 11 day1 dev118   0.77
> 12 day1 dev118   0.80
> 13 day1 dev118   0.86
> 14 day2 dev118   0.71
> 15 day2 dev118   0.70
> 16 day3 dev118   0.77
> 17 day3 dev118   0.77
> 18 day3 dev118   0.77
> 19 day3 dev118   0.80
> 20 day1 rgf108   0.77
> 21 day1 rgf108   0.86
> 22 day1 rgf108   0.82
> 23 day2 rgf108   0.62
> 24 day2 rgf108   0.63
> 25 day3 rgf108   0.66
> 26 day3 rgf108   0.71
> 27 day3 rgf108   0.69
> 28 day3 rgf108   0.69
> >
> >
> > anova(lm(CH50mg~run+sample+run*sample,data=centerpts))
> Analysis of Variance Table
> 
> Response: CH50mg
>            Df   Sum Sq  Mean Sq F value    Pr(>F)
> run         2 0.064308 0.032154 12.5597 0.0003343
> sample      2 0.068649 0.034324 13.4075 0.0002337
> run:sample  4 0.010444 0.002611  1.0199 0.4221699
> Residuals  19 0.048642 0.002560
> >
> >
> > anova(lm(CH50mg~sample+run+run*sample,data=centerpts))
> Analysis of Variance Table
> 
> Response: CH50mg
>            Df   Sum Sq  Mean Sq F value    Pr(>F)
> sample      2 0.061927 0.030964 12.0948 0.0004093
> run         2 0.071029 0.035515 13.8725 0.0001931
> sample:run  4 0.010444 0.002611  1.0199 0.4221699
> Residuals  19 0.048642 0.002560

BTW: The interaction operator is ":" ~run*sample expands to 
~sample+run+run:sample

-- 
   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
_._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._._