[R] Difference between summary.lm() and summary.aov()

[Alexander Sirotkin [at Yahoo]]

Thanks a lot to everybody. Two more questions, if you
don't mind :

How anova() treats non-categorical variables, such as
severity in my case ? I was under impression that
ANOVA is defined for categorical variables only.

I read about drop1() and I understand that it performs
F-test for nested models, correct me if I'm wrong. It
is unclear to me, however, how it manages to do this
F-test for interactions ?

Thanks a lot.

--- Peter Dalgaard <p.dalgaard at biostat.ku.dk> wrote:
> "Alexander Sirotkin [at Yahoo]"
> <alex_s_42 at yahoo.com> writes:
> 
> > John,
> > 
> > What you are saying is that any conclusion I can
> make
> > from summary.aov (for instance, to answer a
> question
> > if physician is a significant variable) will not
> be
> > correct ?
> 
> Summary.aov is for summarizing aov objects, so
> you're lucky to get
> something that is sensible at all. You should use
> anova() to get
> analysis of variance tables. These are sequential so
> that you can use
> them (give or take some quibbles about the residual
> variance) for
> reducing the model from the "bottom up". I.e. if you
> place "physician"
> last, you get the F test for whether that variable
> is significant.
> However, a more convenient way of getting that
> result is to use
> drop1(). Even then there's no simple relation to the
> two
> t-tests, except that the F test tests the hypothesis
> that *both*
> coefficients are zero, where the t-tests do so
> individually. 
>  
> 
> > --- John Fox <jfox at mcmaster.ca> wrote:
> > > Dear Spencer and Alexander,
> > > 
> > > In this case, physician is apparently a factor
> with
> > > three levels, so 
> > > summary.aov() gives you a sequential ANOVA,
> > > equivalent to what you'd get 
> > > from anova(). There no simple relationship
> between
> > > the F-statistic for 
> > > physician, which has 2 df in the numerator, and
> the
> > > two t's. (By the way, I 
> > > doubt whether a sequential ANOVA is what's
> wanted
> > > here.)
> > > 
> > > Regards,
> > >   John
> > > 
> > > At 09:17 AM 12/6/2003 -0800, Spencer Graves
> wrote:
> > > >      The square of a Student's t with "df"
> degrees
> > > of freedom is an F 
> > > > distribution with 1 and "df" degrees of
> freedom.
> > > >      hope this helps.  spencer graves
> > > >
> > > >Alexander Sirotkin [at Yahoo] wrote:
> > > >
> > > >>I have a simple linear model (fitted with
> lm())
> > > with 2
> > > >>independant
> > > >>variables : one categorical and one integer.
> > > >>
> > > >>When I run summary.lm() on this model, I get a
> > > >>standard linear
> > > >>regression summary (in which one categorical
> > > variable
> > > >>has to be
> > > >>converted into many indicator variables) which
> > > looks
> > > >>like :
> > > >>
> > > >>            Estimate Std. Error t value
> Pr(>|t|)
> > > >>(Intercept)  -3595.3     2767.1  -1.299  
> 0.2005
> > > >>physicianB     802.0     2289.5   0.350  
> 0.7277
> > > >>physicianC    4906.8     2419.8   2.028  
> 0.0485 *
> > > >>severity      7554.4      906.3   8.336
> 1.12e-10
> > > ***
> > > >>
> > > >>and when I run summary.aov() I get similar
> ANOVA
> > > table
> > > >>:
> > > >>           Df     Sum Sq    Mean Sq F value   
> > > Pr(>F)
> > > >>physician    2  294559803  147279901  3.3557  
> > > 0.04381
> > > >>*
> > > >>severity     1 3049694210 3049694210 69.4864
> > > 1.124e-10
> > > >>***
> > > >>Residuals   45 1975007569   43889057
> > > >>
> > > >>What is absolutely unclear to me is how
> F-value
> > > and
> > > >>Pr(>F) for the
> > > >>categorical "physician" variable of the
> > > summary.aov()
> > > >>is calculated
> > > >>from the t-value of the summary.lm() table.
> > > >>
> > > >>I looked at the summary.aov() source code but
> > > still
> > > >>could not figure
> > > >>it.
> > > >>
> > > >>Thanks a lot.
> > > >>
> > > >>__________________________________
> > > >>
> > 
> > > >>
> > > >>______________________________________________
> > > >>R-help at stat.math.ethz.ch mailing list
> > >
> >
>
>>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> > > >>
> > > >
> > > >______________________________________________
> > > >R-help at stat.math.ethz.ch mailing list
> > >
> >
>
>https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> > > 
> > >
> >
>
-----------------------------------------------------
> > > John Fox
> > > Department of Sociology
> > > McMaster University
> > > Hamilton, Ontario, Canada L8S 4M4
> > > email: jfox at mcmaster.ca
> > > phone: 905-525-9140x23604
> > > web: www.socsci.mcmaster.ca/jfox
> > >
> >
>
-----------------------------------------------------
> > >
> > 
> > ______________________________________________
> > R-help at stat.math.ethz.ch mailing list
> >
>
https://www.stat.math.ethz.ch/mailman/listinfo/r-help
> > 
> 
> -- 
>    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