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

[Prof Brian Ripley]

On Sun, 7 Dec 2003, Alexander Sirotkin [at Yahoo] wrote:

> 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 ?

If that is your question *both* are incorrect.  The correct function to 
use is drop1() (or equivalently Anova from car with the right options).

For a detailed comparison of two t tests and the F test (for a term fitted
last) see Largey & Spencer (1996) _The Statistician_ 45, 105-9.

Once again, aov() and its methods are designed for classical AoV problems 
which are balanced and in which sequential anova (as implemented here, 
that is with a common denominator) is appropriate and interpreting 
coefficients (as in summary.lm) is not.


> --- 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
> >
> -----------------------------------------------------
> >
> 
> ______________________________________________
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> 
> 

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595