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

[Peter Dalgaard]

"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