# [R] Interpreting summary.lm for a 2 factor anova

Ashim Kapoor ashimkapoor at gmail.com
Fri Dec 2 15:16:51 CET 2016

```Dear Pikal,

All levels except the interactions are compared to the Intercept. I'm a
little confused as to what's going on in interaction terms eg. the cell
wool B : tension M. It's mean is :
28.78 and 28.78 - 44.56 = -15.78 != 21.111.

It's something like 44.56 (intercept) -16.333 (wool B) -.20.556 (tension
M)  + 21.111 (woolB:tensionM) = 28.782.

I don't know how to sum up the above line in terms of differences
succinctly.

Best Regards,
Ashim

On Fri, Dec 2, 2016 at 5:11 PM, PIKAL Petr <petr.pikal at precheza.cz> wrote:

> Hi
>
> You probably could get better answer from experts but it has something to
> do with contrasts.
>
> ?contrasts
>
> Number 44.556 is mean for wool A and tension L and this is the level to
> which every other level is compared.
>
> Cheers
> Petr
>
> > -----Original Message-----
> > From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Ashim
> > Kapoor
> > Sent: Thursday, December 1, 2016 2:48 PM
> > To: r-help at r-project.org
> > Subject: [R] Interpreting summary.lm for a 2 factor anova
> >
> > Dear all,
> >
> > Here is a small example : -
> >
> > > model <- aov(breaks ~ wool * tension, data = warpbreaks)
> > > summary.lm(model)
> >
> > Call:
> > aov(formula = breaks ~ wool * tension, data = warpbreaks)
> >
> > Residuals:
> >      Min       1Q   Median       3Q      Max
> > -19.5556  -6.8889  -0.6667   7.1944  25.4444
> >
> > Coefficients:
> >                Estimate Std. Error t value Pr(>|t|)
> > (Intercept)      44.556      3.647  12.218 2.43e-16 ***
> > woolB           -16.333      5.157  -3.167 0.002677 **
> > tensionM        -20.556      5.157  -3.986 0.000228 ***
> > tensionH        -20.000      5.157  -3.878 0.000320 ***
> > woolB:tensionM   21.111      7.294   2.895 0.005698 **
> > woolB:tensionH   10.556      7.294   1.447 0.154327
> > ---
> > Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> >
> > Residual standard error: 10.94 on 48 degrees of freedom
> > Multiple R-squared:  0.3778,    Adjusted R-squared:  0.3129
> > F-statistic: 5.828 on 5 and 48 DF,  p-value: 0.0002772
> >
> > > model.tables(model,"e")
> > Tables of effects
> >
> >  wool
> > wool
> >       A       B
> >  2.8889 -2.8889
> >
> >  tension
> > tension
> >      L      M      H
> >  8.241 -1.759 -6.481
> >
> >  wool:tension
> >     tension
> > wool L      M      H
> >    A  5.278 -5.278  0.000
> >    B -5.278  5.278  0.000
> >
> >
> > > model.tables(model,"m")
> > Tables of means
> > Grand mean
> >
> > 28.14815
> >
> >  wool
> > wool
> >      A      B
> > 31.037 25.259
> >
> >  tension
> > tension
> >     L     M     H
> > 36.39 26.39 21.67
> >
> >  wool:tension
> >     tension
> > wool L     M     H
> >    A 44.56 24.00 24.56
> >    B 28.22 28.78 18.78
> > >
> >
> > I don't follow the output of summary.lm. I understand the output of
> > model.tables for effects and means. For instance what does 44.556
> > represent ? Is it the grand average ? The grand mean is 28.14815. Can
> > someone help me understand the output of summary.lm ?
> >
> > Best Regards,
> > Ashim
> >
> >       [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
> ________________________________
> Tento e-mail a jakékoliv k němu připojené dokumenty jsou důvěrné a jsou
> Jestliže jste obdržel(a) tento e-mail omylem, informujte laskavě
> neprodleně jeho odesílatele. Obsah tohoto emailu i s přílohami a jeho kopie
> vymažte ze svého systému.
> Nejste-li zamýšleným adresátem tohoto emailu, nejste oprávněni tento email
> jakkoliv užívat, rozšiřovat, kopírovat či zveřejňovat.
> Odesílatel e-mailu neodpovídá za eventuální škodu způsobenou modifikacemi
> či zpožděním přenosu e-mailu.
>
> V případě, že je tento e-mail součástí obchodního jednání:
> - vyhrazuje si odesílatel právo ukončit kdykoliv jednání o uzavření
> smlouvy, a to z jakéhokoliv důvodu i bez uvedení důvodu.
> Odesílatel tohoto e-mailu (nabídky) vylučuje přijetí nabídky ze strany
> příjemce s dodatkem či odchylkou.
> - trvá odesílatel na tom, že příslušná smlouva je uzavřena teprve
> výslovným dosažením shody na všech jejích náležitostech.
> - odesílatel tohoto emailu informuje, že není oprávněn uzavírat za
> společnost žádné smlouvy s výjimkou případů, kdy k tomu byl písemně zmocněn
> nebo písemně pověřen a takové pověření nebo plná moc byly adresátovi tohoto
> existence je adresátovi či osobě jím zastoupené známá.
>
> This e-mail and any documents attached to it may be confidential and are
> intended only for its intended recipients.
> If you received this e-mail by mistake, please immediately inform its
> sender. Delete the contents of this e-mail with all attachments and its
> If you are not the intended recipient of this e-mail, you are not
> authorized to use, disseminate, copy or disclose this e-mail in any manner.
> The sender of this e-mail shall not be liable for any possible damage
> caused by modifications of the e-mail or by delay with transfer of the
> email.
>
> In case that this e-mail forms part of business dealings:
> - the sender reserves the right to end negotiations about entering into a
> contract in any time, for any reason, and without stating any reasoning.
> - if the e-mail contains an offer, the recipient is entitled to
> immediately accept such offer; The sender of this e-mail (offer) excludes
> any acceptance of the offer on the part of the recipient containing any
> amendment or variation.
> - the sender insists on that the respective contract is concluded only
> upon an express mutual agreement on all its aspects.
> - the sender of this e-mail informs that he/she is not authorized to enter
> into any contracts on behalf of the company except for cases in which
> he/she is expressly authorized to do so in writing, and such authorization
> or power of attorney is submitted to the recipient or the person
> represented by the recipient, or the existence of such authorization is
> known to the recipient of the person represented by the recipient.
>

[[alternative HTML version deleted]]

```