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

PIKAL Petr petr.pikal at precheza.cz
Fri Dec 2 12:41:13 CET 2016

```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.

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