# [R] factorial anova

Petra Wallem pwallem at bio.puc.cl
Tue Dec 27 18:55:44 CET 2005

```Thanks a lot to all of your responses, I did follow your adivces, but
finnally to really get it understanded I acctually did the work to
calculate the anova step by step on an excel spread sheet to see if I
get the same SS and MS as is aov output, and yes, they are the same, so
John you are right the data is kind of freak... My only preliminary
survye was to make a boxplot of the interaction, where data is acctually
correlated, but I did not expect that this correlation would result in
identical sum of squares between tretment and interaction... kind of
odd...
functions I was not using...

Happy New 2006, for all of you, enjoy the party!!!
Cheers
Petra
El mar, 27-12-2005 a las 13:13, John Wilkinson escribiÃ³:
> Petra,
>
> It looks as though the problem is with your data.
> Reading it into 'R' gives---
>
> dat
> 1   deciduo pristino  703 88.56
> 2   deciduo pristino  800 90.64
> 3   deciduo pristino  150 95.84
> 4   deciduo pristino  245 87.52
> 5   deciduo pristino 1300 91.68
> 6   deciduo   activo 1900 26.16
> 7   deciduo   activo  840 59.44
> 8   deciduo   activo  323 69.84
> 9   deciduo   activo  112 75.04
> 10  deciduo   activo 1360 51.12
> 11 siemprev   activo  900 41.76
> 12 siemprev   activo  480 65.68
> 13 siemprev   activo  350 78.16
> 14 siemprev   activo  350 37.60
> 15 siemprev   activo  272 58.40
> 16 siemprev pristino  100 94.80
> 17 siemprev pristino   60 95.84
> 18 siemprev pristino   50 97.92
> 19 siemprev pristino  270 94.80
> 20 siemprev pristino  110 97.92
>
>  a straight analysis of variance (aov) model gives--
>
> > summary(dat.aov)
>               Df Sum Sq Mean Sq F value    Pr(>F)
> estado         1 6931.1  6931.1 41.6455 7.974e-06 ***
> Bosque         1   36.6    36.6  0.2197    0.6456
> estado:Bosque  1   36.6    36.6  0.2197    0.6456
> Residuals     16 2662.9   166.4
>
>
> showing that Bosque and its interaction with estado do indeed have
> the same 'sum of squares' of 36.6
>
> a preliminary exploration of the data's factors shows--
>
>
>          deciduo siemprev
> activo    56.320   56.320
> pristino  90.848   96.256
>
>            deciduo  siemprev
> activo   19.232972 16.817800
> pristino  3.239062  1.577238
>
>
> This shows that the levels  of the factors are highly corelated
>
> the linear model and its anova confirms this--
>
> > summary(fit.lm)
>
> Call:
> lm(formula = dosel ~ estado * Bosque, data = dat)
>
> Residuals:
>     Min      1Q  Median      3Q     Max
> -30.160  -2.548   0.312   3.588  21.840
>
> Coefficients:
>                                Estimate Std. Error  t value Pr(>|t|)
> (Intercept)                   5.632e+01  5.769e+00    9.762 3.84e-08 ***
> estadopristino                3.453e+01  8.159e+00    4.232 0.000635 ***
> Bosquesiemprev                1.249e-15  8.159e+00 1.53e-16 1.000000
> estadopristino:Bosquesiemprev 5.408e+00  1.154e+01    0.469 0.645622
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
>
> Residual standard error: 12.9 on 16 degrees of freedom
> Multiple R-Squared: 0.7245,     Adjusted R-squared: 0.6729
> F-statistic: 14.03 on 3 and 16 DF,  p-value: 9.615e-05
>
> > anova(fit.lm)
> Analysis of Variance Table
>
> Response: dosel
>               Df Sum Sq Mean Sq F value    Pr(>F)
> estado         1 6931.1  6931.1 41.6455 7.974e-06 ***
> Bosque         1   36.6    36.6  0.2197    0.6456
> estado:Bosque  1   36.6    36.6  0.2197    0.6456
> Residuals     16 2662.9   166.4
>
>
> the drop function shows that the model would improve by
> dropping the interaction term and so reducing the RSS
> (by 36.56, being the redundant interaction Sum of Sq)
> > drop1(fit.lm).The  AIC confirms  this (the lower the better).
> Single term deletions
>
> Model:
> dosel ~ estado * Bosque
>               Df Sum of Sq     RSS     AIC
> <none>                     2662.90  105.83
> estado:Bosque  1     36.56 2699.46  104.10
>
>
> The only sig effect of the model is thus between estado levels.
> pristino effect being *** sig greater than activo for both levels of
> Bosque ( as the tapply table above clearly shows)
>
> It pays to do a preliminary survry of the data.
>
> I hope that helps,
>
>
> John
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--
Petra Wallem