Re: [R] factorial anova

From: Petra Wallem <pwallem_at_bio.puc.cl>
Date: Wed 28 Dec 2005 - 04:55:44 EST

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...
Thanks again for your comments and suggestions, I learned some new 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 escribió:
> Petra,
>
> It looks as though the problem is with your data.
> Reading it into 'R' gives---
>
> dat<-read.table("clipboard",header=T,sep="")
> dat
> Bosque estado lux dosel
> 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--
>
> > dat.aov<-aov(dosel~estado*Bosque,data=dat)
> > 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--
>
> > with(dat,tapply(dosel,list(estado,Bosque),mean))
>
> deciduo siemprev
> activo 56.320 56.320
> pristino 90.848 96.256
>
> > with(dat,tapply(dosel,list(estado,Bosque),sd))
> 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--
>
> > fit.lm<-lm(dosel~estado*Bosque,data=dat)
> > 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
Centro de Estudios Avanzados en Ecología & Biodiversidad (CASEB) Departamento de Ecología
Facultad de Ciencias Biológicas
Pontificia Universidad Católica de Chile Av. Libertador Bernardo O'Higgins # 340 Casilla 114-D



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