Poids de grains de colza

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Marie-Christine Sauvé
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1 Poids de grains de colza Présentation du problème : On souhaite étudier l effet des 2 facteurs rotation et fertilisation sur le poids des grains de colza. 1 Données observées > colza<-read.table('colza.txt',header=t) > names(colza) #nom des colonnes [1] "Fertilisation" "Rotation" "PdsGrains" > colza Fertilisation Rotation PdsGrains 1 1 A A A A A A A A A A B B B B B B B B B B C C C C C C C C C C A A A A A A A A A

2 40 2 A B B B B B B B B B B C C C C C C C C C C 25.8 > class(colza$rotation) #verifier les types des variables [1] "factor" > class(colza$pdsgrains) [1] "numeric" > class(colza$fertilisation) [1] "integer" > colza$fertilisa<-as.factor(colza$fertilisation) #changer le type de Fertilisation > class(colza$fertilisa) [1] "factor" > table(colza$rotation,colza$fertilisa) 1 2 A B C Description des données > summary(colza$pdsgrains) Min. 1st Qu. Median Mean 3rd Qu. Max > sd(colza$pdsgrains) [1] > # par rotation > by(colza$pdsgrains,colza$rotation,mean) colza$rotation: A [1] colza$rotation: B [1] colza$rotation: C [1]

3 > # par fertilisation > by(colza$pdsgrains,colza$fertilisa,mean) colza$fertilisa: 1 [1] colza$fertilisa: 2 [1] > # par traitement > colza$ferrot=paste(colza$fertilisa,colza$rotation,sep="") > by(colza$pdsgrains,colza$ferrot,mean) colza$ferrot: 1A [1] colza$ferrot: 1B [1] 24 colza$ferrot: 1C [1] colza$ferrot: 2A [1] colza$ferrot: 2B [1] colza$ferrot: 2C [1] > by(colza$pdsgrains,colza$ferrot,sd) colza$ferrot: 1A [1] colza$ferrot: 1B [1] colza$ferrot: 1C [1] colza$ferrot: 2A [1] colza$ferrot: 2B [1] colza$ferrot: 2C [1] > fertil<-rep(c(1,2),each=3) > rotat<-rep(c('a','b','c'),2) > NBy <- c(by(colza$pdsgrains,colza[,c(2,1)],length)) > MeanBy<- c(by(colza$pdsgrains,colza[,c(2,1)],mean)) > StdDevBy <- c(by(colza$pdsgrains,colza[,c(2,1)],sd)) > rbind(fertil,rotat,round(rbind(nby,meanby,stddevby),2)) [,1] [,2] [,3] [,4] [,5] [,6] fertil "1" "1" "1" "2" "2" "2" rotat "A" "B" "C" "A" "B" "C" NBy "10" "10" "10" "10" "10" "10" MeanBy "24.11" "24" "28.64" "15.81" "19.84" "31.75" StdDevBy "8.62" "7.37" "5.86" "7.44" "8.27" "7.25" 3

4 > boxplot( colza$pdsgrains ~ colza$fertilisa*colza$rotation,ylab="pdsgrains",xlab="traitement") PdsGrains A 2.A 1.B 2.B 1.C 2.C traitement > #graphe d'interaction > interaction.plot(colza$rotation,colza$fertilisa,colza$pdsgrains,fixed=true,col=2:3,leg.bty="o") 4

5 colza$fertilisa mean of colza$pdsgrains A B C colza$rotation 3 Modèle d analyse de la variance à 2 facteurs avec interaction > #si on pose un modele d'anova, vérifier que les variables explicatives sont bien > #consideres comme des facteurs par R!!! > class(colza$fertilisa) [1] "factor" > class(colza$rotation) [1] "factor" > moda2i<-lm(pdsgrains ~ Fertilisa * Rotation, + data=colza) > summary(moda2i) Call: lm(formula = PdsGrains ~ Fertilisa * Rotation, data = colza) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-14 *** Fertilisa * RotationB

6 RotationC Fertilisa2:RotationB Fertilisa2:RotationC * Residual standard error: on 54 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 5 and 54 DF, p-value: > #somme des carres > #definition du modele nul > mod0=lm(pdsgrains ~ 1,data=colza) > anova(mod0,moda2i) Model 1: PdsGrains ~ 1 Model 2: PdsGrains ~ Fertilisa * Rotation Res.Df RSS Df Sum of Sq F Pr(>F) *** SCM = SCR = SCT = > #analyse des effets > #type I > anova(moda2i) Response: PdsGrains Df Sum Sq Mean Sq F value Pr(>F) Fertilisa Rotation *** Fertilisa:Rotation Residuals > #type II > library(car) #package a charger > Anova(modA2I) Anova Table (Type II tests) Response: PdsGrains Sum Sq Df F value Pr(>F) Fertilisa Rotation *** Fertilisa:Rotation Residuals SCM = =

7 > par(mfrow=c(2,2)) > plot(moda2i) Residuals vs Fitted Normal Q Q Residuals Standardized residuals Fitted values Theoretical Quantiles Standardized residuals Scale Location Standardized residuals Constant Leverage: Residuals vs Factor Levels Fertilisa : 2 1 Fitted values Factor Level Combinations > #Comparaison des moyennes de Rotation > library(lsmeans) #package a charger > lsmeans(moda2i,pairwise~rotation,adjust="bonferroni") $`Rotation lsmeans` Rotation lsmean SE df lower.cl upper.cl A B C $`Rotation pairwise differences` estimate SE df t.ratio p.value A - B A - C B - C p values are adjusted using the bonferroni method for 3 tests 4 Modèle d analyse de la variance à 2 facteurs sans interaction > moda2si<-lm(pdsgrains ~ Fertilisa + Rotation, + data=colza) > summary(moda2si) Call: lm(formula = PdsGrains ~ Fertilisa + Rotation, data = colza) 7

8 Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-15 *** Fertilisa RotationB RotationC *** Residual standard error: on 56 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 3 and 56 DF, p-value: > #test global du modele > anova(mod0,moda2si) Model 1: PdsGrains ~ 1 Model 2: PdsGrains ~ Fertilisa + Rotation Res.Df RSS Df Sum of Sq F Pr(>F) *** > #type I > anova(moda2si) Response: PdsGrains Df Sum Sq Mean Sq F value Pr(>F) Fertilisa Rotation *** Residuals > #type II > Anova(modA2sI) Anova Table (Type II tests) Response: PdsGrains Sum Sq Df F value Pr(>F) Fertilisa Rotation *** Residuals SCM = = SCR = SCT =

9 > #moyennes ajustees > lsmeans(moda2si,pairwise~rotation,adjust="bonferroni") $`Rotation lsmeans` Rotation lsmean SE df lower.cl upper.cl A B C $`Rotation pairwise differences` estimate SE df t.ratio p.value A - B A - C B - C p values are adjusted using the bonferroni method for 3 tests > par(mfrow=c(2,2)) > plot(moda2si) Residuals Residuals vs Fitted Standardized residuals Normal Q Q Fitted values Theoretical Quantiles Standardized residuals Scale Location Standardized residuals Constant Leverage: Residuals vs Factor Levels Fertilisa : 2 1 Fitted values Factor Level Combinations 5 Modèles d analyse de la variance à 1 facteur > with(colza,boxplot( PdsGrains ~ Rotation)) 9

10 A B C > modar<-lm(pdsgrains ~ Rotation, + data=colza) > summary(modar) Call: lm(formula = PdsGrains ~ Rotation, data = colza) Residuals: Min 1Q Median 3Q Max Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) e-16 *** RotationB RotationC *** Residual standard error: on 57 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 2 and 57 DF, p-value: > anova(mod0,modar) Model 1: PdsGrains ~ 1 10

11 Model 2: PdsGrains ~ Rotation Res.Df RSS Df Sum of Sq F Pr(>F) *** > anova(modar) Response: PdsGrains Df Sum Sq Mean Sq F value Pr(>F) Rotation *** Residuals > with(colza,boxplot(pdsgrains ~ Fertilisa)) > modaf<-lm(pdsgrains ~ Fertilisa, + data=colza) > summary(modaf) Call: lm(formula = PdsGrains ~ Fertilisa, data = colza) Residuals: Min 1Q Median 3Q Max 11

12 Coefficients: Estimate Std. Error t value Pr(> t ) (Intercept) <2e-16 *** Fertilisa Residual standard error: on 58 degrees of freedom Multiple R-squared: , Adjusted R-squared: F-statistic: on 1 and 58 DF, p-value: > anova(mod0,modaf) Model 1: PdsGrains ~ 1 Model 2: PdsGrains ~ Fertilisa Res.Df RSS Df Sum of Sq F Pr(>F) > anova(modaf) Response: PdsGrains Df Sum Sq Mean Sq F value Pr(>F) Fertilisa Residuals

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