Exercícios em aula
Alan Oliveira
Sexta Feira, 8 de maio de 2015
# Definindo o diretório de trabalho
setwd("C:/Users/aluno/Documents")
getwd()## [1] "C:/Users/aluno/Documents"# Pacotes que serão utilizados
library(agricolae)## Warning: package 'agricolae' was built under R version 3.1.3library(ggplot2)## Warning: package 'ggplot2' was built under R version 3.1.3library(asbio)## Warning: package 'asbio' was built under R version 3.1.3## Loading required package: tcltk# Teste Tukey de Aditividade
#Importando os dados
solucao<-read.table("solucao.txt",h=T)
# Verficando os dados
str(solucao)## 'data.frame': 12 obs. of 3 variables:
## $ sol: Factor w/ 3 levels "S1","S2","S3": 1 1 1 1 2 2 2 2 3 3 ...
## $ dia: Factor w/ 4 levels "D1","D2","D3",..: 1 2 3 4 1 2 3 4 1 2 ...
## $ y : int 13 22 18 39 16 24 17 44 5 4 ...summary(solucao)## sol dia y
## S1:4 D1:3 Min. : 1.00
## S2:4 D2:3 1st Qu.:11.00
## S3:4 D3:3 Median :17.50
## D4:3 Mean :18.75
## 3rd Qu.:22.50
## Max. :44.00#Análise Gráfica de dados
# Boxplot: yxsolucao
ggplot(solucao, aes(x= sol, y=y, fill=sol)) +geom_boxplot()
# Boxplot: yxdia
ggplot(solucao, aes(x=dia, y=y, fill=dia)) +geom_boxplot()
# Boxplot: yxsolucao
ggplot(solucao, aes(x=sol, y=y, fill=sol)) +geom_boxplot()
# Boxplot: yxdia
ggplot(solucao, aes(x=dia, y=y, fill=dia)) +geom_boxplot()
# Verificando interação entre Blocos e Níveis do Fato
(solucao)## sol dia y
## 1 S1 D1 13
## 2 S1 D2 22
## 3 S1 D3 18
## 4 S1 D4 39
## 5 S2 D1 16
## 6 S2 D2 24
## 7 S2 D3 17
## 8 S2 D4 44
## 9 S3 D1 5
## 10 S3 D2 4
## 11 S3 D3 1
## 12 S3 D4 22interaction.plot(solucao$dia, solucao$sol, solucao$y, fixed=TRUE)
# Teste de Aditividade de Tukey
# TEsta HO: Não há efeito interação
tukey.add.test(solucao$y, solucao$sol, solucao$dia)##
## Tukey's one df test for additivity
## F = 2.7732343 Denom df = 5 p-value = 0.1567331# Estimação do Modelo como se fosse ANAVA1
mdic<-aov(y~sol,data=solucao)
# Exibe a Tabela da ANAVA
summary(mdic)## Df Sum Sq Mean Sq F value Pr(>F)
## sol 2 703.5 351.8 2.732 0.118
## Residuals 9 1158.7 128.7#Estimação do Modelo com blocagem dos dias
mdbca<-aov(y ~ sol+dia, data=solucao)
summary(mdbca)## Df Sum Sq Mean Sq F value Pr(>F)
## sol 2 703.5 351.8 40.72 0.000323 ***
## dia 3 1106.9 369.0 42.71 0.000192 ***
## Residuals 6 51.8 8.6
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# cv do Pacote Agricolae
cv.model(mdbca)## [1] 15.67573# Análise Gráfica da Normalidade e Homogeneidade das variâncias
plot(mdbca, which=1) # Residuo dos xValores previstos
plot(mdbca, which=2) # grafico qqplot
#### Teste de Shapiro-Wil k s
shapiro.test(mdbca$residuals)##
## Shapiro-Wilk normality test
##
## data: mdbca$residuals
## W = 0.9321, p-value = 0.4027Teste de Bartlett
T e s t e de B a r t l e t t
bartlett.test(y~interaction(sol,dia),data=solucao)
Error inbartlett.test…deve haver ao menos duas observações em cada grupo
###Teste de Tukey Agricolae
HSD.test(mdbca,"sol", group=TRUE, console = TRUE)##
## Study: mdbca ~ "sol"
##
## HSD Test for y
##
## Mean Square Error: 8.638889
##
## sol, means
##
## y std r Min Max
## S1 23.00 11.284207 4 13 39
## S2 25.25 12.996794 4 16 44
## S3 8.00 9.486833 4 1 22
##
## alpha: 0.05 ; Df Error: 6
## Critical Value of Studentized Range: 4.339195
##
## Honestly Significant Difference: 6.376879
##
## Means with the same letter are not significantly different.
##
## Groups, Treatments and means
## a S2 25.25
## a S1 23
## b S3 8### Eficiência do DBCA x DIC
qmr.di=128.7
qmr.db=8.6
qmr.di/qmr.db## [1] 14.96512# Definindo Diretório de Trabalho
setwd("C:/Users/aluno/Documents")
# Pacotes que serão utilizados
library(agricolae)
library(ggplot2)
library(effects) # Gráfico de Efeitos## Warning: package 'effects' was built under R version 3.1.3library(car) # Teste## Warning: package 'car' was built under R version 3.1.3##
## Attaching package: 'car'
##
## The following object is masked from 'package:effects':
##
## Prestige# Importando Dados
bateria<-read.table("bateria.txt" , h =T)# Definindo Diretório de Trabalho
setwd("C:/Users/aluno/Documents")
# Pacotes que serão utilizados
library(agricolae)
library(ggplot2)
library(effects) # Gráfico de Efeitos
library(car) # Teste de Fligner???Killeen# V e r i f i c a n d o o s dad o s
str (bateria)## 'data.frame': 36 obs. of 3 variables:
## $ y : int 130 155 74 180 150 188 159 126 138 110 ...
## $ mat : int 1 1 1 1 2 2 2 2 3 3 ...
## $ temp: int 15 15 15 15 15 15 15 15 15 15 ...summary(bateria)## y mat temp
## Min. : 20.0 Min. :1 Min. : 15
## 1st Qu.: 70.0 1st Qu.:1 1st Qu.: 15
## Median :108.0 Median :2 Median : 70
## Mean :105.5 Mean :2 Mean : 70
## 3rd Qu.:141.8 3rd Qu.:3 3rd Qu.:125
## Max. :188.0 Max. :3 Max. :125# Convertendo Material e Temperatura em Fatores
bateria$mat<-as.factor(bateria$mat)
bateria$temp<-as.factor(bateria$temp)
str(bateria)## 'data.frame': 36 obs. of 3 variables:
## $ y : int 130 155 74 180 150 188 159 126 138 110 ...
## $ mat : Factor w/ 3 levels "1","2","3": 1 1 1 1 2 2 2 2 3 3 ...
## $ temp: Factor w/ 3 levels "15","70","125": 1 1 1 1 1 1 1 1 1 1 ...# Análise Gráfica dos Dados
interaction.plot(bateria$temp, bateria$mat, bateria$y, type="b" , pch=19, fixed=T, xlab="Temperatura_(F)", ylab="Vida_Média_(em_h)" )
# Estimação do Modelo: Forma 1
bateria.aov<-aov(y~mat+temp+mat:temp,data=bateria)
# Estimação do Modelo: : Forma 2
bateria.aov<-aov(y~mat*temp,data=bateria)
# Tabela da ANAVA
summary(bateria.aov)## Df Sum Sq Mean Sq F value Pr(>F)
## mat 2 10684 5342 7.911 0.00198 **
## temp 2 39119 19559 28.968 1.91e-07 ***
## mat:temp 4 9614 2403 3.560 0.01861 *
## Residuals 27 18231 675
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# Verufuca Normalidade e Variâncias Homogêneas
plot(bateria.aov, which=1) # Residuos x Valores previstos
plot(bateria.aov, which=2) #grafico qqnorm
#### Teste de Shapiro-Wilks: H0 : os dados tem dist. aprox. normal
shapiro.test(bateria.aov$residuals)##
## Shapiro-Wilk normality test
##
## data: bateria.aov$residuals
## W = 0.9761, p-value = 0.6117#### Teste de Fligner-Killeen : H0 : Variância dos resíduos
fligner.test(y~interaction(mat,temp), data=bateria)##
## Fligner-Killeen test of homogeneity of variances
##
## data: y by interaction(mat, temp)
## Fligner-Killeen:med chi-squared = 5.667, df = 8, p-value = 0.6845# Gráfico dos Efeitos R base
plot.design(y~mat*temp, data=bateria)
# Gráfico dos Efeitos Pacote effects
plot(allEffects(bateria.aov))
# Necessário para os testes com agricolae
inter <- with(bateria, interaction(mat, temp))
amod <- aov(y~inter, data=bateria)
HSD.test(amod, "inter", group=TRUE, console = TRUE)##
## Study: amod ~ "inter"
##
## HSD Test for y
##
## Mean Square Error: 675.213
##
## inter, means
##
## y std r Min Max
## 1.125 57.50 26.85144 4 20 82
## 1.15 134.75 45.35324 4 74 180
## 1.70 57.25 23.59908 4 34 80
## 2.125 49.50 19.26136 4 25 70
## 2.15 155.75 25.61738 4 126 188
## 2.70 119.75 12.65899 4 106 136
## 3.125 85.50 19.27866 4 60 104
## 3.15 144.00 25.97435 4 110 168
## 3.70 145.75 22.54440 4 120 174
##
## alpha: 0.05 ; Df Error: 27
## Critical Value of Studentized Range: 4.7584
##
## Honestly Significant Difference: 61.82318
##
## Means with the same letter are not significantly different.
##
## Groups, Treatments and means
## a 2.15 155.8
## ab 3.70 145.8
## ab 3.15 144
## ab 1.15 134.8
## ab 2.70 119.8
## bc 3.125 85.5
## c 1.125 57.5
## c 1.70 57.25
## c 2.125 49.5library(pwr)## Warning: package 'pwr' was built under R version 3.1.3pwr.anova.test(k=5, f=.25, sig.level=.05, power=.8)##
## Balanced one-way analysis of variance power calculation
##
## k = 5
## n = 39.1534
## f = 0.25
## sig.level = 0.05
## power = 0.8
##
## NOTE: n is number in each group