# AGIGNATURA: Experimental Designs
# Faculty: Statistical and Information Engineering
# National University of the Altiplano
library(knitr)
library(readxl)
## Warning: package 'readxl' was built under R version 4.0.2
DBCA <- read_excel("DBCA.xlsx")
DBCA
## # A tibble: 16 x 3
## y Bloque Tratamiento
## <dbl> <dbl> <dbl>
## 1 2.12 1 1
## 2 2.4 2 1
## 3 2.9 3 1
## 4 4 4 1
## 5 2.4 1 2
## 6 3.5 2 2
## 7 3.8 3 2
## 8 3.9 4 2
## 9 4.5 1 3
## 10 4.12 2 3
## 11 4.5 3 3
## 12 5 4 3
## 13 2.5 1 4
## 14 2.5 2 4
## 15 2.5 3 4
## 16 3.4 4 4
head(DBCA)
## # A tibble: 6 x 3
## y Bloque Tratamiento
## <dbl> <dbl> <dbl>
## 1 2.12 1 1
## 2 2.4 2 1
## 3 2.9 3 1
## 4 4 4 1
## 5 2.4 1 2
## 6 3.5 2 2
View(DBCA)
DBCA$Tratamiento = factor(DBCA$Tratamiento)
DBCA$Bloque = factor(DBCA$Bloque)
# We use the libraries
library(daewr)
## Warning: package 'daewr' was built under R version 4.0.5
## Registered S3 method overwritten by 'DoE.base':
## method from
## factorize.factor conf.design
library(AlgDesign)
## Warning: package 'AlgDesign' was built under R version 4.0.3
# It allows to know if the design can
BIBsize(t = 4 , k = 2)
## Posible BIB design with b= 6 and r= 3 lambda= 1
# We analyze block 1
mod1 <- aov(y ~ Tratamiento + Bloque, data = DBCA )
mod1
## Call:
## aov(formula = y ~ Tratamiento + Bloque, data = DBCA)
##
## Terms:
## Tratamiento Bloque Residuals
## Sum of Squares 8.1101 3.1901 1.2885
## Deg. of Freedom 3 3 9
##
## Residual standard error: 0.3783737
## Estimated effects may be unbalanced
summary(mod1)
## Df Sum Sq Mean Sq F value Pr(>F)
## Tratamiento 3 8.110 2.7034 18.883 0.000319 ***
## Bloque 3 3.190 1.0634 7.427 0.008309 **
## Residuals 9 1.288 0.1432
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# We analyze block 2
mod2 <- aov(y ~ Bloque + Tratamiento , data = DBCA )
mod2
## Call:
## aov(formula = y ~ Bloque + Tratamiento, data = DBCA)
##
## Terms:
## Bloque Tratamiento Residuals
## Sum of Squares 3.1901 8.1101 1.2885
## Deg. of Freedom 3 3 9
##
## Residual standard error: 0.3783737
## Estimated effects may be unbalanced
summary(mod2)
## Df Sum Sq Mean Sq F value Pr(>F)
## Bloque 3 3.190 1.0634 7.427 0.008309 **
## Tratamiento 3 8.110 2.7034 18.883 0.000319 ***
## Residuals 9 1.289 0.1432
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
# We analyze for all treatments
mod3 <- lm(y ~ Tratamiento + Bloque , data = DBCA )
mod3
##
## Call:
## lm(formula = y ~ Tratamiento + Bloque, data = DBCA)
##
## Coefficients:
## (Intercept) Tratamiento2 Tratamiento3 Tratamiento4 Bloque2
## 2.357 0.545 1.675 -0.130 0.250
## Bloque3 Bloque4
## 0.545 1.195
library(car)
## Warning: package 'car' was built under R version 4.0.5
## Loading required package: carData
car::Anova(mod3, type="III")
## Anova Table (Type III tests)
##
## Response: y
## Sum Sq Df F value Pr(>F)
## (Intercept) 12.7036 1 88.7326 5.871e-06 ***
## Tratamiento 8.1101 3 18.8827 0.0003188 ***
## Bloque 3.1901 3 7.4275 0.0083094 **
## Residuals 1.2885 9
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#Valuers of Just and real
fitted(mod3)
## 1 2 3 4 5 6 7 8 9 10 11
## 2.3575 2.6075 2.9025 3.5525 2.9025 3.1525 3.4475 4.0975 4.0325 4.2825 4.5775
## 12 13 14 15 16
## 5.2275 2.2275 2.4775 2.7725 3.4225
#Plot of Normality
qqPlot(mod3)
## [1] 5 9
mtext("By:Amarillas", side = 3, adj = 1, family = "mono")
bartlett.test(y~Tratamiento, data=DBCA)
##
## Bartlett test of homogeneity of variances
##
## data: y by Tratamiento
## Bartlett's K-squared = 2.1508, df = 3, p-value = 0.5417
#Plot-Box
boxplot(y~Tratamiento ,data=DBCA, col=c("orange","green","blue","red"), main="Diagrama de Cajas de los Tratamientos")
mtext("By:Amarillas", side = 3, adj = 1, family = "mono")
#Hypothesis de Independence
layout(matrix(c(1,2,3,4),1,1))
plot(mod3)
