Cuadrado Latino
library(agricolae)
str(design.lsd)
## function (trt, serie = 2, seed = 0, kinds = "Super-Duper", first = TRUE,
## randomization = TRUE)
trt<-c("A","B","C","D")
outdesign<-design.lsd(trt=trt,serie=2,seed=563)
print(outdesign$sketch)
## [,1] [,2] [,3] [,4]
## [1,] "A" "D" "C" "B"
## [2,] "D" "C" "B" "A"
## [3,] "C" "B" "A" "D"
## [4,] "B" "A" "D" "C"
names(outdesign$book)=c("COD","Marca","Prov","Tipo")
outdesign$book
## COD Marca Prov Tipo
## 1 101 1 1 A
## 2 102 1 2 D
## 3 103 1 3 C
## 4 104 1 4 B
## 5 201 2 1 D
## 6 202 2 2 C
## 7 203 2 3 B
## 8 204 2 4 A
## 9 301 3 1 C
## 10 302 3 2 B
## 11 303 3 3 A
## 12 304 3 4 D
## 13 401 4 1 B
## 14 402 4 2 A
## 15 403 4 3 D
## 16 404 4 4 C
i<-sample(1:16)
outdesign$book[i,]
## COD Marca Prov Tipo
## 7 203 2 3 B
## 9 301 3 1 C
## 3 103 1 3 C
## 10 302 3 2 B
## 13 401 4 1 B
## 8 204 2 4 A
## 14 402 4 2 A
## 15 403 4 3 D
## 12 304 3 4 D
## 16 404 4 4 C
## 6 202 2 2 C
## 1 101 1 1 A
## 5 201 2 1 D
## 2 102 1 2 D
## 11 303 3 3 A
## 4 104 1 4 B
Ejemplo 4.16
df<-read.csv("https://docs.google.com/spreadsheets/d/1BfrgTXlU0QvacIF5zxyxK0zuKUIjrjf4n3iEpQ686DY/export?format=csv")
df$Lote=factor(df$Lote)
df$Dia=factor(df$Dia)
df$Trat=factor(df$Trat)
df$Y=as.numeric(df$Y)
df
## Lote Dia Trat Y
## 1 1 1 A 8
## 2 2 1 C 11
## 3 3 1 B 4
## 4 4 1 D 6
## 5 5 1 E 4
## 6 1 2 B 7
## 7 2 2 E 2
## 8 3 2 A 9
## 9 4 2 C 8
## 10 5 2 D 2
## 11 1 3 D 1
## 12 2 3 A 7
## 13 3 3 C 10
## 14 4 3 E 6
## 15 5 3 B 3
## 16 1 4 C 7
## 17 2 4 D 3
## 18 3 4 E 1
## 19 4 4 B 6
## 20 5 4 A 8
## 21 1 5 E 3
## 22 2 5 B 8
## 23 3 5 D 5
## 24 4 5 A 10
## 25 5 5 C 8
modelo<-lm(Y~Lote+Dia+Trat,data=df)
anova=aov(modelo)
summary(anova)
## Df Sum Sq Mean Sq F value Pr(>F)
## Lote 4 15.44 3.86 1.235 0.347618
## Dia 4 12.24 3.06 0.979 0.455014
## Trat 4 141.44 35.36 11.309 0.000488 ***
## Residuals 12 37.52 3.13
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Prueba de Normalidad de los Residuales
qqnorm(anova$residuals)
qqline(anova$residuals)
shapiro.test(anova$residuals)
##
## Shapiro-Wilk normality test
##
## data: anova$residuals
## W = 0.96606, p-value = 0.5476
library(car)
## Loading required package: carData
leveneTest(df$Y~df$Trat)
## Levene's Test for Homogeneity of Variance (center = median)
## Df F value Pr(>F)
## group 4 0.4444 0.7751
## 20
boxplot(Y~Trat,data=df)
LSD<-LSD.test(anova,"Trat",group=T,console=T)
##
## Study: anova ~ "Trat"
##
## LSD t Test for Y
##
## Mean Square Error: 3.126667
##
## Trat, means and individual ( 95 %) CI
##
## Y std r LCL UCL Min Max
## A 8.4 1.140175 5 6.677038 10.122962 7 10
## B 5.6 2.073644 5 3.877038 7.322962 3 8
## C 8.8 1.643168 5 7.077038 10.522962 7 11
## D 3.4 2.073644 5 1.677038 5.122962 1 6
## E 3.2 1.923538 5 1.477038 4.922962 1 6
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of t: 2.178813
##
## least Significant Difference: 2.436636
##
## Treatments with the same letter are not significantly different.
##
## Y groups
## C 8.8 a
## A 8.4 a
## B 5.6 b
## D 3.4 b
## E 3.2 b
bar.group(x=LSD$groups,horiz=T,col="red",xlim=c(0,12),
xlab="Catalizador",ylab="Método",main="Prueba de Catalizadores")
plot(anova$residuals)
plot(df$Trat,anova$residuals)
Cuadrado Grecolatino
str(design.graeco)
## function (trt1, trt2, serie = 2, seed = 0, kinds = "Super-Duper", randomization = TRUE)
trt1=1:4
trt2=1:4
outdesign=design.graeco(trt1,trt2,seed=543,serie=2)
print(outdesign$sketch)
## [,1] [,2] [,3] [,4]
## [1,] "4 2" "2 4" "1 3" "3 1"
## [2,] "2 3" "4 1" "3 2" "1 4"
## [3,] "1 1" "3 3" "4 4" "2 2"
## [4,] "3 4" "1 2" "2 1" "4 3"
book=outdesign$book
book
## plots row col trt1 trt2
## 1 101 1 1 4 2
## 2 102 1 2 2 4
## 3 103 1 3 1 3
## 4 104 1 4 3 1
## 5 201 2 1 2 3
## 6 202 2 2 4 1
## 7 203 2 3 3 2
## 8 204 2 4 1 4
## 9 301 3 1 1 1
## 10 302 3 2 3 3
## 11 303 3 3 4 4
## 12 304 3 4 2 2
## 13 401 4 1 3 4
## 14 402 4 2 1 2
## 15 403 4 3 2 1
## 16 404 4 4 4 3
t1<-c("$\\alpha$","$\\beta$","$\\gamma$","$\\delta$")
t2<-LETTERS[1:4]
i=outdesign$book$trt1
j=outdesign$book$trt2
book$trt1=sapply(i,function(i) t1[i])
book$trt2=sapply(j,function(j) t2[j])
knitr::kable(book, align = "lccc",caption = "Diseño de Cuadrado Latino")
Diseño de Cuadrado Latino
| 101 |
1 |
1 |
\(\delta\) |
B |
| 102 |
1 |
2 |
\(\beta\) |
D |
| 103 |
1 |
3 |
\(\alpha\) |
C |
| 104 |
1 |
4 |
\(\gamma\) |
A |
| 201 |
2 |
1 |
\(\beta\) |
C |
| 202 |
2 |
2 |
\(\delta\) |
A |
| 203 |
2 |
3 |
\(\gamma\) |
B |
| 204 |
2 |
4 |
\(\alpha\) |
D |
| 301 |
3 |
1 |
\(\alpha\) |
A |
| 302 |
3 |
2 |
\(\gamma\) |
C |
| 303 |
3 |
3 |
\(\delta\) |
D |
| 304 |
3 |
4 |
\(\beta\) |
B |
| 401 |
4 |
1 |
\(\gamma\) |
D |
| 402 |
4 |
2 |
\(\alpha\) |
B |
| 403 |
4 |
3 |
\(\beta\) |
A |
| 404 |
4 |
4 |
\(\delta\) |
C |