##Diseño Cuadrado Latino ###factorial simple en bloques al azar (FSBA)

Un solo un factor Dos razones de bloqueo

lote <- c(rep("Lote1",1), rep("Lote2",1), rep("Lote3",1), rep("Lote4",1), rep("Lote5",1))

genotipo <- c(rep("genA",5), rep("genB",5), rep("genC",5), rep("genD",5), rep("genE",5))

prov <- c("A","E","C","B","D", "C","B","A","D","E", "B","C","D","E","A", "D","A","E","C","B", "E","D","B","A","C")

biom <- c(42,45,41,56,47, 47,54,46,52,49, 55,52,57,49,45, 51,44,47,50,54, 44,50,48,43,46)
 
data <- data.frame(genotipo, lote, prov, biom)
head (data)
##   genotipo  lote prov biom
## 1     genA Lote1    A   42
## 2     genA Lote2    E   45
## 3     genA Lote3    C   41
## 4     genA Lote4    B   56
## 5     genA Lote5    D   47
## 6     genB Lote1    C   47

###Graficos descriptivos

  library(lattice)

bwplot(biom ~ genotipo | prov + lote,
       data)

##Modelo

\[y= \mu + \tau_i + \beta_j + \delta_k + \epsilon_{ijk}\] \[i=1, \dots,p\] \[j=1, \dots,p\] \[k=1, \dots,p\]

tbl= matrix(data$prov, 5)
colnames(tbl) = unique(data$genotipo)
rownames(tbl) = unique(data$lote)
tbl
##       genA genB genC genD genE
## Lote1 "A"  "C"  "B"  "D"  "E" 
## Lote2 "E"  "B"  "C"  "A"  "D" 
## Lote3 "C"  "A"  "D"  "E"  "B" 
## Lote4 "B"  "D"  "E"  "C"  "A" 
## Lote5 "D"  "E"  "A"  "B"  "C"

\[H_0: \mu_ {B_{G_1}} = \mu_ {B_{G_2}} = \mu_ {B_{G_3}} = \mu_ {B_{G_4}} = \mu_ {B_{G_5}}\]

mod<- lm (biom ~ lote + genotipo + prov, data)
anova(mod)
## Analysis of Variance Table
## 
## Response: biom
##           Df Sum Sq Mean Sq F value   Pr(>F)    
## lote       4  17.76   4.440  0.7967 0.549839    
## genotipo   4 109.36  27.340  4.9055 0.014105 *  
## prov       4 286.16  71.540 12.8361 0.000271 ***
## Residuals 12  66.88   5.573                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
bwplot(biom ~ genotipo | prov, 
        data)

interaction.plot(genotipo, prov, biom, lwd=2)

library(ggplot2)
ggplot(data)+aes (x= prov, y= biom, fill=genotipo)+ geom_col( position = 'dodge')

#Revisión de supuesto

res_mod = mod$residuals

#1. Normalidad
shapiro.test(res_mod)
## 
##  Shapiro-Wilk normality test
## 
## data:  res_mod
## W = 0.97691, p-value = 0.8178
#Se cumple el supuesto de normalidad

#2.Igualdad de varianzas 
bartlett.test(res_mod, genotipo)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  res_mod and genotipo
## Bartlett's K-squared = 5.9223, df = 4, p-value = 0.205
#Se cumple el supuesto (Varianzas iguales)
#install.packages("TuckeyC)
library(TukeyC)

tt = TukeyC(mod, 'genotipo')
plot(tt)