##Diseño desbalanciado (FS-BG-CA)

\[Y_{ijk} = \mu + \tau_i + \beta_{j} + \tau\beta_{ij} + \epsilon_{ijk} \\ i = 1,2, \dots, a \\ j = 1,2, \dots, b \\ k = 1,2, \dots, r_1 \] \(a\) número de niveles del facto \(b\) número de bloques \(r_1\) repetición de cada tratamiento

set.seed(123)

aceite = c(
  rnorm(12, 10, 0.8),
  rnorm(12, 11, 0.78),
  rnorm(11, 9, 0.70), 
  
  rnorm(12, 10, 0.8),
  rnorm(12, 11, 0.78),
  rnorm(11, 9, 0.70)
           )

bloque= gl (2,35, 70, c('b1', 'b2'))
metodo = rep(rep(c('t1', 't2', 't3'), 
             c(12,12,11)), 2)
datos= data.frame(metodo, bloque, aceite)
head(datos)
##   metodo bloque    aceite
## 1     t1     b1  9.551619
## 2     t1     b1  9.815858
## 3     t1     b1 11.246967
## 4     t1     b1 10.056407
## 5     t1     b1 10.103430
## 6     t1     b1 11.372052

Corriendo como si fuera balanceado

mod1=aov(aceite~bloque*metodo,datos)
summary(mod1)
##               Df Sum Sq Mean Sq F value   Pr(>F)    
## bloque         1   0.05   0.054   0.107    0.745    
## metodo         2  41.24  20.622  40.834 3.72e-12 ***
## bloque:metodo  2   0.65   0.323   0.640    0.531    
## Residuals     64  32.32   0.505                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Corriendo desbalanceado

mod2 = anova(lm(aceite ~ bloque * metodo, datos))
mod2
## Analysis of Variance Table
## 
## Response: aceite
##               Df Sum Sq Mean Sq F value    Pr(>F)    
## bloque         1  0.054  0.0541  0.1071    0.7446    
## metodo         2 41.243 20.6217 40.8342 3.716e-12 ***
## bloque:metodo  2  0.646  0.3231  0.6399    0.5307    
## Residuals     64 32.321  0.5050                      
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
lote <- c(rep("lote1", 1),
          rep("lote2", 1),
          rep("lote3", 1),
          rep("lote4", 1),
          rep("lote5", 1))
genot <- c(rep("genotA", 5),
          rep("genotB", 5),
          rep("genotC", 5),
          rep("genotD", 5),
          rep("genotE", 5))
proc_sem <- 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") 
biomasa <- 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)

mydata = data.frame(lote, genot, proc_sem, biomasa)
mydata
##     lote  genot proc_sem biomasa
## 1  lote1 genotA        A      42
## 2  lote2 genotA        E      45
## 3  lote3 genotA        C      41
## 4  lote4 genotA        B      56
## 5  lote5 genotA        D      47
## 6  lote1 genotB        C      47
## 7  lote2 genotB        B      54
## 8  lote3 genotB        A      46
## 9  lote4 genotB        D      52
## 10 lote5 genotB        E      49
## 11 lote1 genotC        B      55
## 12 lote2 genotC        C      52
## 13 lote3 genotC        D      57
## 14 lote4 genotC        E      49
## 15 lote5 genotC        A      45
## 16 lote1 genotD        D      51
## 17 lote2 genotD        A      44
## 18 lote3 genotD        E      47
## 19 lote4 genotD        C      50
## 20 lote5 genotD        B      54
## 21 lote1 genotE        E      44
## 22 lote2 genotE        D      50
## 23 lote3 genotE        B      48
## 24 lote4 genotE        A      43
## 25 lote5 genotE        C      46
library(collapsibleTree)
collapsibleTree(mydata, c('lote', 'proc_sem', 'genot'),
                collapsed = FALSE)
library(ggplot2)
ggplot(mydata)+
  aes(biomasa, genot)+
  geom_point(size=5, shape= 15)+
  facet_grid(lote ~ proc_sem)

ggplot(mydata)+
  aes(lote, genot, fill=biomasa)+
  geom_tile()+
  facet_wrap( ~ proc_sem, nrow=1)+
  theme(axis.text.x = element_text(angle = 90) )