DE

set.seed(123)
# Variable respuesta: CONDUCTANCIA ESTOMÁTICA
ce = c(
  rnorm(n = 15, mean = 100, sd = 10),
  rnorm(n = 15, mean = 120, sd = 12)
)
# Factor 1: HORA DE EVALUACIÓN
hora = gl(2, 15, 30, labels = c(6, 12))
# Factor 2: ILUMNACIÓN
ilum = gl(3, 5, 30, c('IB','IM','IA'))
# Bloqueo: PARCELA
parc = gl(5, 1, 30, paste0('B', 1:5))

datos = data.frame(hora, ilum, parc, ce)
head(datos)

##   hora ilum parc        ce
## 1    6   IB   B1  94.39524
## 2    6   IB   B2  97.69823
## 3    6   IB   B3 115.58708
## 4    6   IB   B4 100.70508
## 5    6   IB   B5 101.29288
## 6    6   IM   B1 117.15065

Análisis descriptivo.

library(ggplot2)

## Warning: package 'ggplot2' was built under R version 4.2.3

ggplot(datos)+
  aes(y=ce)+
  geom_boxplot()

ggplot(datos)+
  aes(hora, ce)+
  geom_boxplot()

ggplot(datos)+
  aes(ilum, ce)+
  geom_boxplot()

ggplot(datos)+
  aes(parc, ce)+
  geom_boxplot()

ggplot(datos)+
  aes(ilum, ce, fill=hora)+
  geom_boxplot()

ggplot(datos)+
  aes(parc, ce, fill=hora)+
  geom_col(position = 'dodge')+
  facet_wrap(~ilum)

Modelo

\[y_{ijk} = \mu + \tau_i + \beta_j + (\tau\beta)_{ij}+\delta_k + \epsilon_{ijk}\]

# Analisis de Varianza
mod1 = aov(ce ~ parc + hora + ilum + hora:ilum,
           datos)
summary(mod1)

##             Df Sum Sq Mean Sq F value  Pr(>F)   
## parc         4  262.4    65.6   0.462 0.76262   
## hora         1 1805.8  1805.8  12.725 0.00193 **
## ilum         2  231.5   115.8   0.816 0.45651   
## hora:ilum    2   74.7    37.4   0.263 0.77120   
## Residuals   20 2838.4   141.9                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

mod2 = aov(ce ~ hora + ilum + hora:ilum + parc,
           datos)
summary(mod2)

##             Df Sum Sq Mean Sq F value  Pr(>F)   
## hora         1 1805.8  1805.8  12.725 0.00193 **
## ilum         2  231.5   115.8   0.816 0.45651   
## parc         4  262.4    65.6   0.462 0.76262   
## hora:ilum    2   74.7    37.4   0.263 0.77120   
## Residuals   20 2838.4   141.9                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

resid = mod1$residuals
plot(resid, pch =16, cex=2)
grid(col='red')

# Normalidad
shapiro.test(resid)

## 
##  Shapiro-Wilk normality test
## 
## data:  resid
## W = 0.96166, p-value = 0.3413

datos$trt = interaction(datos$hora,
                        datos$ilum)

ggplot(datos)+
  aes(trt, ce)+
  geom_boxplot()

tapply(datos$ce, datos$trt, var)

##      6.IB     12.IB      6.IM     12.IM      6.IA     12.IA 
##  65.77564 286.70940 135.37080  17.09574  40.89132 229.33821

datos$ce_log = log(datos$ce)
ggplot(datos)+
  aes(trt, ce_log)+
  geom_boxplot()

ce_log_var = tapply(datos$ce_log, datos$trt, var)

sort(ce_log_var)/min(ce_log_var)

##     12.IM      6.IA      6.IB      6.IM     12.IA     12.IB 
##  1.000000  2.824160  4.346150  9.559637 12.433759 15.473325

modlog = aov(ce_log ~ parc + hora + ilum + hora:ilum, datos)
summary(modlog)

##             Df  Sum Sq Mean Sq F value  Pr(>F)   
## parc         4 0.02122 0.00530   0.467 0.75939   
## hora         1 0.14615 0.14615  12.862 0.00185 **
## ilum         2 0.01722 0.00861   0.758 0.48172   
## hora:ilum    2 0.00357 0.00178   0.157 0.85574   
## Residuals   20 0.22726 0.01136                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

reslog = modlog$residuals
shapiro.test(reslog)

## 
##  Shapiro-Wilk normality test
## 
## data:  reslog
## W = 0.96786, p-value = 0.4824

TukeyHSD(modlog, 'hora')

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = ce_log ~ parc + hora + ilum + hora:ilum, data = datos)
## 
## $hora
##           diff        lwr       upr     p adj
## 12-6 0.1395957 0.05840189 0.2207896 0.0018458