T1 = c(66,66,67,67,66,66)
T2 = c(62,63,62,63,64,63)
T3 = c(72,71,72,72,71,70)
T4 = c(80,72,73,72,72,74)
T5 = c(75,77,78,77,77,74)
T6 = c(90,88,87,88,90,91)
T7 = c(64,64,65,63,66,62)
T8 = c(65,66,65,66,66,67)
T9 = c(71,70,71,66,68,69)
T10 = c(60,61,61,62,62,60)

Hipotesis

\[H_0: \mu_{T1}==\mu_{T2}==\mu_{T3}==\mu_{T4}==\mu_{T5}==\mu_{T6}==\mu_{T7}==\mu_{T8}==\mu_{T9}==\mu_{T10}\] \[H_a:\mu_{T1}~!=~\mu_{T2}~!=~\mu_{T3}!=~\mu_{T4}~!=~\mu_{T5}~!=~\mu_{T6}~!=~\mu_{T7}~!=~\mu_{T8}~!=~\mu_{T9}~!=~\mu_{10}~!\]

DA = data.frame(DA=c(T1,T2,T3,T4,T5,T6,T7,T8,T9,T10))
summary(DA)
##        DA       
##  Min.   :60.00  
##  1st Qu.:64.00  
##  Median :67.00  
##  Mean   :69.97  
##  3rd Qu.:72.25  
##  Max.   :91.00
metodo=gl(10,6,60,c("T1","T2","T3","T4","T5","T6","T7","T8","T9","T10"));metodo
##  [1] T1  T1  T1  T1  T1  T1  T2  T2  T2  T2  T2  T2  T3  T3  T3  T3  T3  T3  T4 
## [20] T4  T4  T4  T4  T4  T5  T5  T5  T5  T5  T5  T6  T6  T6  T6  T6  T6  T7  T7 
## [39] T7  T7  T7  T7  T8  T8  T8  T8  T8  T8  T9  T9  T9  T9  T9  T9  T10 T10 T10
## [58] T10 T10 T10
## Levels: T1 T2 T3 T4 T5 T6 T7 T8 T9 T10
dfm = data.frame(DA,metodo)
head(dfm,10)
##    DA metodo
## 1  66     T1
## 2  66     T1
## 3  67     T1
## 4  67     T1
## 5  66     T1
## 6  66     T1
## 7  62     T2
## 8  63     T2
## 9  62     T2
## 10 63     T2
medias= tapply(dfm$DA, dfm$metodo, mean)
boxplot(dfm$DA~dfm$metodo)
points(medias,col="blue",pch=16)
abline(h=mean(dfm$DA), lty=2)

sd=tapply(dfm$DA, dfm$metodo, sd);sd
##        T1        T2        T3        T4        T5        T6        T7        T8 
## 0.5163978 0.7527727 0.8164966 3.1251667 1.5055453 1.5491933 1.4142136 0.7527727 
##        T9       T10 
## 1.9407902 0.8944272
library(pander)
## Warning: package 'pander' was built under R version 4.1.2
ANV=aov(dfm$DA~dfm$metodo)
summary(ANV)
##             Df Sum Sq Mean Sq F value Pr(>F)    
## dfm$metodo   9   3705   411.6   178.4 <2e-16 ***
## Residuals   50    115     2.3                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
fvalue = unlist(summary(ANV))[[7]]
fvalue
## [1] 178.4489
p_value = unlist(summary(ANV))[[9]]
ifelse(p_value<0.05,
       "Rechazo Ho: metodos no iguales ",
       "No rechazo Ho: metodos iguales")
## [1] "Rechazo Ho: metodos no iguales "
residuales=ANV$residuals
#Normalidad de los datos
shapiro.test(residuales)
## 
##  Shapiro-Wilk normality test
## 
## data:  residuales
## W = 0.91358, p-value = 0.0004271
hist(residuales)

#Homogeneidad de varianzas
bartlett.test(residuales,dfm$metodo)
## 
##  Bartlett test of homogeneity of variances
## 
## data:  residuales and dfm$metodo
## Bartlett's K-squared = 25.399, df = 9, p-value = 0.00256
#Datos atipicos 
library(outliers)
grubbs.test(ANV$residuals, type = 10, opposite = FALSE, two.sided = TRUE)
## 
##  Grubbs test for one outlier
## 
## data:  ANV$residuals
## G.19 = 4.41061, U = 0.66469, p-value = 7.523e-05
## alternative hypothesis: highest value 6.16666666666667 is an outlier
#Maximo residual
which.max(ANV$residuals)
## 19 
## 19
ANV$residuals[60]
## 60 
## -1
medias
##       T1       T2       T3       T4       T5       T6       T7       T8 
## 66.33333 62.83333 71.33333 73.83333 76.33333 89.00000 64.00000 65.83333 
##       T9      T10 
## 69.16667 61.00000
modc = aov (dfm$DA~dfm$metodo)
summary(modc)
##             Df Sum Sq Mean Sq F value Pr(>F)    
## dfm$metodo   9   3705   411.6   178.4 <2e-16 ***
## Residuals   50    115     2.3                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1