#  dataset
data <- data.frame(
  group = rep(c("A", "B", "C"), each = 5),
  value = c(254, 263, 241, 237, 251,
            234, 218, 235, 227, 216, 
            200, 222, 197, 206, 204 )
)



print(data)

# ANOVA oneway
anova_mod <- aov(value ~ group, data = data)
summary(anova_mod)

# critical value F 
# qf(1 - alpha, df1, df2)
alpha=0.05
qf(1 - alpha, 2, 12) 

# Conclusions:  25.27 > 3.88 (Reject Ho)

# Test normality of the residuals 
shapiro.test(residuals(anova_mod)) 
#  (H???): data (or residuals) normally distributed  
#  (H???): data (or residuals) not normally distributed 
# pval > alpha --> accept Ho ; pval < alpha --> reject Ho

# Omogeneity of the variances 
bartlett.test(value ~ group, data = data)
# H???: all the variances are equal 
# H1: not all the variances are equal
# pval > alpha --> accept Ho ; pval < alpha --> reject Ho


# figure with group means and conf intervals 
boxplot(value ~ group, data = data,
        main = "ANOVA",
        xlab = "Group", ylab = "Value",
        col = c("lightblue", "lightgreen", "lightpink"))

mean_overall <- mean(data$value)

# Add orizontal line for grand mean 
abline(h = mean_overall, col = "red", lwd = 2, lty = 2)


# post ANOVA --> HSD test  ??? Honest Significant Difference
tukey.one.way<-TukeyHSD(anova_mod)
tukey.one.way

# interpretation of HSD results 
# if confidence interval include the value 0 --> the difference is not statistically significative 
# if  p-vakue < 0.05, the difference is statistically significative 

# conclusion: the mean differences between all the pairs of group is statistically significant