### importing and attaching the dataset [DIET]
library(readxl)
diet <- read_excel("state-data.xlsx", sheet="diet")
# group variable as factor
diet$regime <- factor(diet$regime)
attach(diet)

### some descriptive statistics
mean(coagulation); var(coagulation); sd(coagulation)
median(coagulation); quantile(coagulation)
summary(coagulation)
boxplot(coagulation)

# descriptive statistics by groups
summary(rbind.data.frame(split(coagulation, regime)))
library(ggplot2)
ggplot(diet, aes(x=regime, y=coagulation, color = regime)) + geom_boxplot()

### one-way anova
## testing homoskedasticity of variances (Bartlett's and Levene's tests)
bartlett.test(coagulation ~ regime)
library(car)
leveneTest(coagulation ~ regime, center=mean)

## one-way ANOVA
anova(lm(coagulation ~ regime))

## post-hoc tests
pairwise.t.test(coagulation, regime, p.adjust.method = "none")
pairwise.t.test(coagulation, regime, p.adjust.method = "bonferroni")

tukey.posthoc <- TukeyHSD(aov(lm(coagulation~regime)))
tukey.posthoc
plot(tukey.posthoc)