#############
## Cviceni 1
#############

fullmoon <- read.table("fullmoon.txt", header=TRUE)

summary(fullmoon)

fullmoon$Moon <- factor(fullmoon$Moon, levels=c("Before", "During", "After"))

fullmoon$Month <- factor(fullmoon$Month, levels=c("Aug", "Sep", "Oct", "Nov", "Dec", "Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul"))

fullmoon$Fullmoon <- factor(ifelse(fullmoon$Moon=="During", "Fullmoon", "Before/After"), levels=c("Fullmoon", "Before/After"))

table(fullmoon$Fullmoon, fullmoon$Moon)

summary(fullmoon)

#############
## Cviceni 2
#############

# (a)
# ---
?t.test
t.test(fullmoon$Admission~fullmoon$Fullmoon, var.equal=TRUE)
?oneway.test
oneway.test(fullmoon$Admission~fullmoon$Fullmoon, var.equal=TRUE)

# (b)
# ---
model.fullmoon <- lm(Admission~Fullmoon, data=fullmoon)
summary(model.fullmoon)
confint(model.fullmoon)

# (c)
# ---
model.moon <- lm(Admission~Moon, data=fullmoon)
summary(model.moon)

diff1 <- c(-1/2, 1, -1/2)
mu <- c(1, 1, 1)/3
diff2 <- c(1, 0, -1)/2
A <- rbind(mu, diff1, diff2)
C <- solve(A)
summary(lm(Admission~Moon, data=fullmoon, contrasts=list(Moon=C[, -1])))

# (d)
# ---
summary(model.moon)
t.test(fullmoon$Admission~fullmoon$Fullmoon, var.equal=TRUE)

#############
## Cviceni 3
#############

# (b)
# ---
t.test(fullmoon$Admission~fullmoon$Fullmoon)
oneway.test(fullmoon$Admission~fullmoon$Fullmoon)

# (c)
# ---
t.test(fullmoon$Admission~fullmoon$Fullmoon, var.equal=TRUE)
oneway.test(fullmoon$Admission~fullmoon$Fullmoon, var.equal=TRUE)

# (d)
# ---
boxplot(fullmoon$Admission~fullmoon$Fullmoon)
boxplot(rstandard(model.fullmoon)~fullmoon$Fullmoon)

bartlett.test(Admission~Fullmoon, data=fullmoon)
qqnorm(fullmoon$Admission[13:24])
qqline(fullmoon$Admission[13:24])
qqnorm(fullmoon$Admission[c(1:12, 25:36)])
qqline(fullmoon$Admission[c(1:12, 25:36)])
shapiro.test(fullmoon$Admission[13:24])
shapiro.test(fullmoon$Admission[c(1:12, 25:36)])

1-pchisq(12*log(var(fullmoon$Admission)*35/36/var(fullmoon$Admission[13:24])/11*12) + 24*log(var(fullmoon$Admission)*35/36/var(fullmoon$Admission[c(1:12, 25:36)])/23*24) , df=1)

var.test(Admission~Fullmoon, data=fullmoon)

#############
## Cviceni 4
#############

# (c)
# ---
oneway.test(fullmoon$Admission~fullmoon$Moon)

# (d)
# ---
oneway.test(fullmoon$Admission~fullmoon$Moon, var.equal = TRUE)

library(lmtest)
?lrtest

lrtest(fullmoon$Admission~fullmoon$Moon)

# (e)
# ---
boxplot(fullmoon$Admission~fullmoon$Moon)
boxplot(rstandard(model.moon)~fullmoon$Moon)

###########
# Cviceni 6
###########

# (a)
# ---
?pairwise.t.test
pairwise.t.test(x=fullmoon$Admission, g=fullmoon$Moon, p.adjust.method="bonferroni", pool.sd=TRUE)

pairwise.t.test(x=fullmoon$Admission, g=fullmoon$Moon, p.adjust.method="bonferroni", pool.sd=FALSE)

# (b)
# ---
str(pairwise.t.test(x=fullmoon$Admission, g=fullmoon$Moon, p.adjust.method="none", pool.sd=FALSE))
1-(1-pairwise.t.test(x=fullmoon$Admission, g=fullmoon$Moon, p.adjust.method="none", pool.sd=FALSE)$p.value)^3