# December 10, 2024

### Example 1

Y<-c(4,2,5,2,3,6,3,5,3,6,5,4,6,7,6,5,7,2,3,5)
X<-c(rep("A",5),rep("B",5),rep("C",10))
Y
X

boxplot(Y~X)

t.test(Y~X)

# A vs. B
t.test(Y[1:10]~X[1:10])
# A vs. C
t.test(Y[c(1:5,11:20)]~X[c(1:5,11:20)])
# B vs. C
t.test(Y[6:20]~X[6:20])

t.test(Y[X=='A'|X=='B']~X[X=='A'|X=='B'])
t.test(Y[X=='A'|X=='C']~X[X=='A'|X=='C'])
t.test(Y[X=='B'|X=='C']~X[X=='B'|X=='C'])

choose(3,2)
choose(4,2)
choose(10,2)

anova(lm(Y~X))

summary(aov(Y~X))


### Example 2

warpbreaks

?TukeyHSD

summary(fm1 <- aov(breaks ~ wool + tension, data = warpbreaks))

anova(lm(breaks ~ wool + tension, data = warpbreaks))

TukeyHSD(fm1, "tension", ordered = TRUE)
plot(TukeyHSD(fm1, "tension"))