moa=c(6.8,4.1,7.3,14.2,18.8,9.9,7.4,11.9,5.2,7.8,7.8,8.7,12.7,14.5,10.7,8.4,9.7,
10.6,7.8,4.4,11.4,3.1,4.3,10.1,1.5,7.4,5.2,10.0,3.7,5.5,8.5,7.7,6.8,3.1,
6.4,10.8,1.1,2.9,4.5,5.8,9.4,6.8)
group=c(1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,3,3,3)
group=factor(group)
boxplot(moa~group,names=c("Schizo I","Schizo II","Schizo III"))
f=aov(moa~group)
summary(f)

# Rejecting H0: mu1=mu2=mu3 is only half the story!
# Usually want to know WHICH means are different...
# Tukey's method finds which pairs of means are different
# bounding the "family error rate" at 5%
# Find pairs of means with adjusted p-values smaller than 0.05

TukeyHSD(f)

# 3 is different from 1, 2 is different from 1
# 3 not different from 2
# gives "lines" plot:

# III II I
# ------ -

#############################################
# ANOVA on hours of homework and hours of 
# exercise by political ideology and president
#############################################

pr=factor(c("t","t","c","c","c","c","c","c","c","c","c","o","c","o","c","c","o","t"))
po=factor(c("m","c","l","l","m","l","l","l","l","l","l","c","l","c","l","l","m","c"))
hw=c(22,15,7,10,10,15,14,10,20,20,5,14,20,10,5,10,15,10)
ex=c(5,15,4,4,10,5,0,6,5,7,1,6,90,3,3,5,0,14)
ex[13]=floor(median(ex)) # replace '90' with imputed value

# homework by president

boxplot(hw~pr)
summary(aov(hw~pr))

# homework by political ideology
            
boxplot(hw~po)
summary(aov(hw~po))
       
# exercise by president

boxplot(ex~pr)
summary(aov(ex~pr))
TukeyHSD(aov(ex~pr))

# lines:

# other clinton trump
# ------------- -----

#############################################
# Constant variance?
#############################################

qqnorm(ex[pr=="o"])
qqnorm(ex[pr=="c"])
qqnorm(ex[pr=="t"])

# formal hypothesis test of H0: sigma1=sigma2=sigma3

bartlett.test(ex~pr)

#############################################
# NOTE: if variances *are* different, can use
#############################################

oneway.test(ex~pr)

# oneway.test allows variances to be different across groups
# but also assumes normality.  If you don't have normal data

kruskal.test(ex~pr)

# The Kruskall-Wallace does not assume *anything* and is always valid

# exercise by political ideology

boxplot(ex~po)
summary(aov(ex~po))
TukeyHSD(aov(ex~po))

# lines:

# liberal moderate conservative
# ---------------- ------------