# Frequencies and Crosstabs
#--------------------------

str(airquality)
View(airquality)

# Frequencies
table(airquality$Month)
table(airquality$Day)

# Notice that `summary` does not give you a
# frequency table, because this data is numeric (integer)
summary(airquality$Month)

# One solution is to change the type of the data
month <- factor(airquality$Month, 
                labels=c("May", "June", "July", "Aug", "Sep"))
summary(month)

# Percents
prop.table(table(airquality$Month))
prop.table(summary(month))

# Hypothesis tests - one sample chi-square
chisq.test(summary(month))
chisq.test(summary(month), p=c(2,1,1,1,2), rescale.p=TRUE)

# Crosstabs
table(airquality$Day, airquality$Month)

str(mtcars)
View(mtcars)
# Number of cylinders by V- or straight engine
table(mtcars$cyl, mtcars$vs)




summary(lm(Ozone ~ Month, data=airquality))
tapply(airquality$Ozone, airquality$Month, mean, na.rm=TRUE)

summary(hsb$gender)                 # This works on factors,
						# if there aren't too many categories
summary(hsb$read)                   # but not on numeric variables
summary(as.factor(hsb$read), maxsum=10)

(gender.table <- table(hsb$gender)) # More generally useful
(read.tab <- table(hsb$read))       # Example with lots of categories

str(read.tab)                       # A vector with "named" elements
barchart(read.table)

sort(read.tab, decreasing=TRUE)
cumsum(read.tab/sum(read.tab))

# Percents
??percents
??proportions

prop.table(gender.table)   # starting with the "table" object
prop.test(gender.table)
?prop.test
(gender.test <- prop.test(gender.table, correct=FALSE))
str(gender.test)
(read.prop <- prop.table(read.tab))
(cumsum(read.tab)/200)
barchart(read.prop, xlab="proportion")


# Crosstabs
??crosstabulation

(ses.sch <- with(hsb, table(ses, schtyp)))
xtabs(~ ses + schtyp, data=hsb) # alt a formula-style command

str(ses.sch)
methods(class="table")

summary(ses.sch)
barchart(ses.sch, auto.key=TRUE)

(ses.read <- with(hsb, table(read, ses)))

prop.table(ses.sch)     # cell percents
(ses.prop <- prop.table(ses.sch, 1))  # rows, dimension "1"
barchart(ses.prop, beside=TRUE, group=FALSE)

prop.table(ses.sch, 2)  # columns, dimension "2"

margin.table(ses.sch, 1) # marginal counts
ses.sch
rowSums(ses.sch)

summary(ses.sch)
prop.table(margin.table(ses.sch, 1)) # marginal percents

??chisquare
chisq.test(ses.sch)

# Three-way tables
str(ses.tab <- with(hsb, table(gender, schtyp, ses)))
ftable(ses.tab)

prop.table(ses.tab,2)
apply(ses.tab, 2, sum)
margin.table(ses.tab,2)

dotplot(ses.tab, groups=FALSE)