library(NHANES)
# One factor two levels
nh_adult <- subset(NHANES, Age >= 18)
x<-nh_adult$Gender
y<-nh_adult$Height
library(stats)
tapply(y,x,length)
tapply(y,x,summary)
library(ggplot2)
ggplot(nh_adult, aes(x=Gender, y=Height)) +
  geom_boxplot()
t.test(y~x,alternative="less",var.equal=TRUE) # one-tailed test
summary(lm(y~x))  #test for beta=0 in regression
anova(lm(y~x))    #ANOVA F-test
sqrt(anova(lm(y~x))$F[1])  #This equals the absolute value of the t-statistic
#One factor multiple levels
x<-nh_adult$Race1
tapply(y,x,length)
tapply(y,x,summary)
ggplot(nh_adult, aes(x=Race1, y=Height)) +
  geom_boxplot()
summary(lm(y~x))  #test for beta=0 in regression
anova(lm(y~x))    #ANOVA F-test

# Understanding the use of different constraints
options(contrasts=c("contr.treatment", "contr.treatment"))
# options sets two contrasts. The first giving the function to be used with 
# unordered factors and the second the function to be used with ordered factors. 
# "contr.treatment" is the default corresponding to putting the first alpha to zero. 
summary(lm(y~x))
summary(lm(y~x-1)) #This corresponds to putting the ovreall mean to zero
# contr.sum puts the sum to zero.
options(contrasts=c("contr.sum", "contr.sum"))
summary(lm(y~x))
# This does not report the last coefficient. But you can recover it using 
A<-lm(y~x)
-sum(A$coefficients[2:5])
#Note that the following two are same
A$coefficients[1]-sum(A$coefficients[2:5])
B<-lm(y~x-1)
B$coefficients[5]