###1.t tests:
x<-rnorm(100)
y<-rnorm(200,mean=1,sd=1)
#One sample t test: 
t.test(y,mu=1)
#Two sample t test:
t.test(x,y)
#Two group t test:
z<-c(x,y)
g<-c(rep(1,length(x)),rep(2,length(y)))
t.test(z~g)
#Paired t test:
e1<-rnorm(100)
e2<-rnorm(100)
u<-rnorm(100)
y1<-1+u+e1
y2<-2+u+e2
t.test(y1,y2,paired=TRUE)

###2.Test of equality of variances:
#F test:
var.test(x,y)
#Bartlett test:
bartlett.test(z,g)

###3.Wilcoxon tests:
#One sample test:
wilcox.test(y,mu=1)
#Two sample test:
wilcox.test(x,y)

###4.Test for normality:

library(nortest)
#Anderson-Darling normality test:
ad.test(x)
#Cramer-von Mises test:
cvm.test(x)
#Kolmogorov-Smirnov test: 
lillie.test(x)
#Shapiro-Wilk test:
shapiro.test(x)

###5. Test for equality of distributions from two samples:
ks.test(x,y)

###6. Chi squared test for independence:
library(MASS)
tbl = table(survey$Smoke, survey$Exer) 
chisq.test(tbl)

###7. Fisher's exact test for independence:
fisher.test(tbl)

###8. Correlation test:
cor.test(y1,y2)

###9. Pairwise t test:
a1<-rnorm(100)
a2<-rnorm(100)
a3<-rnorm(100,1,1)
a<-c(a1,a2,a3)
g<-c(rep(1,100),rep(2,100),rep(3,100))
pairwise.t.test(a,g,p.adj="bonferroni")

###10. Power analysis:
library(pwr)
#two proporitons (equal n):
pwr.2p.test(h=0.3,n=80,sig.level=0.05,alternative="greater")

#two sample t test (equal n):
pwr.t.test(d=0.3,power=0.75,sig.level=0.05,type="two.sample",alternative="greater")