#Parameters to simulate sample 1 from a normal population
n1 _ 30
mu1 _ 100
sigma1 _ 10

#Parametets to simulate sample 2 from a normal population
n2 _ 30
mu2 _ 110
sigma2 _ 10

#m denotes the number of simulated t-tests
m _ 1000

#list of main variables 
alpha _ .05
type1 _ 0
type2 _ 0
beta _ 0
power _ 0
pvector _ c()
tvector _ c()
wpvector _ c()
wvector _ c()

for(i in 1:m) {
	x _ rnorm(n1,mu1,sigma1)
	y _ rnorm(n2,mu2,sigma2)
	
	t.output _ t.test(y, x, alternative = "two.sided",mu=0,paired=F,
							var.equal=T, conf.level=.95)
	w.output _ wilcox.test(y, x, alternative="two.sided", mu=0, 
								paired=F, exact=T, correct=T)
								
	#creating vectors for results of the t-tests
	tstat _ t.output$statistic
	pvalue _ t.output$p.value
	tvector _ c(tvector,tstat)
	pvector _ c(pvector, pvalue)
	
	#creating vectors for the results of the wilcox tests
	wstat _ w.output$statistic
	wpvalue _ w.output$p.value
	wvector _ c(wvector, wstat)
	wpvector _ c(wpvector, wpvalue)
}

summary(tvector)
print(sqrt(var(tvector)))
summary(pvector)
print(sqrt(var(pvector)))

if(mu1-mu2 == 0)
	type1_length(pvector [pvector < alpha])/m
	else{type1_0}
		
if(mu1-mu2 != 0)	
	type2_length(pvector [pvector > alpha])/m
	else{type2_0}
		
if(mu1-mu2 == 0)
	wil.type1_length(wpvector [wpvector < alpha])/m
	else{wil.type1_0}
		
if(mu1-mu2 != 0)	
	wil.type2_length(wpvector [wpvector > alpha])/m
	else{wil.type2_0}

		
power_1-type2
print(type1)
print(type2)
print(power)

#settings for t-test plots
x.points_seq(-5,5,.01)
y.points_dt(x.points,n1+n2-2)
x.pts_x.points+mean(tvector)


#plot 1		
plot(c(-5,10),c(0,.7),type="n",bty="l",sub="width=1.5")
lines(x.points,dt(x.points,n1+n2-2),lty=1)
lines(x.pts,y.points,lty=1)

#plot 2
hist(tvector,nclass=20,xlim=c(-5,12),ylim=c(0,.6),xlab="",
		probability=T,col=11)
lines(x.points,dt(x.points,n1+n2-2),col=4)
lines(x.pts,y.points,lty=1,col=4)
legend(-5,.6,c("Simulation Results (alpha = .05)","","     beta     =",
		"","     power   ="))
		


hist(wvector,nclass=20,col=5)
qqnorm(tvector)
qqnorm(wvector)

summary(wvector)
print(wil.type2)
print(1-wil.type2)