Hello!
I am running a very simple mini Monte-Carlo below using the function
tstatistic (right below this sentence):
tstatistic = function(x,y){
m=length(x)
n=length(y)
sp=sqrt( ((m-1)*sd(x)^2 + (n-1)*sd(y)^2)/(m+n-2) )
t=(mean(x)-mean(y))/(sp*sqrt(1/m+1/n))
return(t)
}
alpha=.1; m=10; n=10 # sets alpha, m, n - for run 1
N=10000 # sets the number of simulations
n.reject=0 # counter of num. of rejections
tstat<-vector()
for (i in 1:N){
x = rnorm(m,mean=10,sd=2) # simulates xs from population 1
y=rexp(n,rate=1/10)
t = tstatistic(x,y) # computes the t statistic
tstat = c(tstat,t)
if (abs(t)>qt(1-alpha/2,n+m-2))
n.reject=n.reject+1 # reject if |t| exceeds critical pt
}
true.sig.level=n.reject/N # est. is proportion of rejections
true.sig.level
And then I would like to plot the observed t values (in the vector
"tstat") against the values of the t density with df=18. Somehow, my t
denstity (code line 2 below) does not show up:
plot(density(tstat),xlim=c(-5,8),ylim=c(0,.4),lwd=3)
lines(x,dt(x,df=18))
legend(4,.3,c("exact","t(18)"),lwd=c(3,1))
Thanks a lot!
D.
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