Intro2R: Introduction to R

#This is a model R function that you can alter for other statistics
# Copy this function twice and alter the two copies to make sampling distributions from the T distribution
myTsim<-function(n1=10,sigma1=3,mean1=5,iter=1000,ymax=0.1,...){    # adjust ymax to make graph fit
y1=rnorm(n1*iter,mean=mean1,sd=sigma1)# generate iter samples of size n1

data1.mat=matrix(y1,nrow=n1,ncol=iter,byrow=TRUE) # Each column is a sample size n1

sd1=apply(data1.mat,2,sd) # sd
ybar=apply(data1.mat,2,mean)  # mean

w=(ybar-mean1)/(sd1/sqrt(n1))      #T stat

hist(w,freq=FALSE, ylim=c(0,ymax), # Histogram with annotation
main=substitute(paste("Sample size = ",n[1]," = ",n1," statistic = ",T," iterations= ",iter)),
xlab=expression(paste(T, "Statistic",sep=" ")), las=1)
lines(density(w),col="Blue",lwd=3) # add a density plot
curve(dt(x,n1-1),add=TRUE,col="Red",lty=2,lwd=3) # add a theoretical curve
title=expression(T==frac((bar(y)-mu),s/sqrt(n[1]))) #mathematical annotation -see ?plotmath
legend(locator(1),c("Simulated","Theoretical"),col=c("Blue","Red"),lwd=4,lty=1:2,bty="n",title=title) # Legend #
return(list(w=w,summary=summary(w),sd=sd(w),fun="T")) # some output to use if needed
}
myTsim(iter=10000,ymax=0.45)