#### R script to demonstrate power and the ROC cureves

library(TeachingDemos)

# power calculation for the simple versus simple Normal test

theta0 = 25
sigma0 = 3

theta1 = 30

diff = theta1-theta0

n = 300

# calculate the power

power.examp(n = 30, stdev = 3, diff = diff, alpha = 0.05, xmin = -3, xmax = 3)

# run the power demo

run.power.examp(hscale=1.5, vscale=1.5, wait=FALSE)

# ROC curve demo

roc.demo(x = rnorm(n, theta0, sigma0), y = rnorm(n, theta1, sigma0))

# change n to 100, and theta1 to 27

theta1 = 30

n = 100

roc.demo(x = rnorm(n, theta0, sigma0), y = rnorm(n, theta1, sigma0))

##########################################################################

# distribution demos

vis.normal()
vis.t()
vis.gamma()
vis.binom()

# there is also an MLE demo

if(interactive()){
mle.demo()

m <- runif(1, 50,100)
s <- runif(1, 1, 10)
x <- rnorm(15, m, s)

mm <- mean(x)
ss <- sqrt(var(x))
ss2 <- sqrt(var(x)*11/12)
mle.demo(x)
# now find the mle from the graph and compare it to mm, ss, ss2, m, and s
}