53 lines
1.9 KiB
R
53 lines
1.9 KiB
R
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# Goal: Simulation to study size and power in a simple problem.
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set.seed(101)
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# The data generating process: a simple uniform distribution with stated mean
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dgp <- function(N,mu) {runif(N)-0.5+mu}
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# Simulate one FIXED hypothesis test for H0:mu=0, given a true mu for a sample size N
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one.test <- function(N, truemu) {
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x <- dgp(N,truemu)
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muhat <- mean(x)
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s <- sd(x)/sqrt(N)
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# Under the null, the distribution of the mean has standard error s
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threshold <- 1.96*s
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(muhat < -threshold) || (muhat > threshold)
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} # Return of TRUE means reject the null
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# Do one experiment, where the fixed H0:mu=0 is run Nexperiments times with a sample size N.
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# We return only one number: the fraction of the time that H0 is rejected.
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experiment <- function(Nexperiments, N, truemu) {
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sum(replicate(Nexperiments, one.test(N, truemu)))/Nexperiments
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}
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# Measure the size of a test, i.e. rejections when H0 is true
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experiment(10000, 50, 0)
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# Measurement with sample size of 50, and true mu of 0.
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# Power study: I.e. Pr(rejection) when H0 is false
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# (one special case in here is when the H0 is actually true)
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muvalues <- seq(-.15,.15,.01)
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# When true mu < -0.15 and when true mu > 0.15,
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# the Pr(rejection) veers to 1 (full power) and it's not interesting.
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# First do this with sample size of 50
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results <- NULL
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for (truth in muvalues) {
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results <- c(results, experiment(10000, 50, truth))
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}
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par(mai=c(.8,.8,.2,.2))
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plot(muvalues, results, type="l", lwd=2, ylim=c(0,1),
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xlab="True mu", ylab="Pr(Rejection of H0:mu=0)")
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abline(h=0.05, lty=2)
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# Now repeat this with sample size of 100 (should yield a higher power)
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results <- NULL
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for (truth in muvalues) {
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results <- c(results, experiment(10000, 100, truth))
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}
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lines(muvalues, results, lwd=2, col="blue")
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legend(x=-0.15, y=.2, lwd=c(2,1,2), lty=c(1,2,1), cex=.8,
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col=c("black","black","blue"), bty="n",
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legend=c("N=50", "Size, 0.05", "N=100"))
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