rm(list=ls(all=TRUE))  # clear all variables
# Programmed by Greg Francis (gfrancis@purdue.edu) October 2019

# Explores the multiple testing problem in hypothesis testing

# sample size
n = 200

numPopulations = 10
PopulationMeans = 0* c(1:numPopulations) 
PopulationSDs = 100+0*c(1:numPopulations)

alpha = 0.05 # Type I erorr rate (must be bigger than 0 and less than 1)

numRepeats = 5000

pValues <-0*c(1:numRepeats) # To hold result of t-test

for(rep in c(1:numRepeats)){

	# Draw a random sample from each group and run a test
	minPvalue = 1
	for(i in c(1:numPopulations)){
		Xvalues  <- rnorm(n, mean= PopulationMeans[i], sd= PopulationSDs[i])
		testResults <- t.test(Xvalues, mu=0, conf.level = (1-alpha))	
		if(testResults$p.value	< minPvalue){minPvalue = testResults$p.value	}		
	}
	pValues[rep] <- minPvalue	
}

# Compute proportion of significant test results
propSignificant <-length(pValues[pValues <= alpha])/length(pValues) 

cat("------\n")

cat("With", numPopulations,"populations, the probability of getting at least one significant test is: ", propSignificant, "\n")