# plots the sample variances for a bunch of samples from two different sample sizes

# create a population and a series of two samples with different sizes
population.size = 1000000
population.mean = 300
population.std = 50
population.data = rnorm(population.size,population.mean,population.std)
population.mean = mean(population.data)

sample1.size = 10
sample2.size = 100

# DO NOT CHANGE ANYTHING BELOW HERE OR WORRY ABOUT IT

par(mfrow=c(3, 1))

# plot histogram with normal curve
par(mar=c(1,1,1,1))
h<-hist(population.data, breaks=20, col="red", xlab="Reaction Time",main="",xlim = c(100,500),ylim=c(0,200000)) 
xfit<-seq(min(population.data),max(population.data),length=200) 
yfit<-dnorm(xfit,mean=mean(population.data),sd=sd(population.data)) 
yfit <- yfit*diff(h$mids[1:2])*length(population.data)
lines(xfit, yfit, col="blue", lwd=2)

abline(a = NULL, b = NULL, h = NULL, v = (population.mean-population.std),col=4)
abline(a = NULL, b = NULL, h = NULL, v = (population.mean+population.std),col=4)

# plot the first sample
x = "Sample Size:"
message = paste0(x," ",sample1.size)
sample.data = sample(population.data,sample1.size,replace = TRUE)
sample.var = var(sample.data)
plot(sample.var,numberofsamples,xlim = c(1,5000),,ylim = c(1,numberofsamples))
title(main=message)
Sys.sleep(plot.delay)

plot.delay = 0.1
numberofsamples = 50
# plot 99 more samples
for (plot.counter in 1:numberofsamples-1)
{
sample.data = sample(population.data,sample1.size,replace = TRUE)
sample.var = var(sample.data)
points(sample.var,numberofsamples-plot.counter)
Sys.sleep(plot.delay)
}

# plot the first sample
x = "Sample Size:"
message = paste0(x," ",sample2.size)
sample.data = sample(population.data,sample2.size,replace = TRUE)
sample.var = var(sample.data)
plot(sample.var,numberofsamples,xlim = c(1,5000),ylim = c(1,numberofsamples))
title(main=message)
Sys.sleep(plot.delay)

# plot 99 more samples
for (plot.counter in 1:numberofsamples-1)
{
  sample.data = sample(population.data,sample2.size,replace = TRUE)
  sample.var = var(sample.data)
  points(sample.var,numberofsamples-plot.counter)
  Sys.sleep(plot.delay)
}