Simulating correlated variables

Measures collected in paired/related measure experimental designs are...correlated!

There is a lot of utility in simulating experimental outcomes...for example, when doing a priori power analysis by Monte Carlo, when generating bootstrap distributions, etc.

To simulate paired observations appropriately its important to account for their paired correlations.

Here's a simple R script that accomplishes that, including a check for accuracy, illustrated for a case when 80% correlation is expected.

	#simulate random variables
	x1 <- rnorm(1000, 0, 1)
	x2 <- rnorm(1000, 0, 1)
	plot(x1,x2)
	#correlate them
	r=0.8
	k<- sqrt(1-r^2)
	x2 <- r*x1+k*x2
	#confirm
	plot(x1, x2)
	cor(x1, x2)

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