Source of an algorithm

[David C. Howell]

On one of my web pages I describe an algoritm for generating data with a specified correlation between X and Y. The important part of the algorithm is

• Use the normal random number function available in almost all software to generate two random variables (X and Y).
• Standardize these variables to mean = 0, sd = 1.
• Calculate a = r/sqrt(1-r²), where r is the desired correlation.
• Calculate Z = a*X + Y.
• Adjust the means and variances of X and Z to what you want them to be by simple linear transformations--(e.g., Xnew = Xold*NewSD + NewMean).
• Now the correlation between X and Z will be r.
• The mean of z will be 0.00, and its stand deviation will be sqrt(a² + 1).
• If you don't standardize the variables I would assume that the resulting r will come from a population where rho = r, but I haven't worked this out. If anyone knows for sure, I'd appreciate hearing.

I have recently been asked for the source of that algorithm. It has been around for a long time, and I am certainly not the first to recommend it, but I do not know its source. Can anyone help?

Also, does anyone have an opinion about the last item in that list?

Thanks,
Dave Howell

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David C. Howell
Professor Emeritus
University of Vermont

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