Generating random series with known values of Kendall's tau

Kendall's tau(a) offers statistical advantages to the more common Pearson's correlation and both are common in biomedical research. While generating r andom,X- Y pairs from a known population value of Pearson's correlation is straightforward, the process for generating random sequences for a known va lue of Kendall's tau(a) is more complicated. Algorithms are presented that yield random numbers from a population with a known expected tau (a),. They begin with a small set of values that have a known tau. These values are ' grown' to produce an arbitrarily large population that has the same expecta tion as the smaller set. Two examples are given. One example simulated samp les from a population where tau (a) equaled 0.33 and confidence intervals a re produced. A second example illustrates how the algorithm can be used to provide statistical power estimates for research studies using Kendall's ta u (a) (C) 2000 Elsevier Science Ireland Ltd. All rights reserved.