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 random X-Y pairs from a known population value of Pearson's correlation is straightforward, the process for generating random sequences for a known value 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 expectation as the smaller set. Two examples are given. One example simulated samples from a population where tau(a) equaled 0.33 and confidence intervals are produced. A second example illustrates how the algorithm can be used to provide statistical power estimates for research studies using Kendall's tau(a).