Generating random series with known values of Kendall's tau.

摘要

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).