Confidence intervals for Kendall's tau

I am working on some stats coursework, and have non parametric bivariate data. n=19, so small sample. There are a number of tied ranks, so I'm planning to use Kendall's tau rather than Spearman's rho, as I have found some literature supporting this. My SPSS output has calculated tau = -.982, p <.001. What I have absolutely no idea of is how to calculate the confidence intervals. Am I correct in thinking I can't use the Fisher Z transformation with tau, and if so why not? Do I need to do something with bootstrapping (which I have never done!)? If anyone could help, in as basic terms as possible (very much a beginner!) I would really appreciate it.

• I should have mentioned that I have a basic understanding of how bootstrapping works (thank you youtube!) - I am just unsure if that is an appropriate way of calculating CIs for Kendall's tau-b Commented Jul 21, 2015 at 19:56

This paper discusses the contexts where you can and can't use a normal approximation for Tau. According to Wikipedia, it also looks like the validity of normal/Z depends on how your version of Tau handles ties. My sense is that it's probably safer not to assume that it's Gaussian, especially with relatively low sample sizes.

I couldn't think of a reason why Kendall's Tau wouldn't be compatible with the bootstrap, but I wasn't 100% sure. So I looked it up:

• Here's a paper by Brad Efron, the inventor of the bootstrap, that uses it for Tau (Section 5).

• Here's a paper that spends some time discussing the bootstrap in the context of Tau (mostly Section 4).

Looks like you shouldn't have any serious problems using the bootstrap for tau.

• Very nice. Any idea of whether there's a better way than bootstrapping? Commented Mar 13, 2017 at 18:20
• If we don't have tau's sampling distribution, the only alternatives I'm aware of are to approximate it (e.g. with a Gaussian) or to do some kind of resampling (like bootstrapping). This paper claims that the Gaussian approximation isn't too bad, and gives a formula for a Z-test (section 4). Keep in mind that the different options for handling ties will make a difference here. utdallas.edu/~herve/Abdi-KendallCorrelation2007-pretty.pdf Commented Mar 13, 2017 at 21:41
• (or, in a few words: bootstrapping is probably best, but it's not the only option) Commented Mar 14, 2017 at 2:29