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.
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.