Kendall/Spearman rank correlation

copied from here.
Spearman's rho comes from Charles Spearman's background of psychology, IQ testing and eugenics - it's an easy to calculate robust measure of whether there is an association.

However:
(1) Ease of calculation is unimportant nowadays.
(2) Ease of interpretation is far more important, and interpretation of a particular value for rho is unclear
- even (I suspect) if you are familiar with copulas.
(3) Consequently rho is geared towards testing Ho: correlation=0.
(4) The distribution of rho in small samples is messy - it doesn't tend to Normality as nicely as Kendall's tau.

Kendall's tau, by comparison:
(1) Is now as easy to calculate (as for rho, just hit RETURN).
(2) Has a clear interpretation. Suppose the population has two attributes, x & y (e.g. height & weight). Address the question "what is the probability P that two random members of the population have the same ordering for y as for x?" (e.g.: "what is the probability P that the taller person is heavier?") Then Kendalls' tau is an estimate of (2P-1). [You need to tweak this slightly if ties are possible].
(3) Is consequently useful for modelling (see e.g. partial tau).
(4) Has a sampling distribution that tends rapidly and smoothly towards Normality as sample size increases.

The original poster mentioned "techniques associated with them [rho & tau]". I'm not sure what she meant, but if for example, for some reason, you wanted to test whether some measure of correlation could be assumed to be the same in two populations, then it would make sense to use Kendall's tau (& a t-test could
be used for small samples), whereas with Spearman's rho you'd be in danger of incorrectly invoking Normality to test whether two near-meaningless quantitities were the same.

If you're not interested in testing, but rather in modelling, then I personally see no point in using rho rather than tau, other than pressure to publish despite the inertia of certain journals, referees, and indeed whole disciplines.

I hope the OP finds my even-handed account helpful :-)
-- Ewart Shaw