Correct me if I am wrong: both Kendall’s tau and Spearman’s rho are will result in the same conclusions with respect to whether the value of the underlying population correlation equals zero.
I am applying both tests on the same data in Python's scipy, for some data .When the result is significance, I get slightly different p-values that can lead to a different conclusion. What is wrong? I can add a numerical example if necessary.
I think it is either because my data dimension is short (n=10) or maybe because p-value is calculated with the approximation.
Update: What confused me is this (source=Handbook of Parametric and Nonparametric Statistical Procedures, 2nd edition, page 888):
In spite of the differences between Kendall’s tau and Spearman’s rho, the two statistics employ the same amount of information and, because of this, are equally likely to detect a significant effect in a population. Thus, although for the same set of data different values will be computed for and (unless, as noted in Endnote 2, the correlation between the two variables is +1 or 1), the two measures will essentially result in the same conclusions with respect to whether or not the underlying population correlation equals zero