# Do Kendall’s tau and Spearman’s rho conclude the same hypothesis?

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

Cheers

• These two correlation coefficients are different (read). They are different in magnitude, in significance, and it what precisely they measure. – ttnphns Feb 10 '17 at 8:17
• thanks. that really helped. What confused me is this (source=Handbook of Parametric and Nonparametric Statistical Procedures, 2nd edition, page 888): – Woeitg Feb 10 '17 at 8:23
• "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. – Woeitg Feb 10 '17 at 8:23
• It's not clear what the basis is for the claim "the two statistics employ the same amount of information", nor how that implies "are equally likely to detect a significant effect in a population" (and in fact I am pretty convinced that in the absence of some heavy qualification not stated here, this claim is generally false, even on average - each will have more power against some alternatives). It would be interesting to see more of the justification that was offered – Glen_b Feb 10 '17 at 10:10
• Tnx for comment. Do you know any textbook/paper in favor of your statement: "in the absence of some heavy qualification [...], this claim is generally false". It can be extremely helpful for my thesis – Woeitg Feb 10 '17 at 10:42