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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

Woeitg
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    These two correlation coefficients are different ([read](http://stats.stackexchange.com/q/18112/3277)). They are different in magnitude, in significance, and it what precisely they measure. – ttnphns Feb 10 '17 at 08:17
  • 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 08:23
  • "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 08:23
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    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
  • The two methods are compared in most books on so-called nonparametric statistics for instance Chris Leach's Introduction to statistics: a nonparametric approach for the social sciences has a brief description but it just happens to be on my shelf and I am sure your library has other similar books. But the link to which @ttnphns refers is much more detailed and repays reading. – mdewey Feb 10 '17 at 13:52
  • @Woe It's no good simply offering you a reference -- you'd then have two references that contradict each other with no obvious way to resolve the contradiction The way to show specific claims are wrong is to give counterexamples (though claims offered without convincing reasons to accept them should be regarded with doubt in any case). It's possible to offer counterexamples to some of the specific claims Sheskin makes on that page (including some you quote) – Glen_b Feb 10 '17 at 15:31
  • However, it should be noted that my use of "generally" is intended in the mathematical sense (i.e. if taken as a statement that always holds, it's false) but it's possible Sheskin's use of "essentially" (and "generally", elsewhere on the same page) means something more like "usually". Certainly examples where the Kendall correlation is larger than the Spearman in absolute size are readily found, and ones where the Kendall is significant while the Spearman is not are easy to find (as are cases where the Kendall is not but the Spearman is) – Glen_b Feb 10 '17 at 15:39
  • What is it you need to be able to say for your thesis? – Glen_b Feb 10 '17 at 15:40

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