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I am trying to understand how to correctly interpret "significant rank correlation" in the context of Kendall Tau-B. What can I conclude if the correlation is 1? The relationship is monotonic?

Edit: Google Scholar search

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  • $\begingroup$ In which context did you find 'significant rank correlation'? Did you find it in a paper? $\endgroup$
    – Simone
    Jan 24, 2016 at 2:57
  • $\begingroup$ For example at unistat.com at the bottom of 6.2.1.3. Kendall’s Rank Correlation. $\endgroup$
    – phell
    Jan 24, 2016 at 3:17

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In this scenario, "significant rank correlation" means that the value you obtained for your Kendall's $\tau_B$ is significantly different from 0. Indeed, the value you obtained for $\tau_B$ might be just due to chance because of small sample size, i.e. small number of objects. You might have to get familiar with statistical hypothesis testing.

In statistical hypothesis testing for correlation measures, you usually compute a $p$-value which is function of the effect size of the correlation and the sample size. When the $p$-value is low, you can reject the hypothesis of 0 correlation with some chosen level of confidence. An example about Kendall's $\tau_B$ in R is here.

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  • $\begingroup$ Null hypothesis is no correlation. If p is smaller than 0.05 (95% confidence interval) the hypothesis is rejected on this level which means there is correlation. Does $\tau_B$ show the level of monotonicity (strictly growing is +1 and strictly declining is -1) while the p value tells how often I would find $\tau_B$ within the confidence interval if I did the experiment many times? $\endgroup$
    – phell
    Jan 25, 2016 at 9:21
  • $\begingroup$ Yes $\tau_B$ accounts for the level of monotonicity between your variables. A $p$-value shows how strongly you can reject the hypothesis of 0 correlation. However, be careful when you talk about reproducibility of results: nature.com/news/scientific-method-statistical-errors-1.14700 $\endgroup$
    – Simone
    Jan 25, 2016 at 9:42
  • $\begingroup$ Would it be better to say that I am 95% certain that $\tau_B$ is in this interval? $\endgroup$
    – phell
    Jan 25, 2016 at 9:49
  • $\begingroup$ That is also another different thing. A $p$-value is not the same as a confidence interval $\endgroup$
    – Simone
    Jan 25, 2016 at 9:55

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