Spearman's rho and Kendall's tau

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Confidence tables for Spearman's rho and Kendall's tau can be found in Zar, J.H. Biostatistical Analysis, which provides critical values for Spearman's rho up to n=100. The values in these tables are derived from various distributions, including those by Owen (1962), de Jonge & van Montford (1972), Franklin (1988a), and Olds (1938). For a deeper understanding, Zar's 1972 paper and Franklin's works from 1988 offer comprehensive discussions on the topic. These references are valuable resources for anyone researching these statistical measures. Accessing these materials will enhance the understanding of the confidence intervals associated with Spearman's rho and Kendall's tau.
choschech
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Hi,

does anyone know where to get confidence tables for Spearman's rho and Kendall's tau for up to 50 data pairs?
Which distributions are the values in these tables derived from?
 
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Hi

Don't know about Kendall's tau, but citical values (is that what you meant) of Spearmans rho for up to n=100 are given in Zar, J.H. Biostatistical analysis. Various distributions are used, depending on n, e.g. those of Owen 1962; de Jonge & van Montford (1972); Franklin (1988a) and Olds (1938). A good discussion of this topic is given in Zar, J.H. (1972) J. Amer. Statist. Assoc. 67: 578-580 and in Franklin (1988a) J. Statist. Computa. Simula. 29:255-269 & Franklin (1988b) Communic. Statist.-Theor. Meth. 17: 55-59.
 
Thanks,

these references have been a great help!
 
I was reading a Bachelor thesis on Peano Arithmetic (PA). PA has the following axioms (not including the induction schema): $$\begin{align} & (A1) ~~~~ \forall x \neg (x + 1 = 0) \nonumber \\ & (A2) ~~~~ \forall xy (x + 1 =y + 1 \to x = y) \nonumber \\ & (A3) ~~~~ \forall x (x + 0 = x) \nonumber \\ & (A4) ~~~~ \forall xy (x + (y +1) = (x + y ) + 1) \nonumber \\ & (A5) ~~~~ \forall x (x \cdot 0 = 0) \nonumber \\ & (A6) ~~~~ \forall xy (x \cdot (y + 1) = (x \cdot y) + x) \nonumber...

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