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I did not get many responses over how to compute $p$ values given Spearman $\rho$ and Pearson $r$ so I will try something else:

I see that when you are using the Spearman $\rho$ value, you can use this to determine critical values depending on $n$:

http://web.anglia.ac.uk/numbers/biostatistics/spearman/local_folder/critical_values.html

However I also see this for Pearson's $r$:

http://www.gifted.uconn.edu/siegle/research/correlation/corrchrt.htm

How would I compute these directly (given arbitrary significance level, degrees of freedom, $r$, etc) instead of relying on a pre-computed table?

I see absolutely nothing online illustrating how this is done. I am comparing my results against these calculators (which work for small sample sizes): www.socscistatistics.com/tests/

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  • $\begingroup$ For Pearson's, calculate the standard error and then get the t-statistic. That can be used to get the p. For Spearman, I'm not sure. (I will try to write an answer later, if no one else does.) $\endgroup$ – Jeremy Miles May 5 '15 at 18:48
  • $\begingroup$ @JeremyMiles Are you referring to SE = 1/sqrt(n-3) and t = r*sqrt((n-2)/(1-r^2)) ? $\endgroup$ – user62753 May 5 '15 at 18:50
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The standard reference for Spearman's distribution is Best, D.J. and D.E. Roberts (1975) "Algorithm AS 89: The Upper Tail Probabilities of Spearman's rho", Applied Statistics, 24:377-379. You can read in JSTOR for free.

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  • $\begingroup$ I read through this reference and it does not seem to illustrate anything not already mentioned, for instance t = r*sqrt((n-2)/(1-r^2)). I don't know how to use this to compute a p value or a critical value for r. $\endgroup$ – user62753 May 5 '15 at 19:02

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