What significance test is used for spearmanr in SciPy?

Question

What type of significance test is used in scipy.stats.spearmanr to produce the p-value it spits out? The documentation simply says that its a two-sided p-value, but with respect to what distribution? Is it a t-distribution?

Answer 1

According to the documentation,

the p-value roughly indicates the probability of an uncorrelated system producing datasets that have a Spearman correlation at least as extreme as the one computed from these datasets. The p-values are not entirely reliable but are probably reasonable for datasets larger than 500 or so.

When you look into the source code, you can see that they calculate a t-value:

% rs is rho
t = rs * np.sqrt((n-2) / ((rs+1.0)*(1.0-rs)))

and then calculate the p value assuming a t-distribution with two degrees of freedom:

prob = distributions.t.sf(np.abs(t),n-2)*2

This is also explained on Wikipedia as one option for calculating statistical significance.