scipy: significance of the return values of spearmanr (correlation)
It's up to you to choose the level of significance (alpha). To be coherent you shall choose it before running the test. The function will return you the lowest alpha you can choose for which you reject the null hypothesis (H0) [reject H0 when p-value < alpha or equivalently -p-value>-alpha].
You therefore know that the lowest value for which you reject the null hypothesis (H0) is p-value (2.3569040685361066e-65). Therefore being p-value incredibly small your null hypothesis is rejected for any relevant level of alpha (usually alpha = 0.05).
The output of spearmanr (Spearman correlation) of X,Y gives me the following:
Correlation: 0.54542821980327882
P-Value:     2.3569040685361066e-65
where len(X)=len(Y)=800.
My questions are as follows:
0) What is the confidence (alpha?) here ? 
1) If correlation coefficient > alpha, the hypothesis of the correlation being a coincidence is rejected, thus there is correlation. Is this true ?
Thanks in advance..