While interpreting the correlation between ranks, should I use the rho value (for spearman method), tau value (for kendall's tau method), w value ( for kendall's w method) or should I take in consideration the p-value?
And does having NaNs values in the ranks impact the interpretation of the correlation?
The correlation score is the "rho" or "tau" value. This is a normalized score in $[-1,1]$:
This value is directly interpretable. For example a value 0.1 means a very weak (probably insignificant) positive correlation, a value of -0.8 means a strong negative correlation.
The p-value is an additional information indicating whether the correlation score is significantly different from 0. In other words, it represents how likely this score is due to chance or not. Naturally a non-significant correlation score should be interpreted with caution.
NaN values cannot be taken into account in any correlation score. They are probably ignored in your implementation, otherwise you would obtain an error message.
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