I am running Spearman correlation between 2 variables weight and freight both being numeric.  The output I have received from correlation is P value - 0.00E+000 and Rank R Squared is 0.61 and which means they are moderately correlated however I am not able to interpret the p value. Is this because of large number of values I am dealing with? I have 2 million rows of data for both the variables.
I have some pairs of datasets (n=200 or thereabouts), of samples which are non-negative and not normally distributed. I think these pairs of variables are related, probably linearly.   Calculating Spearman's rank correlation on these datasets gives some strange results. The correlation coefficients show that the pairs of variables are weakly, positively correlated (e.g. rho of around 0.4), but the p-values are very low (e.g. 4.1e-10).  My vague understanding of this is that the variables are weakly, positively correlated but the probability of unrelated variables producing the same correlation is very low. Does this mean we can be reasonably certain that a positive correlation exists or have I misunderstood?
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