First, are you talking about rounding error (due to floating point
arithmetics) or statistical sampling error?

If you are talking about the latter, I suggest you look it up in a
statistics text book. E.g. if x and y are normally distributed, then

t = r * sqrt( (n-2)/(1-r**2) )

has a Student t-distribution with n-2 degrees of freedom. And if you
don't know how to get the p-value from that, you should not be messing
with statistics anyway.

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