Let say I have a frequency table of two variables $x$ and $y$ having or not having some property.
$$ \begin{array}{lcr} \mbox{} & x & y \\ \mbox{has property} & 20 & 2 \\ \mbox{does not have property} & 61 & 79 \end{array}\ $$
What does it really mean to have positive (right hand side p-value) or negative (left-hand side p-value) association. Can I think of it as of correlation between variables $x$ and $y$? Why then for table
$$ \begin{array}{lcr} \mbox{} & x & x \\ \mbox{has property} & 20 & 20 \\ \mbox{does not have property} & 61 & 61 \end{array}\ $$
I get large p-value not rejecting the null hypothesis?
EDIT: Null hypothesis states that variables are independent, that is the proportions do not differ among $x$,$y$ vs. has/does not have property. The right / left p-value regards associations on the diagonals of the tables like here